to_o return_v or_o bend_v upward_o again_o so_o that_o the_o plain_a of_o the_o upper_a superficies_n of_o the_o oil_n may_v cut_v that_o end_n of_o the_o siphon_n where_o the_o flame_n be_v between_o the_o top_n of_o the_o mouth_n of_o it_o next_o the_o socket_n and_o the_o return_n thereof_o upward_o then_o by_o a_o counterpoise_n so_o suspend_v this_o siphon_n that_o it_o may_v follow_v the_o oil_n as_o it_o waste_v and_o fit_a into_o the_o return_n of_o the_o siphon_n a_o socket_n and_o wick_n for_o the_o flame_n to_o be_v continue_v a_o contrivance_n somewhat_o of_o this_o kind_n you_o have_v in_o divers_a author_n and_o therefore_o i_o shall_v spend_v less_o time_n in_o the_o description_n thereof_o let_v a_o a_o a_o a_o in_o the_o six_o figure_n then_o represent_v a_o large_a cylindrical_a viol_n of_o glass_n through_o the_o mouth_n b_o of_o which_o the_o cavity_n thereof_o may_v be_v fill_v with_o oil_n and_o also_o the_o end_n d_o and_z float_n c_o of_o a_o convenient_a siphon_n may_v be_v put_v in_o this_o siphon_n d_o d_o d_o p_o g_o must_v be_v make_v long_o enough_o that_o the_o float_n c_o may_v reach_v the_o bottom_n of_o the_o vessel_n when_o the_o oil_n be_v spend_v and_o the_o other_o end_n thereof_o must_v be_v so_o curve_v that_o the_o knee_n of_o the_o siphon_n p_o may_v be_v below_o the_o superficies_n of_o the_o oil_n e_o f_o and_o yet_o that_o the_o socket_n h_n make_v for_o hold_v the_o wick_n for_o the_o flame_n i_o may_v be_v somewhat_o above_o it_o this_o siphon_n d_o d_o d_o p_o g_o with_o its_o socket_n and_o float_n shall_v be_v so_o counterpoise_v with_o a_o weight_n m_o hung_v over_o a_o pulley_n k_o by_o a_o string_n l_o that_o the_o float_n may_v not_o sink_v deep_a into_o the_o surface_n of_o the_o liquor_n but_o swim_v as_o it_o be_v at_o the_o top_n this_o do_v if_o the_o wick_n i_o be_v light_v the_o surface_n of_o the_o oil_n will_v be_v keep_v always_o at_o the_o same_o distance_n below_o the_o flame_n that_o it_o be_v first_o put_v at_o in_o the_o first_o three_o four_o and_o five_o way_n the_o flame_n of_o the_o lamp_n descend_v equal_a space_n with_o the_o superficies_n of_o the_o oil_n in_o the_o vessel_n and_o therefore_o though_o for_o some_o use_v it_o be_v very_o convenient_a as_o in_o annealing_n where_o thing_n be_v to_o be_v cool_v by_o degree_n yet_o for_o many_o other_o it_o be_v not_o especial_o in_o lamp_n furnace_n where_o the_o same_o heat_n be_v to_o be_v continue_v and_o in_o some_o case_n gradual_o increase_v for_o such_o case_n therefore_o the_o first_o and_o second_o way_n will_v be_v very_o convenient_a in_o some_o other_o case_n the_o six_o and_o seven_o way_n which_o do_v much_o the_o same_o thing_n the_o six_o way_n than_o be_v this_o through_o a_o arm_n or_o siphon_n like_o the_o branch_n of_o a_o lamp_n hang_v against_o a_o wall_n fix_v in_o any_o convenient_a place_n the_o oil_n from_o the_o receptacle_n be_v continual_o and_o equal_o supply_v to_o the_o flame_n of_o the_o lamp_n by_o the_o raise_n of_o the_o receptacle_n as_o fast_o as_o the_o oil_n waste_v so_o as_o to_o keep_v the_o superficies_n of_o the_o oil_n always_o in_o the_o same_o horizontal_n plain_n the_o receptacle_n be_v raise_v by_o a_o counterpoise_n hang_v upon_o a_o fusey_n which_o fusey_n be_v a_o part_n of_o a_o archimedean_a spiral_n let_v c_o c_o then_o in_o the_o seven_o figure_n represent_v the_o receptacle_n for_o the_o oil_n be_v a_o cylindrical_a or_o prismatical_a vessel_n of_o what_o bigness_n or_o length_n you_o please_v to_o this_o by_o two_o ear_n at_o l_o l_o fasten_v two_o line_n or_o rope_n k_o k_o the_o end_n of_o both_o which_o be_v fasten_v to_o the_o wheel_n or_o pulley_n g_z though_o one_o of_o they_o do_v run_v over_o the_o pulley_n f._n fit_a into_o this_o receptacle_n be_v make_v a_o cylindrical_a or_o prismatical_a plug_n a_o a_o which_o be_v fix_v in_o some_o convenient_a place_n so_o as_o not_o to_o rise_v or_o sink_v and_o through_o the_o middle_n thereof_o pass_v a_o siphon_n b_o b_o b_o the_o one_o end_n whereof_o extend_v like_o the_o branch_n of_o a_o candle_n or_o lamp_n sustain_v the_o socket_n d_o for_o the_o flame_n e_o which_o be_v feed_v with_o oil_n through_o the_o siphon_n b_o b_o b_o by_o the_o rise_a receptacle_n c_o c._n to_o the_o side_n of_o the_o pulley_n g_o be_v fasten_v a_o fusey_n h_n make_v with_o very_o great_a care_n of_o one_o revolution_n of_o a_o archimedean_a spiral_n not_o begin_v from_o the_o centre_n but_o from_o some_o convenient_a distance_n from_o it_o where_o the_o weight_n i_o hang_v may_v just_o counterpoise_v the_o receptacle_n c_o c_o when_o quite_o empty_a of_o oil_n the_o other_o hang_v counterpoise_n tangent_fw-la to_o the_o large_a part_n of_o this_o spiral_n must_v be_v so_o far_o distant_a from_o the_o centre_n of_o the_o wheel_n g_o that_o the_o same_o weight_n i_o may_v just_o counterpoise_v the_o say_a receptacle_n fill_v topful_a of_o oil_n and_o the_o fusey_n must_v be_v file_v true_a to_o a_o spiral_n draw_v with_o great_a care_n of_o one_o revolution_n between_o those_o two_o point_n i_o say_v here_o of_o one_o revolution_n because_o i_o have_v suppose_v the_o wheel_n or_o pulley_n g_o big_o enough_o by_o one_o revolution_n of_o it_o to_o draw_v up_o the_o receptacle_n the_o whole_a space_n it_o be_v to_o be_v raise_v for_o if_o the_o say_v pulley_n be_v so_o small_a as_o to_o require_v two_o three_o four_o or_o more_o revolution_n then_o must_v the_o piece_n of_o the_o spiral_n between_o those_o point_n be_v draw_v of_o two_o three_o four_o or_o more_o revolution_n proportionable_o which_o be_v very_o artificial_o and_o mechanical_o perform_v the_o receptacle_n c_o c_o will_n be_v raise_v by_o the_o same_o degree_n by_o which_o the_o oil_n be_v consume_v at_o e_o and_o the_o upper_a superficies_n thereof_o shall_v always_o be_v in_o the_o same_o horizontal_n line_n mm._n the_o geometrical_a and_o mechanical_a reason_n of_o which_o be_v so_o very_o plain_a i_o hope_v i_o shall_v not_o need_v to_o spend_v any_o more_o time_n in_o the_o explication_n thereof_o than_o only_o to_o say_v that_o by_o mean_n of_o the_o archimedean_a spiral-fusey_a the_o power_n of_o the_o weight_n i_o upon_o the_o pulley_n g_o decrease_v in_o the_o same_o proportion_n as_o the_o weight_n of_o the_o oil_n in_o the_o receptacle_n c_o c_o be_v diminish_v by_o its_o consumption_n the_o seven_o way_n than_o be_v by_o a_o cylindrical_a or_o prismatical_a plug_n fit_v into_o a_o cylindrical_a or_o prismatical_a receptacle_n and_o let_v down_o into_o it_o by_o a_o counterpoise_n hang_v upon_o a_o spiral_n fusey_n the_o oil_n be_v so_o raise_v in_o that_o receptacle_n as_o always_o to_o stand_v brimful_a or_o to_o the_o same_o horizontal_n height_n till_o the_o whole_a oil_n be_v consume_v the_o contrivance_n of_o this_o way_n will_v be_v very_o easy_o understand_v by_o any_o one_o that_o shall_v peruse_v the_o delineation_n in_o the_o eight_o figure_n and_o examine_v it_o by_o this_o follow_a description_n let_v a_o a_o in_o the_o eight_o figure_n then_o represent_v a_o cylindrical_a or_o prismatical_a receptacle_n stand_v fix_v upon_o a_o table_n or_o pedestal_n from_o the_o side_n of_o which_o issue_v a_o hollow_a arm_n or_o branch_n b_o b_o bear_v the_o socket_n for_o the_o wick_n c_o where_o the_o flame_n d_o be_v continue_v into_o the_o cavity_n of_o this_o receptacle_n be_v fit_v a_o cylindrical_a or_o prismatical_a plug_n e_o e_o big_a enough_o to_o fill_v the_o whole_a capacity_n thereof_o and_o yet_o not_o so_o close_o but_o that_o it_o may_v free_o slip_v up_o and_o down_o the_o cavity_n of_o the_o say_a receptacle_n without_o sink_v let_v this_o plug_n be_v make_v considerable_o heavy_a than_o the_o oil_n of_o the_o receptacle_n that_o be_v let_v the_o counterpoise_n l_o hang_v upon_o the_o little_a wheel_n m_o just_o reduce_v its_o gravity_n to_o be_v equal_a to_o that_o of_o the_o oil_n then_o let_v the_o point_n i_o where_o the_o perpendicular_a touch_v the_o spiral_n be_v so_o far_o remove_v from_o the_o centre_n of_o the_o wheel_n h_n that_o the_o counterpoise_n l_o may_v just_o take_v off_o its_o whole_a gravity_n and_o suffer_v it_o to_o have_v no_o degree_n of_o gravity_n or_o pressure_n downward_o then_o draw_v the_o spiral_n n_z o_o p_o according_a to_o the_o direction_n i_o give_v in_o the_o former_a way_n and_o the_o effect_n will_v be_v produce_v the_o geometrical_a and_o mechanical_a demonstration_n of_o which_o be_v very_o plain_a to_o any_o one_o that_o shall_v consider_v that_o as_o the_o plug_n e_o e_z by_o sink_v into_o the_o receptacle_n a_o a_o so_o far_o as_o to_o raise_v the_o oil_n to_o the_o horizontal_n superficies_n m_o
m_o will_n lose_v its_o gravity_n by_o the_o same_o degree_n by_o which_o it_o sink_v into_o the_o receptacle_n and_o that_o be_v always_o proportionable_a to_o the_o diminish_n of_o the_o oil_n in_o the_o receptacle_n by_o the_o flame_n so_o the_o weight_n l_o will_v lose_v its_o power_n upon_o the_o wheel_n h_n by_o the_o same_o degree_n by_o which_o the_o plug_n descend_v by_o reason_n the_o line_n by_o which_o it_o be_v suspend_v become_v a_o tangent_fw-la to_o a_o proportionate_o short_a radius_fw-la of_o the_o spiral_n of_o the_o ray_n of_o the_o spiral_n i_o know_v indeed_o that_o both_o in_o this_o and_o the_o former_a fusey_n there_o lie_v a_o objection_n against_o the_o true_a form_n of_o the_o spiral_n because_o the_o line_n k_o k_o of_o the_o weight_n l_o do_v not_o touch_v the_o spiral_n in_o a_o point_n level_n with_o the_o centre_n but_o in_o one_o somewhat_o above_o it_o and_o in_o this_o latter_a somewhat_o beneath_o it_o but_o though_o that_o be_v a_o seem_a material_a one_o yet_o as_o to_o practise_v it_o signify_v very_o little_a for_o first_o it_o will_v not_o be_v difficult_a to_o prove_v that_o this_o may_v be_v mechanical_o draw_v true_a enough_o that_o there_o shall_v be_v no_o sensible_a error_n and_o if_o the_o error_n be_v not_o sensible_a it_o be_v no_o error_n in_o practical_a mechanic_n next_o be_v it_o the_o true_a spiral_n yet_o it_o will_v not_o be_v more_o geometrical_o delineate_v than_o this_o which_o be_v here_o require_v and_o at_o best_o it_o will_v prove_v but_o a_o mechanical_a approach_n which_o be_v sufficient_a for_o the_o effect_n to_o be_v produce_v by_o it_o these_o two_o last_o contrivance_n do_v keep_v the_o flame_n of_o the_o lamp_n always_o in_o the_o same_o place_n and_o of_o the_o same_o strength_n and_o fullness_n but_o the_o succeed_a way_n though_o they_o maintain_v the_o flame_n in_o the_o same_o degree_n of_o strength_n and_o nourishment_n yet_o by_o their_o motion_n upward_o they_o may_v be_v make_v to_o increase_v and_o intend_v the_o heat_n produce_v by_o they_o in_o the_o body_n posit_v above_o they_o which_o be_v of_o great_a use_n in_o many_o chemical_a and_o philosophical_a experiment_n the_o eight_o way_n than_o be_v this_o make_v a_o cylindrical_a or_o prismatical_a receptacle_n for_o the_o oil_n exact_o like_o the_o former_a with_o its_o arm_n socket_n wick_n etc._n etc._n and_o fit_a into_o it_o a_o cylindrical_a or_o prismatical_a plug_n as_o in_o the_o former_a that_o may_v be_v able_a to_o fill_v the_o say_a receptacle_n fix_v this_o plug_n fast_o into_o some_o wall_n or_o standard_n so_o that_o it_o shall_v not_o be_v able_a to_o stir_v then_o by_o the_o help_n of_o two_o line_n fasten_v to_o a_o counterpoise_n at_o one_o end_n and_o the_o other_o to_o the_o ear_n of_o the_o receptacle_n so_o counterpoise_v the_o say_a receptacle_n that_o it_o shall_v have_v no_o weight_n or_o gravity_n downward_o but_o hang_v in_o a_o perfect_a equilibrium_fw-la i_o say_v whatever_o quantity_n of_o oil_n there_o be_v in_o the_o say_a vessel_n the_o superficies_n thereof_o shall_v always_o be_v in_o the_o plain_n which_o be_v equal_a to_o the_o top_n of_o the_o oil_n when_o the_o vessel_n be_v fill_v as_o high_a as_o be_v desire_v which_o will_v very_o plain_o appear_v to_o any_o one_o that_o shall_v examine_v and_o consider_v well_o this_o follow_a description_n and_o compare_v it_o with_o the_o delineation_n of_o the_o instrument_n in_o the_o nine_o figure_n where_o a_o a_o represent_v a_o receptacle_n for_o the_o oil_n of_o any_o convenient_a capacity_n make_v cylindrical_a or_o prismatical_a to_o which_o be_v fasten_v a_o hollow_a neck_n or_o arm_n b_o b_o for_o bear_v the_o socket_n c_o to_o which_o through_o its_o cavity_n be_v make_v hollow_a be_v convey_v the_o oil_n or_o pabulum_fw-la for_o the_o continuance_n of_o the_o flame_n d_o into_o this_o receptacle_n fit_v a_o cylindrical_a or_o prismatical_a plug_n so_o as_o it_o may_v pretty_a equal_o fill_v the_o say_a cavity_n of_o the_o receptacle_n yet_o not_o so_o as_o any_o way_n to_o hinder_v the_o slide_n on_o upon_o it_o of_o the_o receptacle_n let_v this_o plug_n then_o be_v fix_v by_o the_o top_n in_o any_o convenient_a place_n perpendicular_o and_o set_v the_o receptacle_n underneath_o it_o counterpoise_v the_o same_o when_o fill_v up_o with_o oil_n by_o a_o counterpoise_n i_o which_o be_v fasten_v to_o the_o two_o string_n f_o f_o f_o f_o by_o which_o the_o receptacle_n be_v to_o hang_v which_o two_o string_n for_o their_o more_o easy_a slide_n to_o and_o fro_o move_v upon_o the_o two_o pulley_n or_o truckle_n g_o g_z that_o be_v fix_v to_o the_o same_o frame_n to_o which_o the_o plug_n e_o e_z be_v fix_v which_o be_v so_o adjust_v as_o fast_o as_o the_o flame_n d_o consume_v the_o oil_n out_o of_o the_o receptacle_n a_o a_o the_o counterpoise_n i_o raise_v the_o say_a receptacle_n on_o upon_o the_o plug_n so_o far_o till_o the_o top_n of_o the_o oil_n be_v equal_a to_o the_o height_n it_o be_v at_o first_o counterpoise_v at_o to_o which_o height_n it_o always_o keep_v it_o till_o the_o whole_a be_v consume_v this_o last_o way_n of_o poise_v the_o liquor_n or_o oil_n do_v make_v the_o superficies_n thereof_o run_v high_a and_o high_o as_o the_o quantity_n thereof_o be_v more_o and_o more_o consume_v which_o for_o divers_a expedient_n in_o mechanic_n natural_a philosophy_n and_o chemistry_n be_v of_o excellent_a use_n as_o i_o may_v hereafter_o have_v opportunity_n to_o manifest_v upon_o many_o occasion_n where_o i_o shall_v make_v use_n of_o they_o and_o it_o will_v be_v i_o fear_v too_o tedious_a to_o the_o reader_n to_o have_v they_o here_o enumerate_v but_o because_o it_o may_v not_o possible_o be_v ungrateful_a to_o he_o to_o have_v some_o use_n of_o this_o principle_n here_o hint_v i_o shall_v now_o specify_v a_o few_o and_o hereafter_o add_v many_o more_o together_o with_o a_o great_a number_n of_o other_o poise_n for_o liquor_n which_o serve_v for_o very_o differ_v effect_n in_o their_o kind_n not_o less_o considerable_a but_o rather_o somewhat_o more_o strange_a as_o be_v yet_o far_o remove_v from_o the_o common_a practice_n and_o discourse_n of_o hydraulick_n the_o first_o use_n then_o that_o i_o shall_v mention_v of_o this_o liquorpoise_n shall_v be_v in_o hydraulick_n viz._n to_o make_v a_o cistern_n of_o whatever_o bigness_n and_o depth_n be_v require_v to_o deliver_v all_o its_o water_n at_o the_o top_n or_o so_o near_o unto_o it_o as_o it_o shall_v be_v desire_v by_o which_o mean_v nothing_o of_o the_o descent_n of_o the_o water_n fall_v into_o the_o cistern_n be_v lose_v but_o without_o any_o labour_n or_o trouble_v the_o whole_a quantity_n of_o water_n that_o be_v deliver_v at_o the_o top_n into_o the_o cistern_n be_v re-delivered_n again_o out_o of_o the_o cistern_n at_o the_o top_n this_o may_v be_v do_v by_o the_o first_o second_o and_o seven_o way_n of_o poise_a liquor_n this_o that_o or_o the_o other_o of_o which_o may_v be_v more_o convenient_a to_o this_o that_o or_o another_o effect_n or_o operation_n to_o be_v perform_v by_o it_o which_o must_v be_v choose_v and_o apply_v with_o judgement_n according_a to_o the_o occasion_n and_o the_o circumstance_n of_o it_o every_o of_o the_o three_o though_o they_o all_o agree_v together_o in_o the_o produce_v the_o effect_n of_o keep_v the_o superficies_n perficies_fw-la of_o the_o water_n to_o the_o same_o level_n and_o there_o deliver_v it_o have_v yet_o each_o of_o they_o their_o several_a propriety_n which_o make_v some_o one_o of_o the_o three_o more_o proper_a and_o adapt_v to_o one_o design_n than_o either_o of_o the_o other_o two_o and_o each_o of_o the_o other_o two_o in_o some_o other_o effect_n and_o application_n may_v be_v much_o more_o useful_o apply_v than_o the_o first_o by_o this_o mean_v the_o whole_a depth_n of_o the_o cistern_n be_v gain_v and_o all_o that_o water_n that_o be_v use_v to_o be_v deliver_v at_o the_o bottom_n be_v now_o deliver_v at_o the_o top_n and_o consequent_o gain_v the_o advantage_n of_o the_o perpendicular_a height_n of_o the_o cistern_n to_o be_v employ_v for_o any_o use_n for_o turn_v a_o automaton_n or_o convey_v the_o stream_n far_o or_o to_o a_o high_a level_n a_o second_o effect_n performable_a by_o these_o poise_n may_v be_v for_o deliver_v any_o quantity_n of_o water_n with_o a_o equal_a degree_n of_o swiftness_n so_o as_o to_o continue_v a_o equal_a supply_n of_o water_n till_o the_o whole_a cistern_n or_o receptacle_n be_v empty_v the_o spend_v of_o the_o water_n in_o the_o cistern_n not_o at_o all_o abate_v the_o stream_n without_o the_o counterpoise_n always_o keep_v the_o cistern_n full_a and_o maintain_v the_o current_n till_o the_o last_o this_o may_v be_v useful_a for_o saw_v or_o grind_v
four_o as_o the_o root_n of_o 64._o that_o be_v of_o 19+17+15+13_n at_o the_o end_n of_o the_o ten_o or_o whole_a as_o the_o root_n of_o 100_o that_o be_v as_o equal_a to_o 100_o now_o since_o the_o velocity_n be_v in_o the_o same_o proportion_n to_o the_o root_n of_o the_o space_n as_o the_o root_n of_o the_o space_n be_v to_o the_o time_n it_o be_v easy_a to_o determine_v the_o particular_a time_n in_o which_o every_o one_o of_o these_o space_n be_v pass_v for_o divide_v the_o space_n by_o the_o velocity_n correspond_v the_o quotient_n give_v the_o particular_a time_n to_o explain_v this_o more_o intelligible_o let_v a_o in_o the_o four_o figure_n represent_v the_o end_n of_o a_o spring_n not_o bend_v or_o at_o least_o counterpoise_v in_o that_o posture_n by_o a_o power_n fix_v to_o it_o and_o movable_a with_o it_o draw_v the_o line_n a_o b_o c_o and_o let_v it_o represent_v the_o way_n in_o which_o the_o end_n of_o the_o spring_n by_o additional_a power_n be_v to_o be_v move_v draw_v to_o the_o end_n of_o it_o c_o at_o right_a angle_n the_o line_n c_o δ_n d_o d_o and_o let_v c_o d_o represent_v the_o power_n that_o be_v sufficient_a to_o bend_v or_o move_v the_o end_n of_o the_o spring_n a_o to_o c_o then_o draw_v the_o line_n d_o a_o and_o from_o any_o point_n of_o the_o line_n a_o c_o as_o b_o b._n draw_v line_n parallel_v to_o c_o d_o cut_v the_o line_n d_o a_o in_o e_o e_o the_o line_n b_o e_o b_o e_o will_v represent_v the_o respective_a power_n requisite_a to_o bend_v the_o end_n of_o the_o spring_n a_o to_o b_o which_o line_n b_o e_z b_o e_o c_o d_o will_n be_v in_o the_o same_o proportion_n with_o the_o length_n of_o the_o bent_n of_o the_o spring_n a_o b_o a_o b_o a_o c._n and_o because_o the_o spring_n have_v in_o every_o point_n of_o the_o line_n of_o bend_v a_o c_o a_o particular_a power_n therefore_o imagine_v infinite_a line_n draw_v from_o every_o point_n of_o a_o c_o parallel_n to_o c_o d_o till_o they_o touch_v the_o line_n a_o d_o they_o will_v all_o of_o they_o fill_v and_o compose_v the_o triangle_n a_o c_o d._n the_o triangle_n therefore_o a_o c_o d_o will_n represent_v the_o aggregate_v of_o the_o power_n of_o the_o spring_n bend_v from_o a_o to_o c_o and_o the_o lesser_a triangle_n a_o b_o e_o a_o b_o e_o will_n represent_v the_o aggregate_v of_o all_o the_o power_n of_o the_o spring_n bend_v from_o a_o to_o b_o b_o and_o the_o spring_n bend_v to_o any_o point_n of_o the_o line_n a_o c_o and_o let_v go_v from_o thence_o will_v exert_v in_o its_o return_n to_o a_o all_o those_o power_n which_o be_v equal_a to_o the_o respective_a ordinates_n b_o e_o b_o e_o in_o the_o triangle_n the_o sum_n of_o all_o which_o make_v up_o the_o triangle_n a_o b_o e_o a_o b_o e._n and_o the_o aggregate_v of_o the_o power_n with_o which_o it_o return_v from_o any_o point_n as_o from_o c_o to_o any_o point_n of_o the_o space_n c_o a_o as_o to_o b_o b_o be_v equal_a to_o the_o trapezium_fw-la c_o d_o e_o b_o c_o d_o e_o b_o or_o the_o excess_n of_o the_o great_a triangle_n above_o the_o less_o have_v therefore_o show_v a_o image_n to_o represent_v the_o flexure_n and_o the_o power_n so_o as_o plain_o to_o solve_v and_o answer_v all_o question_n and_o problem_n concern_v they_o in_o the_o next_o place_n i_o come_v to_o represent_v the_o velocity_n appropriate_v to_o the_o several_a power_n the_o velocity_n then_o be_v always_o in_o a_o subduplicate_v proportion_n of_o the_o power_n that_o be_v as_o the_o root_n of_o the_o power_n impress_v and_o the_o power_n impress_v be_v as_o the_o trapezium_fw-la or_o the_o excess_n of_o the_o triangle_n or_o square_n of_o the_o whole_a space_n to_o be_v pass_v above_o the_o square_n of_o the_o space_n yet_o unpassed_a if_o upon_o the_o centre_n a_o and_o space_n a_o c_o c_z being_z the_o point_n from_o which_o the_o spring_n be_v suppose_v let_v go_v a_o circle_n be_v describe_v as_o c_o g_o g_o f_o and_o ordinates_n draw_v from_o any_o point_n of_o c_o a_o the_o space_n to_o be_v past_a as_o from_o b_o b_o to_o the_o say_a circle_n as_o b_o g_z b_o g_o these_o line_n b_o g_z b_o g_o will_v represent_v the_o velocity_n of_o the_o spring_n return_v from_o c_o to_z b_o b_o etc._n etc._n the_o say_v ordinates_n being_n always_o in_o the_o same_o proportion_n with_o the_o root_n of_o the_o trapezium_n c_o d_o e_o b_o c_o d_o e_o b_o for_o putting_z a_o c_o =_o to_o a_o and_o a_o b_o =_o b_o b_o g_o will_n always_o be_v equal_a to_o the_o square_a of_o the_o ordinate_a be_v always_o equal_a to_o the_o rectangle_n of_o the_o intercept_a part_n of_o the_o diameter_n have_v thus_o find_v the_o velocity_n to_o wit_n b_o g_o b_o g_o a_o f_o to_o find_v the_o time_n correspond_v on_o the_o diameter_n a_o c_o draw_v a_o parabola_fw-la c_o h_o f_o who_o vertex_fw-la be_v c_o and_o which_o pass_v through_o the_o point_n f._n the_o ordinates_n of_o this_o parabola_fw-la b_o h_n b_o h_n a_o f_o be_v in_o the_o same_o proportion_n with_o the_o root_n of_o the_o space_n c_o b_o c_o b_o c_o a_o then_z making_z g_z b_o to_z h_z b_o as_o h_z b_o to_z ay_o b_o and_o through_o the_o point_n c_o i_o i_o f_o draw_v the_o curve_v c_z i_o i_o i_o f_o the_o respective_a ordinates_n of_o this_o curve_v shall_v represent_v the_o proportionate_a time_n that_o the_o spring_n spend_v in_o return_v the_o space_n c_o b_o c_o b_o c_o a._n if_o the_o power_n or_o stiffness_n of_o the_o spring_n be_v great_a than_o what_o i_o before_o suppose_v and_o therefore_o must_v be_v express_v by_o the_o triangle_n c_o de_fw-fr a._n then_o the_o velocity_n will_v be_v the_o ordinates_n in_o a_o ellipse_n as_o c_o γ_n γ_n n_n great_a than_o the_o circle_n as_o it_o will_v also_o if_o the_o power_n be_v the_o same_o and_o the_o bulk_n move_v by_o the_o spring_n be_v less_o then_o will_v the_o s-like_a line_n of_o time_n meet_v with_o the_o line_n a_o f_o at_o a_o point_n as_o x_o within_o the_o point_n f._n but_o if_o the_o power_n of_o the_o spring_n be_v weak_a than_o i_o suppose_v then_o will_v c_o δ_n e_o e_o a_o represent_v the_o power_n and_o c_o γ_n γ_n o_o the_o ellipsis_n of_o velocity_n who_o ordinates_n b_o γ_n b_o γ_n a_o o_o will_v give_v the_o particular_a velocity_n and_o the_o s-like_a line_n of_o time_n will_v extend_v beyond_o n._n the_o same_o will_v happen_v suppose_v the_o body_n move_v by_o the_o spring_n to_o be_v proportionate_o heavy_a and_o the_o power_n of_o the_o spring_n the_o same_o with_o the_o first_o and_o suppose_v the_o power_n of_o the_o spring_n the_o same_o as_o at_o first_o bend_v only_o to_o b_o 2_o and_o from_o thence_o let_v go_v b_o 2_o e_z a_o be_v the_o triangle_n of_o its_o power_n the_o ordinates_n of_o the_o circle_n b_o g_o l_o be_v the_o line_n of_o its_o velocity_n and_o the_o ordinates_n of_o the_o s-like_a line_n b_o i_o f_o be_v the_o live_v of_o time_n have_v thus_o show_v you_o how_o the_o velocity_n of_o a_o spring_n may_v be_v compute_v it_o will_v be_v easy_a to_o calculate_v to_o what_o distance_n it_o will_v be_v able_a to_o shoot_v or_o throw_v any_o body_n that_o be_v move_v by_o it_o and_o this_o must_v be_v do_v by_o compare_v the_o velocity_n of_o the_o ascent_n of_o a_o body_n throw_v with_o the_o velocity_n of_o the_o descent_n of_o gravity_n allowance_n be_v also_o make_v for_o the_o resistance_n and_o impediment_n of_o the_o medium_n through_o which_o it_o pass_v for_o instance_n suppose_v a_o bow_n or_o spring_n fix_v at_o 16_o foot_n above_o a_o horizontal_n floor_n which_o be_v near_o the_o space_n that_o a_o heavy_a body_n from_o rest_n will_v descend_v perpendicular_o in_o a_o second_o of_o time_n if_o a_o spring_n deliver_v the_o body_n in_o the_o horizontal_n line_n with_o a_o velocity_n that_o move_v it_o 16_o foot_n in_o a_o second_o of_o time_n then_o shall_v it_o fall_v at_o 16_o foot_n from_o the_o perpendicular_a point_n on_o the_o floor_n over_o which_o it_o be_v deliver_v with_o such_o velocity_n and_o by_o its_o motion_n shall_v describe_v in_o the_o air_n or_o space_n through_o which_o it_o pass_v a_o parabola_fw-la if_o the_o spring_n be_v bend_v to_o twice_o the_o former_a tension_n so_o as_o to_o deliver_v the_o body_n with_o double_a the_o velocity_n in_o a_o horizontal_n line_n that_o be_v with_o a_o velocity_n that_o move_v 32_o foot_n in_o a_o second_o then_o shall_v the_o body_n touch_v the_o floor_n in_o a_o point_n very_o near_o at_o 32_o foot_n from_o the_o aforesaid_a perpendicular_a point_n and_o the_o
then_o either_o of_o those_o two_o of_o tycho_n brahe_n or_o this_o set_v down_o by_o hevelius_n which_o be_v much_o the_o same_o with_o one_o of_o those_o which_o be_v 100_o year_n since_o make_v use_n of_o by_o tycho_n and_o describe_v and_o be_v by_o he_o attribute_v to_o a_o english_a mathematician_n but_o because_o this_o industrious_a and_o careful_a person_n put_v himself_o to_o the_o trouble_n of_o make_v and_o examine_v the_o division_n himself_o i_o can_v hearty_o have_v wish_v he_o have_v think_v upon_o some_o such_o way_n as_o this_o which_o i_o here_o describe_v and_o call_v a_o compendium_n of_o diagonal_a division_n it_o be_v a_o way_n whereby_o as_o 89_o 90_o of_o the_o trouble_n be_v save_v in_o perform_v the_o manual_a operation_n thereof_o so_o i_o judge_v it_o to_o be_v much_o more_o certain_a exact_a and_o plain_a than_o the_o other_o way_n of_o diagonal_o my_o reason_n for_o the_o first_o be_v plain_a the_o division_n of_o one_o degree_n serve_v for_o the_o whole_a ninety_o and_o my_o reason_n for_o the_o second_o be_v first_o because_o it_o be_v much_o plain_a to_o be_v distinguish_v then_o by_o the_o help_n of_o the_o edge_n of_o a_o ruler_n lie_v over_o the_o diagonal_o one_o be_v able_a to_o see_v but_o one_o part_n of_o the_o diagonal_a and_o second_o i_o think_v it_o much_o better_a than_o a_o small_a fiducial_a thread_n which_o be_v very_o apt_a to_o be_v bend_a and_o break_v if_o it_o lie_v close_o to_o the_o superficies_n of_o the_o diagonal_a and_o if_o it_o lie_v at_o a_o distance_n a_o skew_z glance_n of_o the_o eye_n will_v much_o alter_v the_o seem_a intersection_n of_o the_o diagonal_o which_o in_o this_o way_n be_v both_o prevent_v the_o way_n then_o in_o short_a be_v nothing_o but_o this_o take_v a_o thin_a piece_n of_o clear_a looking-glass_n plate_n well_o smooth_v and_o polish_a on_o both_o side_n and_o large_a enough_o one_o way_n to_o cover_v the_o whole_a breadth_n of_o the_o rim_z of_o the_o quadrant_n on_o which_o the_o diagonal_n be_v to_o be_v make_v and_o the_o other_o way_n to_o cover_v two_o or_o three_o degree_n this_o i_o do_v the_o big_a that_o the_o side_n of_o the_o arm_n may_v not_o shadow_v or_o darken_v the_o division_n and_o numbring_n suppose_v a_o a_o a_o a_o in_o the_o 29_o figure_n plate_n 2._o to_o represent_v such_o a_o plate_n upon_o this_o plate_n describe_v with_o great_a care_n a_o degree_n of_o the_o quadrant_n you_o will_v have_v divide_v and_o complete_a it_o with_o all_o its_o parallel_a circle_n and_o diagonal_n as_o you_o will_v have_v do_v any_o one_o degree_n upon_o the_o quadrant_n and_o if_o the_o rim_z of_o the_o quadrant_n be_v very_o broad_a in_o proportion_n to_o its_o radius_fw-la you_o may_v by_o the_o table_n of_o natural_a secant_v or_o tangent_n set_v the_o parallel_n at_o their_o due_a distance_n but_o if_o the_o rim_z be_v narrow_a it_o will_v be_v sufficient_o accurate_a to_o make_v their_o distance_n equal_a these_o division_n must_v be_v do_v with_o compass_n point_v with_o small_a diamant_n point_n in_o the_o manner_n of_o those_o wherewith_o glasier_n cut_v their_o glass_n the_o glass_n be_v thus_o divide_v and_o line_v number_n the_o diagonal_o and_o place_n it_o in_o the_o frame_n of_o the_o ruler_n with_o the_o line_a side_n next_o the_o quadrant_n so_o that_o move_v it_o to_o and_o fro_o the_o side_n of_o the_o glass_n may_v immediate_o touch_v the_o brass_n rim_z of_o the_o quadrant_n this_o brass_n rim_z must_v be_v divide_v into_o 90_o equal_a part_n or_o degree_n and_o at_o each_o division_n straight_o line_n draw_v from_o the_o circumference_n to_o ward_n the_o centre_n the_o whole_a breadth_n of_o the_o limb_n at_o least_o as_o much_o as_o be_v make_v use_n of_o for_o the_o glass-plate_n for_o the_o breadth_n of_o the_o diagonal_o the_o frame_n to_o carry_v this_o plate_n be_v a_o convenient_a cavity_n leave_v in_o the_o movable_a arm_n of_o the_o quadrant_n the_o whole_a manner_n of_o which_o will_v be_v better_o understand_v by_o the_o delineation_n thereof_o to_o which_o i_o shall_v therefore_o refer_v the_o reader_n the_o distance_n of_o the_o parallel_a circle_n if_o unequal_a may_v be_v easy_o set_v down_o true_a according_a to_o the_o number_n of_o natural_a tangent_n or_o secant_v with_o a_o pair_n of_o compass_n contrive_v like_o beam-compass_n but_o have_v its_o point_n to_o be_v set_v at_o any_o distance_n desire_v by_o the_o help_n of_o a_o screw_n move_v upon_o one_o side_n of_o the_o beam_n which_o i_o may_v have_v occasion_n to_o describe_v elsewhere_o more_o proper_o and_o therefore_o will_v here_o omit_v it_o next_o if_o this_o way_n have_v not_o please_v i_o can_v have_v wish_v he_o have_v know_v this_o follow_v which_o be_v altogether_o as_o easy_a and_o as_o geometrical_o true_a which_o i_o have_v contrive_v and_o have_v make_v small_a instrument_n thereby_o to_o show_v very_a minute_n division_n very_o easy_o and_o very_o plain_o i_o strike_v then_o upon_o the_o limb_n of_o the_o quadrant_n i_o will_v divide_v be_v first_o make_v exceed_v smooth_a and_o plain_a a_o circute_n very_o fine_a and_o as_o light_o as_o possible_o i_o can_v so_o it_o be_v but_o discernible_a and_o by_o the_o help_n of_o a_o very_a large_a quadrantal_a divide_v plate_n of_o ten_o foot_n radius_fw-la i_o divide_v the_o say_a quadrant_n in_o the_o faint_a circle_n abovementioned_a into_o 90_o part_n or_o degree_n then_o by_o a_o peculiar_a contrivance_n of_o a_o very_a curious_a point_n that_o strike_v with_o a_o spring_n which_o i_o describe_v in_o another_o discourse_n the_o say_a degree_n be_v mark_v upon_o the_o plate_n by_o curious_a small_a round_o and_o deep_a hole_n these_o be_v by_o another_o line_n without_o it_o which_o be_v divide_v and_o figure_v the_o common_a way_n distinguish_v and_o number_v by_o figure_n according_a to_o the_o common_a manner_n then_o for_o the_o sub-division_n i_o make_v a_o small_a holdfast_n by_o a_o screw_n which_o be_v fix_v on_o to_o the_o movable_a arm_n of_o the_o quadrant_n this_o serve_v to_o hold_v the_o end_n of_o a_o diagonal_a hair_n the_o other_o end_n of_o which_o be_v strain_v over_o the_o supplementary_a degree_n till_o it_o lie_v direct_o over_o some_o prickt-hole_n of_o the_o curious_a division_n on_o the_o limb_n of_o the_o quadrant_n this_o give_v i_o the_o sub-division_n of_o the_o quadrant_n to_o what_o accurateness_n i_o desire_v the_o supplementary_a degree_n be_v a_o degree_n of_o a_o very_a large_a circle_n put_v on_o upon_o a_o small_a rule_n fix_v on_o to_o the_o side_n of_o the_o movable_a arm_n who_o magnitude_n and_o distance_n be_v find_v by_o this_o proportion_n as_o the_o distance_n between_o the_o end_n of_o the_o small_a holdfast_n and_o the_o point_a circle_n be_v to_o the_o radius_fw-la of_o that_o circle_n so_o make_v the_o distance_n between_o the_o say_a end_n and_o the_o supplementary_a circle_n to_o the_o radius_fw-la of_o that_o circle_n this_o will_v be_v more_o plain_a by_o a_o scheme_n let_v a_o a_o a_o in_o the_o 32th_o figure_n represent_v a_o quadrant_n b_o b_o b_o a_o very_o fine_a circle_n strike_v on_o the_o limb_n of_o the_o quadrant_n from_o the_o centre_n l_o which_o by_o a_o large_a quadrant_n of_o 10_o foot_n radius_fw-la i_o divide_v into_o degree_n and_o by_o a_o spring_a point_n strike_v so_o many_o small_a point_n and_o number_v they_o to_o 90._o beginning_n at_o m_o and_o number_v towards_o i._o let_v d_o d_o represent_v the_o movable_a arm_n c_o c_o the_o holdfast_n fix_v upon_o the_o side_n of_o that_o arm_n which_o by_o a_o small_a screw_n pinch_v and_o hold_v fast_o a_o very_a fine_a hair_n at_o k_n ee_fw-mi the_o small_a ruler_n fix_v at_o right_a angle_n with_o the_o line_n l_o k_o f_o in_o this_o line_n through_o the_o point_n l_o and_o k_n i_o take_v a_o point_n as_o f_o and_z through_z f_z i_o strike_v a_o part_n of_o a_o circle_n f_o g_o who_o centre_n be_v somewhere_o in_o the_o line_n f_o k_o l_o produce_v which_o i_o find_v by_o resolve_v this_o proportion_n as_o k_n i_o be_v to_o l_o i_o so_o will_n k_o f_o be_v to_o the_o radius_fw-la of_o the_o supplementary_a circle_n f_o g_o which_o will_v fall_v somewhere_o in_o f_z k_o l_o produce_v towards_o l_o then_o take_v a_o degree_n of_o that_o circle_n which_o will_v extend_v from_o f_o to_o g_o and_o divide_v it_o into_o as_o minute_n division_n as_o be_v necessary_a and_o number_v they_o from_o f_z to_z g._n now_o to_o find_v what_o angle_n the_o sight_n d_o d_o make_v with_o the_o sight_n m_o m_o i_o strain_v the_o hair_n h_o k_o till_o i_o find_v it_o lie_v over_o the_o next_o division_n point_v towards_o the_o right_a hand_n and_o observe_v in_o the_o ruler_n e_o e_o what_o part_n of_o a_o
may_v at_o all_o vary_v the_o angle_n nor_o any_o unequal_a thickness_n in_o the_o limb_n of_o the_o quadrant_n but_o that_o the_o turn_v only_o of_o the_o screw_n shall_v produce_v a_o variation_n and_o that_o exact_o proportionate_a to_o the_o number_n of_o revolution_n and_o the_o part_n thereof_o show_v by_o the_o index_n the_o way_n to_o know_v exact_o what_o the_o obliquity_n of_o the_o screw_v aught_o to_o be_v to_o make_v the_o tooth_n upon_o the_o limb_n perpendicular_a be_v to_o number_v how_o many_o thread_n of_o the_o screw_v there_o be_v in_o a_o know_a length_n and_o what_o the_o compass_n of_o the_o say_v screw_n or_o the_o cylinder_n out_o of_o which_o it_o be_v make_v be_v and_o multiply_v the_o say_a compass_n by_o the_o number_n of_o revolution_n into_o a_o product_n the_o proportion_n of_o that_o product_n to_o the_o know_a length_n will_v give_v the_o obliquity_n of_o the_o screw_n the_o product_n be_v the_o radius_fw-la and_o the_o know_a length_n the_o tangent_fw-la of_o obliquity_n thus_o suppose_v in_o the_o length_n of_o 4_o inch_n there_o be_v 83_o thread_n of_o the_o screw_n and_o that_o the_o compass_n of_o the_o cylinder_n of_o the_o screw_v be_v ⌊_o 92_o centesm_n of_o a_o inch_n i_o multiply_v the_o ⌊_o 92_o by_o 83_o the_o number_n of_o revolution_n and_o it_o give_v i_o 76_o ⌊_o 36_o that_o be_v 76_o inch_n and_o 36_o centesm_n of_o a_o inch_n make_v this_o product_n the_o radius_fw-la and_o the_o know_a length_n viz._n 4_o inch_n the_o tangent_fw-la of_o the_o obliquity_n of_o the_o thread_n of_o the_o screw_v to_o the_o axis_n thereof_o or_o of_o the_o axis_n of_o the_o screw_v to_o the_o plain_a of_o the_o quadrant_n the_o demonstration_n of_o this_o be_v so_o plain_a that_o i_o need_v not_o insist_v upon_o it_o for_o the_o length_n of_o the_o thread_n of_o the_o screw_n be_v the_o secant_fw-la the_o compass_n of_o the_o cylinder_n be_v the_o radius_fw-la and_o the_o bigness_n of_o the_o thread_n or_o the_o distance_n between_o two_o thread_n be_v the_o tangent_fw-la in_o a_o right_a angle_a triangle_n and_o the_o screw_n be_v such_o a_o right_a angle_a triangle_n wound_n about_o a_o cylinder_n put_v the_o tangent_fw-la thereof_o parallel_n to_o the_o axis_n of_o the_o cylinder_n and_o consequent_o in_o the_o mechanical_a â—ryal_n of_o these_o proportion_n the_o more_o thread_n be_v take_v to_o make_v that_o comparison_n or_o measurement_n the_o more_o exact_a be_v the_o inclination_n find_v the_o consideration_n of_o which_o do_v plain_o show_v how_o exact_a a_o way_n of_o division_n this_o by_o the_o help_n of_o the_o screw_n be_v for_o the_o whole_a quadrant_n be_v thereby_o resolve_v into_o one_o grand_a diagonal_a the_o same_o with_o triangle_n the_o length_n of_o the_o thread_n upon_o the_o compass_n of_o the_o cylinder_n be_v the_o diagonal_a and_o the_o distance_n of_o the_o two_o end_n of_o those_o thread_n in_o a_o line_n parallel_n to_o the_o axis_n be_v the_o space_n to_o be_v divide_v by_o it_o and_o consequent_o by_o augment_v the_o bigness_n or_o compass_n of_o the_o cylinder_n and_o diminish_v the_o thread_n you_o may_v augment_v the_o diagonal_a in_o any_o proportion_n assign_v or_o by_o make_v the_o hand_n or_o index_n upon_o the_o end_n thereof_o of_o double_a treble_a quadruple_a decuple_n etc._n etc._n of_o the_o semi-diameter_n of_o the_o cylinder_n out_o of_o which_o the_o screw_n be_v make_v you_o may_v duplicate_v triplicate_v quadruplicate_v decuplicate_v etc._n etc._n the_o say_a length_n of_o the_o diagonal_a in_o proportion_n to_o the_o space_n to_o be_v divide_v the_o next_o thing_n then_o to_o be_v describe_v be_v the_o screw-frame_n make_v of_o iron_n much_o of_o the_o shape_n represent_v by_o h_z h_z h_z in_o the_o first_o and_o 11_o figure_n this_o frame_n by_o the_o help_n of_o a_o screw_n through_o the_o aforesaid_a plate_n who_o head_n be_v express_v by_o the_o round_a head_n k_n be_v fix_v on_o to_o the_o long_a plate_n from_o the_o centre_n and_o by_o the_o help_n of_o the_o screw_v i_o be_v force_v and_o keep_v down_o very_o close_o upon_o the_o edge_n of_o the_o limb_n of_o the_o quadrant_n the_o frame_n have_v 4_o collar_n for_o the_o screw-pin_n to_o run_v against_o which_o be_v indeed_o but_o half_a collar_n serve_v only_o to_o keep_v the_o screw_v steady_a two_o of_o these_o be_v make_v with_o most_o care_n mark_v with_o m_o m_o in_o the_o 11_o figure_n against_o m_o i_o do_v rest_v the_o shoulder_n of_o the_o screw-pin_n 3_o which_o be_v keep_v close_o home_o against_o it_o by_o the_o cylinder_n g_o g_o in_o the_o 10_o and_o 11_o figure_n the_o sharp_a conical_a point_n of_o this_o screw_v 9_o 9_o go_v into_o the_o conical_a hole_n at_o the_o end_n of_o the_o say_v cylinder_n g_o g_o g._n the_o shape_n of_o this_o cylinder_n and_o the_o screw_v by_o which_o it_o be_v force_v against_o the_o end_n of_o the_o screw_v 99_o be_v represent_v in_o the_o 10_o figure_n 7_o in_o the_o 9th_o figure_n represent_v the_o conical_a point_n 3_o the_o place_n lie_v against_o the_o choler_n m_o i_o 6_o the_o screw_v that_o move_v upon_o the_o edge_n of_o the_o limb_n of_o the_o quadrant_n 5_o the_o nut_n or_o opinion_n by_o which_o the_o screw_n be_v turn_v by_o a_o rod_n from_o the_o centre_n express_v alone_o in_o the_o 8_o figure_n but_o the_o manner_n how_o it_o lie_v in_o the_o frame_n be_v express_v by_o p_o p_o 0_o 0_o 0_o in_o fig._n 1.0_o 0_o 0_o represent_v the_o rod_n p_o p_o the_o handle_n by_o which_o it_o be_v turn_v q_o q_o the_o nut_n or_o opinion_n that_o turn_v the_o opinion_n 5_o of_o the_o screw_n s_o r_o the_o collar_n or_o holes_n that_o hold_v it_o fast_o to_o the_o movable_a plate_n or_o arm_n of_o the_o quadrant_n s_o s_o represent_v two_o small_a piece_n that_o clip_v the_o edge_n of_o the_o limb_n and_o serve_v to_o keep_v the_o screw-frame_n steady_a and_o true_a in_o its_o oblique_a posture_n and_o move_v equal_o on_o the_o limb_n by_o a_o strong_a spring_v of_o one_o side_n of_o it_o t_z t_z represent_v the_o index-plate_n which_o be_v divide_v into_o what_o number_n of_o part_n be_v think_v necessary_a 1_o 2_o 3_o 4_o or_o 5_o hundred_o part_n according_a to_o the_o bigness_n of_o the_o thread_n of_o the_o screw_v at_o 6_o a_o great_a thread_n require_v a_o more_o minute_n division_n and_o a_o small_a thread_n require_v a_o more_o gross_a these_o division_n be_v point_v at_o by_o the_o index_n 8_o at_o the_o end_n of_o the_o screw_n and_o the_o number_n of_o revolution_n or_o thread_n be_v mark_v on_o the_o limb_n of_o the_o quadrant_n and_o point_v at_o by_o the_o tongue_n e_o e_o upon_o the_o which_o be_v fasten_v a_o small_a pin_n f_o serve_v to_o carry_v a_o lens_n over_o the_o point_n of_o the_o tongue_n which_o make_v the_o number_n of_o thread_n appear_v more_o plain_a and_o big_a the_o manner_n of_o do_v which_o upon_o the_o frame_n of_o the_o screw_n be_v so_o easy_a that_o i_o shall_v not_o spend_v more_o time_n in_o the_o explication_n thereof_o and_o the_o manner_n of_o make_v the_o whole_a instrument_n will_v be_v easy_a enough_o to_o any_o ingenious_a workman_n but_o if_o any_o person_n desire_v one_o of_o they_o to_o be_v make_v without_o trouble_v himself_o to_o direct_v and_o oversee_v a_o workman_n he_o may_v employ_v mr._n tompion_n a_o watchmaker_n in_o water-lane_n near_o fleetstreet_n this_o person_n i_o recommend_v as_o have_v employ_v he_o to_o make_v that_o which_o i_o have_v whereby_o he_o have_v see_v and_o experience_v the_o difficulty_n that_o do_v occur_v therein_o and_o find_v he_o to_o be_v very_o careful_a and_o curious_a to_o observe_v and_o follow_v direction_n and_o to_o complete_a and_o perfect_a his_o work_n so_o as_o to_o make_v it_o accurate_a and_o fit_a for_o use_v by_o the_o help_n of_o these_o indices_fw-la it_o will_v be_v easy_a and_o plain_a to_o see_v how_o many_o revolution_n of_o the_o screw_n and_o what_o part_n of_o a_o revolution_n make_v a_o quadrant_n of_o a_o circle_n and_o consequent_o it_o will_v be_v easy_a to_o make_v a_o small_a table_n which_o shall_v show_v what_o part_n of_o a_o quadrant_n divide_v into_o degree_n minute_n and_o second_o will_v be_v design_v by_o the_o revolution_n and_o part_n of_o the_o revolution_n of_o the_o screw_n as_o for_o instance_n if_o i_o find_v that_o 1600_o revolution_n and_o ⌊_o 912_o make_v a_o quadrant_n than_o 17_o ⌊_o 788_o revolution_n make_v a_o degree_n and_o ⌊_o 296_o millesm_n of_o a_o revolution_n make_v a_o minute_n and_o about_o 5_o millesm_n make_v a_o second_o thence_o it_o will_v be_v easy_a to_o find_v if_o you_o observe_v a_o angle_n to_o contain_v 294_o ⌊_o 358_o that_o be_v 294_o revolution_n and_o 358_o millesm_n
arm_n to_o any_o angle_n may_v not_o vary_v the_o centre_n of_o the_o ball_n or_o cross_n out_o of_o the_o point_n where_o the_o two_o axe_n cut_v each_o other_o both_o these_o arm_n be_v to_o be_v make_v so_o as_o to_o be_v incline_v to_o any_o angle_n that_o be_v that_o the_o axis_n of_o the_o medium_fw-la take_v hold_v of_o by_o the_o arm_n of_o iron_n may_v be_v make_v to_o incline_v to_o the_o axis_fw-la of_o the_o rod_n on_o which_o they_o be_v in_o any_o angle_n desire_v and_o be_v set_v to_o that_o angle_n to_o be_v steady_o fix_v which_o may_v be_v do_v by_o a_o pin_n screw_v or_o wedge_n the_o way_n i_o make_v use_n of_o for_o the_o azimuth-instrument_n describe_v in_o the_o 73_o p._n of_o my_o animadversion_n be_v this_o which_o be_v delineate_v and_o explain_v in_o the_o 9th_o fig._n where_o g_z represent_v a_o socket_n of_o brass_n movable_a cylindrical_o round_a about_o the_o end_n or_o neck_n b_o of_o the_o axis_n or_o rod_n b_o b_o the_o same_o with_o a_o b_o in_o the_o 22_o fig._n of_o my_o animadversion_n and_o fixable_a in_o any_o posture_n desire_v by_o help_n of_o a_o side-screw_a h_z such_o as_o be_v very_o common_o make_v use_n of_o for_o most_o instrument_n that_o be_v fix_v upon_o the_o end_n of_o a_o three_o legged_a staff_n and_o be_v common_o call_v a_o cylinder_n and_o socket_n this_o socket_n of_o brass_n have_v a_o small_a rod_n of_o iron_n k_o fix_v into_o it_o at_o k_n which_o be_v near_o the_o middle_n of_o its_o concave_a part_n through_o this_o rod_n there_o be_v make_v a_o small_a eye_n or_o hole_n and_o through_o that_o hole_n a_o wedge-like_a pin_n m_z be_v thrust_v serve_v to_o keep_v the_o semicircular_a iron-arm_n c_o c_o steady_a and_o fix_v in_o any_o posture_n they_o shall_v be_v rectify_v to_o the_o semicircular-arm_n c_o c_o be_v to_o be_v make_v of_o very_o good_a iron_n or_o rather_o steel_n and_o to_o have_v a_o channel_n or_o grove_n quite_o through_o the_o middle_n of_o one_o of_o they_o and_o extend_v the_o whole_a length_n of_o a_o quadrant_a of_o a_o circle_n namely_o from_o n_z to_z o_o because_o according_a to_o the_o variety_n of_o occasion_n it_o may_v be_v vary_v to_o any_o point_n between_o n_z and_z o_o and_o it_o be_v to_o be_v observe_v that_o the_o iron-rod_n k_o must_v be_v so_o far_o fix_v out_o of_o the_o axis_fw-la of_o the_o socket_n g_o as_o n_z be_v distant_a from_o i_o or_o o_o from_o p_o the_o middle_n of_o the_o iron-arm_n between_o i_o and_o i_o that_o so_o when_o there_o be_v occasion_n the_o centre-hole_n or_o hand_n i_o may_v be_v move_v to_o p_o and_o fasten_v at_o q_o must_v be_v make_v a_o joint_n in_o the_o semicircular-arm_n so_o that_o when_o the_o end_n n_z of_o the_o arm_n be_v fix_v in_o or_o near_a k_n the_o other_o arm_n c_o may_v fall_v back_o from_o the_o point_n i_o otherwise_o the_o circular_a motion_n in_o many_o case_n can_v be_v continue_v quite_o round_o and_o communicate_v from_o one_o rod_n to_o the_o other_o by_o help_n of_o the_o medium_fw-la or_o plate_n x._o the_o several_a piece_n of_o this_o joint_n as_o they_o be_v apart_o and_o distinct_a you_o may_v see_v in_o the_o 9th_o figure_n and_o as_o they_o be_v join_v all_o together_o sit_v for_o motion_n you_o may_v see_v in_o the_o ten_o figure_n to_o which_o also_o the_o description_n of_o every_o part_n be_v adjoin_v in_o word_n refer_v to_o by_o the_o help_n of_o literal_a mark_n i_o hope_v will_v make_v it_o sufficient_o plain_a to_o any_o artist_n to_o understand_v three_o the_o medium_n ball_n or_o cross_n x_o must_v be_v make_v of_o a_o bigness_n suitable_a to_o the_o arm_n and_o cylinder_n and_o great_a care_n must_v be_v have_v that_o all_o the_o end_n point_n or_o handle_n lie_v exact_o in_o the_o same_o plain_a and_o that_o they_o be_v all_o equal_o distant_a from_o their_o centre_n at_o least_o that_o any_o two_o opposite_a one_o be_v so_o make_v because_o it_o be_v not_o absolute_o necessary_a that_o they_o shall_v be_v so_o all_o four_o though_o in_o most_o case_n it_o be_v best_a and_o far_o the_o handle_n or_o pivot_n ought_v to_o be_v exact_o round_a conical_a or_o cylindrical_a and_o the_o middle_a line_n of_o they_o to_o cut_v each_o other_o at_o right_a angle_n or_o upon_o a_o square_a and_o in_o general_a that_o all_o thing_n about_o the_o say_a joint_n be_v so_o contrive_v and_o wrought_v that_o the_o axis_n of_o the_o two_o rod_n may_v always_o cut_v each_o other_o in_o the_o centre_n of_o the_o medium_n cross_n or_o plate_n and_o that_o the_o say_a centre_n whatever_o change_n happen_v to_o the_o joint_n may_v always_o keep_v exact_o in_o the_o same_o very_a point_n without_o any_o alteration_n the_o shape_n of_o this_o medium_fw-la may_v be_v either_o a_o cross_n who_o four_o end_n have_v each_o of_o they_o a_o cylinder_n which_o be_v the_o weak_a way_n it_o be_v describe_v in_o the_o 9_o and_o 10_o figure_n by_o the_o cross_n x_o or_o second_o it_o may_v be_v make_v of_o a_o thick_a plate_n of_o brass_n upon_o the_o edge_n of_o which_o be_v fix_v four_o pivot_n which_o serve_v for_o the_o handle_v of_o the_o iron-arm_n to_o take_v hold_n of_o this_o be_v much_o better_a than_o the_o former_a but_o have_v not_o that_o strength_n and_o steadiness_n that_o a_o large_a ball_n have_v which_o be_v the_o way_n i_o most_o approve_v of_o as_o be_v strong_a steady_a and_o handsome_a these_o be_v delineate_v in_o the_o aforesaid_a figure_n by_o x_o x_o and_o x_o x_o x._o if_o it_o be_v a_o elliptical_a dial_n to_o be_v describe_v by_o the_o orthographical_a projection_n the_o former_a way_n for_o describe_v tangent_fw-la dial_n give_v the_o line_n that_o divide_v the_o ellipsis_n of_o the_o equinox_n in_o its_o true_a proportion_n and_o if_o you_o will_v have_v the_o line_n that_o divide_v the_o ellipsis_n of_o either_o tropic_a or_o of_o any_o other_o parallel_a circle_n you_o must_v rectify_v the_o semicircular_a arm_n c_o c_o of_o the_o axis_n b_o b_o to_o the_o degree_n of_o the_o declination_n of_o that_o parallel_n and_o they_o proceed_v as_o before_o you_o have_v the_o line_n which_o from_o the_o aforesaid_a circle_n divide_v the_o ellipsis_n of_o that_o parallel_n according_o perpendicular_n also_o let_v fall_n from_o the_o end_n of_o the_o cross_n 11_o give_v the_o true_a ellipsis_n in_o the_o orthographical_a projection_n answer_v to_o that_o parallel_n these_o line_n thus_o find_v be_v the_o true_a azimuth_n line_n of_o the_o point_n or_o division_n of_o that_o parallel_n and_o be_v this_o way_n trace_v out_o exact_o without_o any_o trouble_n of_o calculation_n which_o for_o some_o purpose_n in_o survey_v navigation_n etc._n etc._n be_v of_o very_o great_a use_n as_o i_o shall_v afterward_o show_v the_o universality_n of_o this_o contrivance_n for_o resolve_v almost_o all_o spherical_a question_n make_v it_o of_o very_o great_a use_n in_o navigation_n if_o it_o be_v adapt_v as_o it_o ought_v to_o be_v especial_o for_o the_o common_a seaman_n use_n who_o with_o a_o very_a few_o rule_n will_v be_v able_a immediate_o to_o find_v the_o hour_n and_o azimuth_n of_o any_o point_n in_o the_o heaven_n sufficient_o accurate_a for_o most_o observation_n that_o can_v be_v make_v at_o sea_n of_o which_o more_o hereafter_o for_o make_v the_o hand_n or_o index_n of_o a_o clock_n move_v in_o the_o shadow_n of_o the_o style_n make_v upon_o the_o face_n of_o the_o dial_n and_o expose_v to_o the_o sun_n this_o joint_n be_v make_v to_o join_v the_o arbour_n of_o the_o wheel_n that_o go_v round_o in_o twenty_o four_o hour_n with_o the_o arbour_n of_o the_o hand_n perform_v it_o without_o any_o other_o wheel_n or_o pinion_v in_o the_o dial_n or_o face_n part_n of_o the_o clock_n if_o the_o arbour_n of_o the_o clock_n that_o shall_v have_v carry_v the_o hand_n round_o in_o twenty_o four_o hour_n be_v make_v to_o have_v the_o same_o inclination_n to_o the_o plain_a of_o the_o dial_n that_o the_o axis_n have_v whether_o parallel_n to_o the_o axis_n or_o not_o it_o matter_n not_o at_o all_o so_o that_o the_o hand_n be_v rectify_v according_o as_o it_o ought_v to_o be_v and_o that_o the_o style_n of_o the_o dial_n arise_v from_o the_o centre_n of_o the_o dial_n out-through_a which_o the_o arbour_n be_v produce_v for_o carry_v the_o hand_n and_o place_v in_o its_o parallel_n respect_n to_o the_o axis_n as_o it_o ought_v to_o be_v for_o a_o tangent_fw-la dial._n for_o the_o shadow-line_n of_o the_o axis_n upon_o the_o plain_a of_o the_o dial_n be_v always_o carry_v round_o the_o centre_n of_o a_o dial_n in_o a_o plain_a which_o pass_v through_o the_o axis_n or_o style_n and_o make_v equal_a progression_n about_o it_o in_o equal_a space_n
but_o yet_o so_o much_o must_v be_v leave_v that_o it_o may_v move_v very_o free_o upon_o its_o centre_n c_o a_o whole_a semicircle_n this_o do_v and_o the_o receptacle_n be_v fill_v with_o oil_n the_o same_o effect_n will_v follow_v as_o in_o the_o first_o contrivance_n and_o the_o demonstration_n of_o it_o be_v much_o the_o same_o i_o shall_v not_o now_o spend_v time_n to_o explain_v it_o but_o rather_o proceed_v to_o the_o description_n of_o a_o three_o way_n of_o keep_v the_o liquor_n counterpoise_v to_o the_o same_o level_n the_o three_o way_n than_o be_v take_v any_o round_a vessel_n who_o concavity_n and_o convexity_n be_v turn_v upon_o a_o axis_n and_o suspend_v that_o vessel_n upon_o two_o small_a pivot_n but_o yet_o big_a enough_o to_o bear_v the_o say_a vessel_n fill_v with_o oil_n etc._n etc._n fasten_v in_o the_o pole_n of_o that_o axis_n and_o leave_v or_o cut_v open_a a_o six_o part_v more_o or_o less_o as_o you_o please_v of_o the_o side_n thereof_o that_o thereby_o any_o thing_n may_v be_v put_v into_o or_o take_v out_o of_o the_o cavity_n of_o the_o vessel_n then_o poise_v the_o vessel_n exact_o on_o those_o centre_n that_o no_o side_n be_v heavy_a than_o the_o other_o then_o fit_a into_o it_o a_o float_n of_o brass_n silver_n tin_n lead_v etc._n etc._n convex_v on_o the_o under_o side_n so_o as_o just_a to_o fill_v to_o the_o cavity_n of_o the_o vessel_n and_o on_o the_o upper_a side_n plain_a or_o convex_v or_o any_o other_o convenient_a figure_n it_o matter_n not_o much_o make_v this_o float_n as_o heavy_a as_o you_o can_v at_o the_o bottom_n and_o as_o light_a as_o may_v be_v at_o the_o top_n but_o yet_o of_o such_o weight_n as_o may_v well_o float_v upon_o the_o top_n of_o the_o oil_n etc._n etc._n let_v one_o end_n of_o this_o be_v fasten_v by_o a_o wire_n or_o string_n so_o as_o that_o end_n thereof_o may_v always_o touch_v that_o point_n of_o the_o concave_n of_o the_o vessel_n to_o which_o it_o be_v tie_v and_o that_o the_o rest_n thereof_o may_v turn_v and_o follow_v the_o sink_n of_o the_o oil_n and_o through_o the_o end_n of_o it_o near_o the_o place_n where_o it_o be_v fasten_v let_v a_o pipe_n go_v through_o it_o to_o receive_v the_o wick_n which_o pipe_n have_v no_o communication_n with_o the_o cavity_n of_o the_o hollow_a float_n this_o do_v fill_v the_o vessel_n as_o full_a as_o convenient_a with_o oil_n and_o light_v the_o wick_n and_o you_o shall_v find_v that_o as_o the_o fire_n consume_v the_o oil_n the_o vessel_n will_v turn_v upon_o its_o pole_n and_o keep_v the_o superficies_n of_o the_o oil_n always_o at_o the_o same_o distance_n from_o the_o flame_n that_o it_o be_v put_v at_o at_o first_o till_o the_o whole_a be_v consume_v this_o will_v be_v make_v more_o conceivable_a by_o a_o figure_n and_o explanation_n thereof_o which_o therefore_o take_v as_o follow_v in_o the_o five_o figure_n a_o c_o b_o b_o represent_v a_o hollow_a vessel_n the_o cavity_n whereof_o be_v very_o exact_o turn_v upon_o a_o axis_n who_o pole_n be_v in_o p_o the_o space_n between_o a_o and_o b_o in_o the_o side_n thereof_o be_v leave_v open_a into_o the_o cavity_n of_o it_o this_o vessel_n be_v suspend_v upon_o its_o pole_n at_o p_o so_o as_o to_o be_v free_a to_o move_v round_o upon_o they_o and_o exact_o poise_v as_o no_o one_o side_n thereof_o be_v heavy_a than_o another_o to_o the_o hollow_a of_o this_o vessel_n be_v fit_v a_o float_n d_o of_o brass_n latton_n silver_n lead_v etc._n etc._n who_o underside_n be_v make_v of_o a_o convexity_n just_o fit_a for_o the_o concavity_n of_o the_o vessel_n as_o may_v be_v see_v at_o k_o d_o i_o and_o the_o upper_a straight_o or_o plain_a let_v this_o float_n be_v make_v somewhat_o light_a than_o the_o oil_n or_o liquor_n on_o which_o it_o be_v to_o swim_v so_o that_o a_o part_n thereof_o may_v float_v above_o the_o superficies_n thereof_o let_v one_o end_n thereof_o e_o be_v fasten_v to_o the_o side_n of_o the_o vessel_n a_o little_a below_o the_o brim_n b_o through_o the_o end_n of_o this_o float_n be_v put_v a_o pipe_n and_o wick_n h_o for_o the_o flame_n i_o then_o pour_v in_o oil_n by_o the_o open_a side_n a_o q_o b_o fill_v the_o same_o till_o it_o carry_v the_o float_n up_o to_o touch_v the_o hollow_a of_o the_o vessel_n then_o light_a the_o wick_n and_o you_o will_v find_v that_o the_o lamp_n will_v consume_v the_o oil_n and_o this_o contrivance_n will_v continual_o supply_v it_o till_o the_o whole_a be_v consume_v and_o the_o poise_n be_v move_v to_o touch_v the_o concave_n of_o the_o aforesaid_a vessel_n for_o when_o the_o vessel_n be_v fill_v up_o to_o f_o g_o the_o float_n d_o will_v touch_v at_o o_o and_o e_o and_o the_o cavity_n above_o f_o g_o being_n empty_v the_o vessel_n will_v be_v as_o be_v describe_v in_o the_o figure_n the_o open_a part_n a_o b_o be_v upward_o and_o as_o the_o flame_n consume_v the_o oil_n the_o side_n of_o the_o vessel_n b_o will_v descend_v downward_o towards_o b_o 1_o and_o so_o by_o b_o 1_o b_o 2_o b_o 3_o to_z b_o 4_o where_o the_o whole_a quantity_n of_o oil_n will_v be_v consume_v and_o the_o bottom_n of_o the_o float_n will_v touch_v the_o hollow_a side_n of_o the_o vessel_n in_o all_o which_o gradual_a waste_n of_o the_o oil_n the_o superficies_n thereof_o will_v lie_v at_o the_o same_o distance_n below_o the_o upper_a side_n of_o the_o float_n d_o that_o it_o have_v at_o first_o and_o consequent_o at_o the_o same_o distance_n from_o the_o bottom_n of_o the_o flame_n the_o reason_n of_o all_o which_o will_v be_v very_o easy_a to_o be_v understand_v by_o any_o one_o that_o shall_v serious_o on_o this_o delineation_n consider_v that_o the_o float_n d_o must_n necessitate_v the_o vessel_n a_o c_o b_o to_o move_z on_o its_o axis_n b_o according_a as_o its_o oil_n waste_v because_o one_o end_n thereof_o e_o be_v fasten_v to_o the_o brim_n of_o the_o vessel_n b_o the_o other_o end_n o_o be_v loose_a will_n as_o the_o oil_n waste_v descend_v towards_o n_n whence_o the_o end_n e_o must_v hang_v heavy_a on_o the_o brim_n b_o and_o consequent_o must_v move_v it_o down_o towards_o b_o till_o the_o upper_a side_n f_o g_o of_o the_o float_n be_v reduce_v to_o a_o parallelism_n with_o the_o superficies_n of_o the_o remain_a oil_n and_o the_o end_n e_o have_v no_o gravitation_n on_o the_o brim_n b_o which_o motion_n will_v be_v continue_v as_o the_o oil_n waste_v and_o the_o brim_n b_o will_v be_v move_v downward_o by_o the_o point_n b_o 1_n b_o 2_o b_o 3_o to_z b_o 4._o i_o shall_v not_o therefore_o spend_v any_o more_o time_n in_o the_o geometrical_a demonstration_n thereof_o but_o proceed_v to_o explain_v a_o four_o way_n by_o which_o the_o flame_n and_o superficies_n of_o the_o oil_n keep_v always_o at_o the_o distance_n they_o be_v first_o put_v at_o the_o four_o way_n than_o be_v the_o make_v the_o socket_n of_o the_o wick_n to_o swim_v upon_o the_o top_n of_o the_o oil_n so_o that_o the_o socket_n may_v sink_v as_o well_o as_o the_o oil_n by_o reason_n it_o be_v sustain_v by_o that_o and_o by_o that_o only_a the_o vessel_n or_o receptacle_n be_v general_o make_v of_o glass_n and_o it_o be_v best_o of_o a_o hemispherical_a figure_n the_o light_n cast_v itself_o through_o the_o body_n of_o the_o oil_n as_o well_o as_o of_o the_o glass_n this_o be_v so_o plain_a and_o obvious_a and_o so_o common_o use_v and_o practise_v that_o i_o need_v not_o spend_v more_o time_n in_o the_o explanation_n or_o demonstration_n thereof_o but_o proceed_v to_o describe_v a_o five_o way_n the_o five_o way_n than_o be_v much_o upon_o the_o same_o principle_n with_o the_o four_o but_o avoid_v several_a inconvenience_n to_o which_o that_o be_v subject_a for_o whereas_o the_o flame_n in_o the_o four_o be_v necessitate_v to_o be_v within_o the_o capacity_n or_o the_o receptacle_n in_o this_o five_o it_o may_v be_v at_o any_o distance_n and_o so_o be_v make_v much_o more_o convenient_a to_o be_v come_v at_o and_o to_o be_v dress_v and_o trim_v take_v then_o a_o vessel_n of_o glass_n cylindrical_n be_v best_a as_o a_o glass_n bottle_n and_o fit_a to_o it_o a_o siphon_n long_o enough_o to_o draw_v the_o oil_n from_o the_o bottom_n of_o the_o say_a vessel_n make_v the_o one_o end_n of_o this_o siphon_n extend_v at_o what_o distance_n you_o think_v convenient_a for_o the_o place_v the_o flame_n of_o the_o lamp_n and_o so_o order_v it_o that_o it_o may_v always_o draw_v from_o the_o receptacle_n by_o its_o arm_n to_o feed_v the_o flame_n which_o it_o will_v do_v if_o the_o end_n of_o the_o siphon_n be_v make_v where_o the_o socket_n of_o the_o lamp_n be_v place_v
of_o the_o head_n seem_v much_o about_o the_o brightness_n of_o ♄_o when_v near_o the_o horizon_n and_o be_v about_o 25_o second_n in_o diameter_n as_o be_v represent_v by_o a_o not_o perfect_o define_v but_o hazy_a the_o cloudy_a part_n or_o beard_n of_o the_o body_n encompass_v it_o on_o all_o side_n but_o that_o part_n of_o the_o coma_n b_o which_o be_v next_o towards_o the_o sun_n be_v the_o narrow_a nor_o be_v this_o coma_n well_o define_v but_o the_o outward_a part_n of_o it_o be_v faint_a and_o faint_a however_o they_o be_v regular_o enough_o terminate_v to_o make_v the_o outward_a most_o bound_n of_o it_o of_o a_o kind_n of_o parabolical_a figure_n the_o most_o bend_a part_n of_o which_o be_v towards_o the_o sun_n and_o most_o define_v and_o the_o bright_a star_n of_o it_o be_v as_o i_o have_v express_v it_o about_o four_o of_o its_o diameter_n distant_a from_o the_o say_v parabolical_a limb_n the_o light_a part_n of_o the_o ambient_fw-la cloud_n seem_v to_o spread_v gradual_o towards_o that_o side_n of_o it_o which_o be_v opposite_a to_o the_o sun_n but_o those_o which_o be_v next_o the_o middle_a be_v the_o bright_a and_o always_o as_o they_o be_v far_o and_o far_o from_o the_o star_n in_o the_o head_n the_o faint_a and_o pale_a they_o be_v i_o can_v not_o observe_v any_o representation_n like_o those_o which_o be_v give_v we_o by_o mr._n hevelius_n in_o his_o cometography_n neither_o in_o the_o head_n nor_o the_o blaze_n no_o more_o than_o i_o can_v in_o those_o which_o appear_v in_o the_o year_n 1664._o and_o 1665._o as_o may_v be_v easy_o take_v notice_n of_o by_o compare_v these_o which_o i_o have_v here_o delineate_v with_o those_o the_o middle_a part_n of_o the_o blaze_n cc_o which_o ascend_v from_o the_o star_n in_o the_o middle_n seem_v the_o bright_a and_o of_o this_o medulla_n or_o stem_n those_o part_n be_v bright_a which_o be_v near_o situate_v to_o the_o say_v star_n the_o side_n of_o it_o grow_v faint_a and_o faint_a as_o they_o be_v far_o from_o the_o head_n and_o though_o they_o have_v brightness_n enough_o to_o make_v they_o appear_v in_o a_o dark_a and_o clear_a sky_n yet_o the_o dawn_n quick_o make_v they_o vanish_v and_z disappear_z as_o do_v any_o haziness_n of_o the_o sky_n and_o according_a as_o the_o light_n increase_v so_o be_v the_o blaze_n diminish_v after_o the_o order_n of_o the_o taper_v prick_v line_n express_v in_o the_o three_o figure_n by_o a_o a_o a_o b_o b_o b_o c_o c_o c_o d_o d_o d_o etc._n etc._n and_o even_o in_o a_o clear_a and_o dark_a sky_n towards_o the_o far_a end_n of_o the_o blaze_n they_o often_o disappear_v for_o some_o short_a space_n of_o time_n though_o the_o middle_n or_o stem_n continue_v and_o so_o it_o cause_v the_o remain_a appearance_n to_o resemble_v the_o figure_n of_o a_o very_a slender_a birchen_a whisk_n or_o brush_n much_o like_o that_o represent_v in_o the_o first_o figure_n the_o 22._o from_o half_a a_o hour_n after_o two_o till_o half_a a_o hour_n after_o three_o the_o north-east_n part_n of_o the_o heaven_n to_o i_o be_v cloudy_a and_o the_o sky_n between_o the_o cloud_n be_v hazy_a and_o the_o dawn_n strike_v much_o high_a than_o the_o day_n before_o so_o that_o i_o can_v not_o find_v it_o the_o 23._o with_o several_a friend_n i_o observe_v it_o again_o the_o sky_n be_v clear_a and_o confirm_v myself_o in_o all_o my_o former_a observation_n take_v again_o diligent_a notice_n of_o all_o circumstance_n remarkable_a both_o with_o my_o naked_a eye_n and_o with_o perspective-glass_n and_o i_o have_v this_o morning_n a_o very_a notable_a observation_n in_o order_n to_o measure_v the_o bigness_n of_o the_o star_n and_o its_o coma_n which_o encompass_a it_o by_o compare_v it_o with_o somewhat_o fix_v for_o some_o few_o minute_n before_o three_o of_o the_o clock_n the_o head_n of_o it_o pass_v just_a behind_o the_o type_n or_o top-post_n of_o a_o tower_n not_o far_o distant_a and_o be_v quite_o eclipse_v by_o it_o and_o as_o soon_o as_o it_o appear_v to_o have_v past_o it_o seem_v yet_o contiguous_a i_o observe_v it_o with_o my_o six_o foot_n telescope_n and_o find_v the_o coma_n or_o whole_a head_n to_o appear_v full_a as_o big_a as_o the_o say_a type_n or_o timber_n post_n and_o the_o nucleus_n or_o star_n in_o the_o middle_n of_o it_o to_o be_v very_o near_o of_o the_o same_o bigness_n of_o the_o iron_n spindle_n upon_o which_o the_o weathercock_n be_v fix_v whence_o upon_o examine_v the_o bigness_n of_o the_o say_a part_n since_o by_o a_o accurate_a instrument_n i_o judge_v the_o head_n or_o coma_n be_v about_o 4_o ⅙_n minute_n in_o diameter_n and_o the_o nucleus_n or_o star_n about_o 25_o second_n i_o take_v notice_n this_o morning_n that_o it_o have_v much_o alter_v the_o position_n in_o the_o heaven_n which_o it_o have_v upon_o saturday_n morning_n and_o that_o the_o blaze_n of_o it_o be_v very_o much_o deflect_v out_o of_o the_o line_n it_o appear_v in_o the_o last_o time_n and_o with_o a_o small_a crossstaff_n take_v the_o distance_n of_o it_o from_o alamak_n and_o from_o genib_n in_o the_o left_a side_n of_o perseus_n i_o judge_v it_o to_o be_v in_o the_o midway_n between_o the_o flower-de-luce_n aforesaid_a and_o algol_n or_o the_o head_n of_o medusa_n that_o be_v about_o 14_o degree_n of_o ♉_o and_o 17_o degree_n of_o northern_a latitude_n so_o that_o i_o judge_v its_o motion_n almost_o east_n but_o a_o little_a deflect_a south_n i_o be_v not_o much_o solicitous_a of_o make_v observation_n of_o its_o true_a place_n as_o not_o design_v my_o present_a enquiry_n to_o be_v for_o what_o kind_n of_o motion_n it_o have_v conceive_v its_o motion_n to_o be_v towards_o the_o sun_n and_o so_o of_o very_o little_a duration_n and_o expect_v to_o hear_v a_o account_n of_o that_o from_o other_o place_n and_o person_n that_o be_v better_o furnish_v with_o instrument_n and_o convenience_n for_o observation_n of_o that_o kind_n than_o i_o be_v then_o the_o blaze_n extend_v itself_o in_o a_o right_a line_n towards_o the_o star_n in_o the_o right_a thigh_n of_o cassiopea_n be_v a_o star_n of_o the_o three_o magnitude_n it_o be_v length_n at_o first_o be_v about_o 7_o or_o 8_o degree_n and_o do_v sometime_o seem_v long_o sometime_o short_a as_o i_o note_v before_o without_o seem_v to_o have_v any_o other_o motion_n in_o it_o but_o the_o diurnal_a motion_n the_o same_o with_o the_o fix_a star_n on_o earth_n whence_o i_o collect_v that_o the_o head_n of_o it_o point_v towards_o the_o seventeen_o degree_n of_o taurus_n in_o the_o ecliptic_a though_o the_o sun_n at_o that_o time_n be_v about_o the_o thirteen_o degree_n of_o the_o same_o sign_n the_o 24._o with_o several_a other_o i_o attend_v the_o appearance_n of_o it_o but_o the_o sky_n in_o that_o part_n of_o the_o heaven_n be_v overcast_v with_o cloud_n the_o 25._o i_o expect_v to_o have_v a_o far_a observation_n of_o it_o from_o half_a a_o hour_n after_o two_o till_o a_o quarter_n after_o four_o but_o notwithstanding_o the_o south-easter_o wind_n and_o the_o clarify_n quality_n of_o the_o air_n which_o before_o half_a a_o hour_n after_o three_o have_v partly_o carry_v off_o and_o partly_o dissolve_v the_o black_a thick_a cloud_n with_o which_o the_o north-east_n part_n of_o this_o horizon_n be_v overcast_v about_o three_o of_o the_o clock_n and_o leave_v that_o part_n of_o the_o heaven_n where_o the_o comet_n shall_v have_v appear_v clear_a and_o without_o cloud_n yet_o the_o air_n be_v very_o high_a and_o heavy_a as_o the_o barometer_n show_v the_o upper_a part_n of_o it_o be_v so_o fill_v with_o the_o dawn_a light_n of_o the_o morning_n that_o neither_o the_o blaze_n head_n or_o star_n of_o the_o comet_n appear_v to_o i_o in_o the_o least_o nor_o have_v i_o any_o sight_n of_o it_o since_o the_o like_a appearance_n of_o the_o great_a height_n of_o vapour_n in_o the_o air_n when_o it_o be_v very_o heavy_a i_o have_v often_o take_v notice_n of_o and_o have_v observe_v that_o the_o twilight_n and_o dawn_n between_o the_o night_n and_o appear_v of_o the_o sun_n be_v very_o much_o alter_v thereby_o and_o that_o a_o heavy_a air_n when_o the_o vapour_n be_v raise_v high_a will_v make_v the_o length_n of_o they_o much_o great_a and_o consequent_o the_o night_n short_a and_o a_o light_a air_n on_o the_o contrary_a shorten_v they_o do_v lengthen_v the_o night_n these_o be_v the_o most_o remarkable_a circumstance_n i_o take_v notice_n of_o in_o this_o comet_n be_v altogether_o physical_a and_o design_v only_o for_o enquirng_a into_o the_o constitution_n of_o these_o wonderful_a body_n the_o account_n and_o opinion_n we_o have_v hitherto_o have_v of_o they_o of_o that_o kind_n be_v very_o unfatisfactory_a though_o other_o observation_n to_o wit_n
it_o but_o as_o to_o the_o three_o i_o hope_v the_o indefatigable_a labour_n and_o skill_n of_o monsieur_n hevelius_n will_v short_o supply_v the_o present_a defect_n though_o it_o have_v be_v much_o to_o be_v wish_v that_o the_o instrument_n he_o have_v make_v use_n of_o have_v be_v fit_v with_o telescopical_a sight_n these_o table_n if_o well_o do_v will_v alone_o as_o to_o the_o business_n of_o comet_n at_o least_o supply_v the_o place_n of_o all_o other_o instrument_n almost_o save_v only_o a_o thread_n especial_o if_o they_o be_v so_o delineate_v in_o table_n after_o the_o tangent_fw-la projection_n as_o that_o the_o minute_n of_o every_o degree_n may_v be_v very_o distinguishable_a which_o will_v not_o swell_v the_o map_n of_o the_o heaven_n into_o a_o extraordinary_a large_a volume_n and_o may_v possible_o be_v the_o cheap_a instrument_n for_o this_o purpose_n a_o astronomer_n can_v be_v furnish_v withal_o for_o have_v such_o a_o volume_n of_o table_n it_o will_v be_v very_o easy_a with_o a_o thread_n and_o one_o eye_n screen_v only_o with_o a_o spectacle_n make_v of_o a_o thin_a plate_n of_o brass_n with_o a_o small_a hole_n through_o it_o instead_o of_o a_o glass_n to_o observe_v what_o place_n the_o comet_n possess_v among_o the_o fix_a star_n for_o have_v by_o the_o help_n of_o the_o say_a thread_n observe_v what_o two_o star_n lie_v in_o the_o same_o line_n with_o the_o comet_n on_o one_o side_n of_o it_o and_o what_o other_o two_o star_n lie_v in_o a_o line_n with_o it_o which_o be_v at_o right_a angle_n as_o near_o as_o may_v be_v with_o the_o former_a line_n by_o find_v out_o those_o four_o star_n in_o the_o table_n order_v according_a to_o the_o tangent_fw-la projection_n and_o with_o a_o ruler_n draw_v line_n over_o they_o respective_o where_o those_o line_n do_v intersect_v there_o will_v be_v the_o true_a place_n of_o the_o comet_n from_o which_o it_o will_v not_o be_v difficult_a to_o find_v out_o the_o true_a longitude_n and_o latitude_n of_o it_o by_o a_o sector_n with_o tangent_n now_o as_o these_o table_n of_o all_o the_o fix_a star_n visible_a to_o the_o naked_a eye_n will_v serve_v for_o find_v its_o place_n whilst_o very_o big_a and_o swift_a of_o motion_n so_o the_o like_a table_n of_o the_o small_a telescopical_a star_n that_o lie_v near_o its_o way_n when_o almost_o disappear_v and_o move_v very_o slow_a will_v by_o the_o help_n of_o a_o pair_n of_o measure_v compass_n place_v within_o the_o eye-glass_n of_o the_o telescope_n and_o a_o straight_a line_n or_o hair_n draw_v across_o it_o serve_v to_o find_v the_o true_a motion_n and_o way_n of_o it_o when_o only_o visible_a with_o a_o telescope_n according_a to_o which_o method_n i_o make_v the_o annex_v scheme_n and_o observation_n of_o the_o last_o appearance_n of_o the_o comet_n now_o since_o neither_o from_o my_o own_o nor_o from_o any_o other_o observation_n that_o i_o have_v hitherto_o meet_v with_o there_o can_v be_v any_o certain_a conclusion_n draw_v of_o the_o distance_n of_o these_o comet_n save_v only_o this_o that_o their_o distance_n be_v very_o great_a and_o much_o high_a than_o the_o body_n of_o the_o moon_n because_o else_o there_o must_v have_v be_v a_o considerable_a parallax_n cause_v by_o the_o diurnal_a motion_n the_o next_o enquiry_n will_v be_v what_o other_o way_n there_o be_v of_o know_v its_o distance_n now_o though_o none_o can_v be_v more_o demonstrative_a than_o the_o parallax_n find_v this_o way_n by_o the_o diurnal_a motion_n yet_o there_o be_v some_o other_o which_o seem_v more_o easy_a arise_v from_o the_o consideration_n of_o the_o motion_n that_o may_v be_v think_v to_o be_v concern_v in_o the_o produce_v the_o appearance_n and_o though_o they_o be_v whole_o hypothetical_a and_o so_o need_v some_o other_o argument_n to_o prove_v the_o ground_n and_o principle_n on_o which_o they_o be_v found_v yet_o since_o there_o be_v not_o very_o many_o considerable_a one_o want_v to_o make_v they_o probable_a and_o rational_a i_o shall_v here_o add_v somewhat_o of_o my_o inquiry_n after_o the_o distance_n position_n motion_n magnitude_n etc._n etc._n of_o these_o comet_n by_o these_o mean_n of_o these_o way_n there_o be_v several_a depend_v upon_o several_a supposition_n which_o produce_v very_o differ_v effect_n as_o to_o the_o magnitude_n distance_n motion_n and_o way_n of_o the_o same_o comet_n the_o supposition_n be_v these_o either_o that_o the_o earth_n move_v in_o a_o annual_a orb_n about_o the_o sun_n as_o the_o sun_n be_v suppose_v by_o other_o to_o move_v about_o the_o earth_n or_o that_o the_o earth_n be_v perfect_o fix_v and_o have_v no_o such_o motion_n next_o that_o the_o comet_n move_v either_o in_o a_o straight_a line_n or_o in_o a_o curve_v line_n and_o the_o curve_v be_v either_o a_o circle_n or_o some_o other_o regular_a or_o irregular_a curve_v further_o that_o the_o motion_n of_o the_o comet_n in_o these_o line_n be_v either_o by_o equal_a or_o unequal_a space_n in_o equal_a time_n now_o according_a as_o we_o take_v this_o or_o those_o of_o these_o differ_a supposition_n and_o compound_v they_o together_o so_o will_v the_o product_n of_o they_o be_v strange_o differ_v among_o the_o great_a variety_n of_o composition_n of_o these_o principle_n or_o supposition_n these_o seem_v the_o most_o simple_a and_o consequent_o be_v any_o otherwise_o prove_v will_v best_o determine_v the_o true_a distance_n and_o way_n of_o the_o comet_n first_o to_o suppose_v the_o earth_n to_o stand_v still_o and_o the_o comet_n to_o move_v equal_a space_n in_o equal_a time_n in_o a_o circle_n second_o to_o suppose_v the_o earth_n to_o move_v in_o a_o annual_a orb_n about_o the_o sun_n and_o the_o comet_n to_o move_v through_o the_o aether_n or_o expansum_fw-la equal_a space_n in_o equal_a time_n in_o a_o straight_a line_n three_o to_o suppose_v the_o earth_n to_o move_v as_o above_o in_o its_o annual_a orb_n and_o the_o comet_n also_o to_o move_v equal_a space_n in_o equal_a line_n in_o a_o circle_n the_o other_o be_v indeterminate_a and_o infinite_a and_o nothing_o can_v be_v conclude_v from_o they_o as_o to_o the_o distance_n magnitude_n motion_n etc._n etc._n of_o comet_n for_o the_o line_n or_o way_n of_o the_o comet_n may_v be_v place_v at_o any_o distance_n if_o we_o will_v suppose_v it_o move_v in_o a_o uncertain_a curve_v with_o unequal_a degree_n of_o velocity_n and_o indeed_o upon_o a_o supposal_n of_o a_o inequality_n of_o motion_n nothing_o of_o its_o way_n or_o distance_n can_v by_o any_o of_o these_o supposition_n be_v find_v out_o this_o fault_n have_v that_o of_o tycho_n brahe_n where_o he_o suppose_v a_o unequal_a motion_n of_o it_o in_o its_o orb_n about_o the_o orb_n of_o venus_n which_o be_v found_v upon_o the_o first_o hypothesis_n but_o have_v introduce_v into_o it_o some_o inequality_n of_o motion_n beside_o his_o own_o supposition_n that_o it_o be_v move_v about_o the_o sun_n and_o the_o sun_n about_o the_o earth_n see_v the_o five_o figure_n keplers_n way_n which_o be_v after_o the_o second_o hypothesis_n have_v the_o same_o fault_n for_o he_o suppose_v the_o annual_a motion_n of_o the_o earth_n and_o the_o motion_n of_o the_o comet_n in_o a_o straight_a line_n but_o introduce_v a_o acceleration_n of_o motion_n in_o the_o tangent_fw-la towards_o the_o latter_a end_n the_o three_o way_n i_o have_v here_o take_v and_o from_o the_o best_a observation_n i_o can_v meet_v with_o i_o have_v delineate_v its_o respect_n or_o angle_n to_o the_o sun_n and_o according_o suppose_v it_o to_o move_v equal_a space_n in_o equal_a time_n in_o a_o curve_v which_o for_o so_o much_o of_o it_o as_o the_o comet_n be_v observe_v to_o pass_v be_v very_o near_o a_o circle_n i_o find_v this_o circle_n will_v fall_v as_o it_o be_v express_v in_o the_o seven_o figure_n where_o it_o be_v obvious_a to_o take_v notice_n that_o when_o the_o comet_n be_v near_a to_o the_o earth_n namely_o about_o the_o 19_o or_o 20._o of_o december_n that_o it_o be_v not_o near_a than_o a_o eleven_o part_n of_o the_o distance_n of_o the_o sun_n that_o on_o the_o 23_o it_o be_v twice_o as_o far_o that_o on_o the_o 29._o it_o be_v four_o time_n as_o far_o that_o on_o the_o 15._o of_o january_n it_o be_v as_o far_o as_o the_o sun_n and_o on_o the_o 14._o of_o february_n it_o be_v above_o twice_o as_o far_o distant_a as_o the_o sun_n that_o this_o way_n or_o orb_n of_o the_o comet_n be_v here_o bend_a so_o as_o if_o it_o be_v a_o entire_a circle_n one_o part_n of_o it_o will_v go_v without_o the_o orb_n of_o jupiter_n as_o the_o other_o which_o be_v here_o delineate_v come_v within_o the_o orb_n of_o the_o earth_n that_o the_o plain_a of_o this_o orb_n be_v incline_v to_o the_o plain_a of_o the_o ecliptic_a about_o 18_o degree_n that_o if_o
contribute_v to_o the_o production_n than_o any_o peculiar_a and_o incommunicable_a nature_n of_o the_o matter_n because_o have_v have_v the_o curiosity_n to_o make_v some_o trial_n upon_o so_o obvious_a a_o material_a as_o quick_a lime_n though_o the_o success_n do_v not_o answer_v my_o design_n yet_o neither_o be_v it_o so_o bad_a but_o that_o some_o luminous_a quality_n be_v produce_v in_o the_o lime_n by_o the_o action_n of_o the_o fire_n and_o a_o saline_a liquor_n and_o i_o scarce_o question_v but_o other_o material_n will_v be_v find_v capable_a of_o be_v make_v luminous_a by_o the_o same_o or_o the_o like_a operation_n that_o be_v employ_v by_o baldwinus_n when_o that_o learned_a man_n shall_v think_v sit_v to_o communicate_v his_o way_n to_o the_o public_a but_o to_o return_v to_o what_o i_o be_v say_v that_o the_o contact_n of_o the_o air_n may_v be_v rather_o hurtful_a than_o advantageous_a to_o the_o phosphorus_n i_o shall_v only_o add_v here_o as_o matter_n of_o fact_n for_o my_o conjecture_n about_o light_n belong_v to_o my_o yet_o unpublisht_a note_n of_o the_o origine_fw-la of_o quality_n that_o whereas_o the_o contact_n of_o the_o air_n though_o it_o be_v not_o free_a do_v in_o a_o few_o day_n destroy_v the_o luminousness_n of_o a_o good_a phosphorus_n yet_o have_v include_v another_o in_o a_o receiver_n whence_o we_o afterward_o pump_v out_o the_o air_n this_o matter_n though_o inferior_a to_o the_o other_o in_o vividness_n be_v so_o little_o spoil_v by_o lie_v open_a in_o our_o vacuum_n that_o at_o the_o end_n of_o not_o only_o some_o week_n but_o some_o month_n i_o find_v that_o the_o beam_n of_o a_o candle_n pass_v to_o it_o through_o the_o receiver_n will_v notwithstanding_o the_o vacuum_n it_o yet_o continue_v in_o suffice_v to_o re-excite_a in_o it_o a_o manifest_a light_n thus_o far_o be_v the_o communication_n of_o this_o excellent_a person_n who_o it_o be_v hope_v may_v be_v further_o prevail_v with_o to_o communicate_v those_o other_o accurate_a observation_n and_o curious_a researche_n he_o have_v make_v concern_v the_o light_n of_o the_o bononian_n stone_n and_o the_o phosphoros_n baldwini_n which_o be_v indeed_o true_o admirable_a and_o very_o much_o differ_v from_o the_o usual_a process_n of_o nature_n for_o the_o exhibit_v of_o light_n before_o i_o take_v leave_n of_o my_o astronomical_a reader_n i_o shall_v here_o acquaint_v they_o with_o some_o collection_n i_o have_v make_v of_o other_o astronomical_a matter_n and_o discovery_n which_o i_o hope_v will_v not_o be_v less_o please_v to_o they_o than_o they_o be_v at_o first_o to_o i_o the_o discovery_n be_v new_a and_o not_o less_o significant_a the_o first_o be_v a_o letter_n from_o johannes_n carolus_n gallet_n l._n l._n d._n and_o provost_n of_o the_o church_n of_o st._n symphorean_n at_o avignon_n direct_v thus_o clarissimo_fw-it eruditissimoque_fw-la viro_fw-la d._n johanni_n dominico_n cassino_n matheseos_fw-la professori_fw-la celeberrimo_fw-la astronomo_fw-la praestantissimo_fw-la &_o academiae_fw-la regiae_n scientiarum_fw-la alumno_fw-la meritissime_fw-la contain_v a_o account_n of_o his_o observation_n of_o mercury_n pass_v under_o the_o sun_n mr._n gallet_n then_o acquaint_v mr._n cassini_n with_o his_o observation_n of_o ☿_o sub_fw-la ☉_o and_o the_o whole_a method_n and_o process_n of_o his_o observation_n first_o he_o fit_v two_o excellent_a telescope_n the_o glass_n of_o which_o be_v give_v he_o by_o mr._n jac._n borrellius_n one_o of_o the_o academy_n royal_a of_o paris_n the_o one_o of_o twenty_o three_o foot_n he_o fit_v with_o a_o glass_n cover_v with_o smoke_n place_v in_o the_o outward_a focus_n of_o the_o eye-glass_n the_o other_o of_o three_o foot_n he_o fix_v to_o the_o arm_n of_o his_o quadrant_n of_o the_o same_o radius_fw-la this_o be_v so_o exquisite_a that_o compare_v with_o one_o of_o divini_fw-la which_o be_v choose_v by_o the_o care_n of_o honorato_fw-mi fabri_fw-la and_o procure_v by_o mounseur_fw-fr de_fw-fr beanchamp_n it_o be_v find_v to_o represent_v the_o object_n clear_a by_o this_o the_o figure_n of_o the_o sun_n be_v cast_v on_o a_o opposite_a table_n on_o which_o he_o have_v draw_v a_o circle_n of_o the_o bigness_n proper_a to_o the_o distance_n and_o magnify_v of_o the_o glass_n to_o contain_v the_o whole_a face_n of_o the_o sun_n and_o by_o parallel_n circle_n have_v subdivide_v the_o same_o into_o digit_n and_o sexagesimal_n he_o have_v also_o place_v three_o thread_n in_o the_o interior_a focus_n of_o the_o glass_n that_o the_o middlemost_a go_v through_o the_o centre_n and_o the_o two_o outward_a touch_v the_o limb_n of_o the_o sun_n by_o their_o shadow_n on_o the_o table_n he_o have_v also_o a_o pendulum_n clock_n that_o vibrate_v thrice_o in_o a_o second_o thus_o accoutre_v he_o watch_v the_o five_o and_o six_o day_n from_o sun_n rise_v to_o sun_n set_v and_o the_o seven_o after_o the_o cloudy_a sky_n have_v seem_v to_o delude_v his_o curiosity_n till_o eleven_o a_o clock_n almost_o it_o than_o begin_v to_o open_v and_o discover_v to_o he_o mercury_n get_v within_o the_o eastern_a limb_n of_o the_o sun_n about_o 1_o 16_o of_o its_o semidiameter_n at_o length_n the_o cloud_n be_v disperse_v the_o sun_n be_v 27°_n 45._o high_a or_o at_o 10_o h._n 54′_n ☿_o itself_o mark_v out_o its_o own_o place_n in_o the_o disk_n of_o the_o ☉_o by_o its_o own_o shadow_n cast_v on_o the_o table_n by_o the_o short_a tube_n then_o he_o dispose_v the_o shadow_n of_o the_o aforesaid_a thread_n so_o parallel_v to_o the_o equator_fw-la that_o this_o figure_n of_o the_o sun_n shall_v move_v between_o the_o outward_a one_o and_o that_o the_o middle_n shall_v mark_v out_o the_o parallel_n describe_v by_o the_o centre_n of_o the_o sun_n in_o motion_n at_o the_o same_o time_n he_o take_v the_o declination_n of_o ☿_o from_o this_o middle_a parallel_n and_o the_o right_a ascension_n by_o the_o number_n of_o vibration_n of_o the_o pendulum_n from_o the_o western_a limb_n of_o the_o sun_n take_v by_o the_o shadow_n of_o a_o perpendicular_a cross-line_n to_o the_o other_o 3._o by_o the_o same_o mean_n also_o he_o measure_v the_o diameter_n of_o the_o sun_n and_o of_o mercury_n then_o to_o the_o end_n he_o may_v give_v less_o cause_n of_o doubt_n according_a to_o his_o usual_a custom_n he_o procure_v several_a friend_n who_o be_v present_a and_o witness_n of_o all_o the_o observation_n after_o the_o four_o mention_v in_o the_o table_n during_o the_o observation_n he_o take_v notice_n of_o these_o remarkable_a accident_n first_o that_o mercury_n through_o the_o long_a tube_n be_v very_o black_a and_o of_o a_o elliptical_a figure_n who_o long_a diameter_n be_v parallel_v to_o the_o equator_fw-la but_o in_o the_o species_n through_o the_o lesser_a telecope_n it_o appear_v round_o and_o of_o a_o dusky_a red_n like_o a_o spot_n observe_v by_o he_o in_o the_o sun_n from_o the_o nine_o to_o the_o fifteen_o of_o april_n second_o that_o the_o diameter_n of_o mercury_n go_v out_o of_o the_o disc_n of_o the_o sun_n when_o it_o touch_v the_o periphery_n seem_v to_o be_v of_o four_o time_n the_o diameter_n it_o appear_v of_o through_o the_o whole_a phase_n so_o that_o mr._n beauchamp_n who_o watch_v the_o exit_z with_o the_o long_a tube_n whilst_o he_o himself_o mind_v the_o quadrant_n in_o order_n to_o take_v the_o altitude_n of_o the_o sun_n at_o the_o time_n of_o the_o exit_z cry_v out_o o_o how_o large_a do_v i_o see_v the_o diameter_n of_o mercury_n now_o it_o do_v not_o only_o leave_v the_o sun_n but_o be_v confuse_v with_o it_o or_o as_o it_o be_v melt_v into_o it_o and_o present_o it_o vanish_v the_o sun_n be_v then_o 13._o 23′_n high_a he_o further_o add_v that_o before_o he_o leave_v to_o speak_v of_o the_o sun_n he_o will_v here_o insert_v a_o observation_n that_o he_o have_v make_v of_o four_o spot_n he_o have_v see_v in_o the_o sun_n in_o the_o first_o of_o october_n last_o st._n no._n with_o this_o his_o long_a telescope_n one_o only_a of_o which_o be_v visible_a by_o the_o species_n cast_v with_o the_o lesser_a glass_n octob._n die_v hora_fw-la declinat_fw-la maculae_fw-la principalis_fw-la à _fw-la paral_n centri_fw-la ☉_o differentia_fw-la temp_n inter_fw-la limbum_fw-la ☉_o occident_n &_o maculam_fw-la tempus_fw-la transitus_fw-la disci_fw-la solaris_fw-la 1_o 10_o 0_o 4_o 44_o austr_n 1_o 4_o 20_o 2_o 10_o 0_o 2_o 10_o 0_o 2_o 43_o aust_z  _fw-fr 49_o 0_o 2_o 10_o 20_o 3_o 10_o 30_o 1_o 21_o aust_z  _fw-fr 35_o 40_o 2_o 10_o 20_o 4_o 10_o 35_o 0_o 40_o aust_z  _fw-fr 25_o 40_o 2_o 10_o 30_o 6_o 10_o 0_o 3_o 0_o boreal_a  _fw-fr 3_o 20_o 2_o 10_o 4_o thus_o submit_v his_o method_n to_o the_o judgement_n of_o the_o learned_a cassini_n and_o earnest_o desire_v his_o thought_n thereon_o he_o end_v his_o letter_n and_o date_n it_o from_o avignon_n nou._n 21._o 1677._o to_o this_o letter_n