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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
the_o motion_n of_o the_o ascend_a stream_n or_o beard_n be_v but_o slow_a there_o need_v no_o very_a quick_a supply_n of_o other_o part_n we_o see_v also_o into_o what_o a_o vast_a quantity_n of_o smoke_n a_o small_a parcel_n of_o a_o combustible_a body_n may_v be_v turn_v from_o all_o which_o particular_n it_o be_v not_o unlikely_a but_o that_o the_o comet_n may_v be_v a_o body_n move_v with_o a_o regular_a circular_a or_o elliptical_a motion_n as_o the_o planet_n be_v that_o it_o may_v be_v a_o body_n of_o such_o a_o constitution_n as_o that_o the_o fluid_a aether_n through_o which_o it_o pass_v may_v dissolve_v it_o much_o after_o the_o manner_n as_o a_o meâ—struum_fw-la such_o as_o aquafortis_n spirit_n of_o niter_n etc._n etc._n do_v a_o dissoluble_a body_n that_o by_o this_o mean_n there_o may_v be_v a_o slow_a but_o continual_a eruption_n of_o somewhat_o opacous_a part_n which_o may_v by_o their_o dissolution_n afford_v a_o sufficient_a quantity_n of_o light_a to_o make_v as_o great_a a_o appearance_n as_o any_o of_o the_o comet_n that_o this_o stream_n or_o beard_n may_v by_o the_o resistance_n of_o the_o aether_n be_v a_o little_a deflected_a back_n ward_n in_o the_o same_o manner_n as_o a_o ascend_a stream_n of_o smoke_n will_v be_v by_o the_o resistance_n of_o the_o air_n if_o the_o burn_a body_n be_v move_v this_o or_o that_o way_n through_o it_o that_o the_o body_n of_o the_o comet_n may_v be_v both_o as_o ancient_a and_o as_o lasting_a as_o the_o world_n and_o that_o this_o which_o have_v late_o appear_v may_v have_v appear_v heretofore_o and_o may_v likewise_o hereafter_o appear_v again_o that_o it_o be_v probable_a the_o near_a distance_n of_o it_o be_v much_o great_a than_o that_o of_o the_o moon_n that_o the_o length_n of_o its_o beard_n be_v long_o than_o its_o distance_n from_o the_o earth_n and_o consequent_o several_a time_n long_o than_o the_o distance_n between_o the_o earth_n and_o the_o moon_n that_o its_o visible_a way_n among_o the_o star_n be_v very_o differ_v from_o a_o great_a circle_n especial_o towards_o the_o latter_a end_n when_o it_o become_v retrograde_a that_o its_o way_n through_o the_o aether_n can_v not_o be_v suppose_v equal_a in_o a_o straight_a line_n though_o it_o may_v be_v suppose_v equal_a in_o a_o curve_v or_o circle_n that_o the_o exact_a way_n of_o it_o can_v not_o be_v certain_o determine_v by_o the_o best_a observation_n i_o have_v yet_o meet_v with_o and_o that_o therefore_o the_o best_a help_n we_o have_v to_o guess_v of_o its_o way_n and_o distance_n be_v by_o its_o manner_n of_o move_v as_o to_z appearance_n among_o the_o fix_a star_n which_o i_o have_v already_o show_v to_o be_v explicable_a by_o various_a hypothesis_n for_o both_o the_o earth_n and_o comet_n may_v be_v suppose_v to_o be_v move_v either_o both_o one_o way_n or_o contrary_a way_n or_o cross_a way_n the_o earth_n may_v be_v suppose_v to_o stand_v still_o and_o the_o comet_n only_o to_o be_v move_v and_o the_o like_a these_o requisite_n therefore_o be_v hitherto_o want_v in_o the_o observation_n i_o have_v meet_v with_o of_o this_o comet_n all_o that_o can_v be_v say_v of_o it_o will_v at_o best_a be_v but_o conjectural_a and_o hypothetical_a since_o nothing_o can_v be_v reasonable_o build_v upon_o those_o observation_n where_o the_o truth_n of_o they_o be_v dubious_a want_v therefore_o sound_a material_n to_o work_v upon_o in_o this_o comet_n i_o have_v recourse_n to_o the_o observation_n of_o the_o noble_a dane_n tycho_n brahe_n be_v sufficient_o satisfy_v both_o of_o the_o ability_n industry_n and_o veracity_n of_o that_o excellent_a author_n who_o leave_v nothing_o unattempted_a for_o the_o perfect_a of_o such_o observation_n as_o seem_v to_o he_o requisite_a for_o the_o complete_n a_o history_n of_o that_o comet_n which_o appear_v in_o 1577._o and_o from_o those_o observation_n of_o his_o i_o endeavour_v to_o trace_v the_o way_n of_o it_o according_a to_o several_a hypothesis_n and_o find_v that_o suppose_v the_o earth_n not_o to_o be_v move_v with_o a_o annual_a motion_n but_o only_o a_o diurnal_a about_o its_o own_o axis_n the_o way_n of_o comet_n will_v fall_v in_o a_o line_n very_o near_o approach_v the_o nature_n of_o a_o circle_n though_o neither_o into_o a_o exact_a circle_n nor_o a_o exact_a ellipse_n and_o therefore_o seem_v irregular_a and_o not_o at_o all_o probable_a again_o suppose_v it_o move_v about_o the_o sun_n as_o tycho_n have_v do_v we_o find_v from_o his_o calculation_n of_o it_o he_o be_v fain_o to_o allow_v it_o a_o quick_a and_o slow_a motion_n in_o its_o orbit_n to_o solve_v the_o phaenomena_n which_o seem_v to_o i_o but_o a_o shift_n that_o will_v serve_v to_o help_v out_o any_o lame_a hypothesis_n whatsoever_o and_o that_o grant_v and_o the_o parallax_n of_o the_o comet_n unknown_a i_o will_v undertake_v very_o easy_o to_o make_v out_o almost_o any_o hypothesis_n which_o be_v the_o fault_n also_o of_o mr._n horox_n his_o hypothesis_n wherein_o he_o suppose_v the_o earth_n to_o be_v move_v about_o the_o sun_n and_o the_o comet_n like_o a_o rocket_n to_o be_v shoot_v out_o of_o the_o sun_n and_o by_o degree_n to_o return_v to_o it_o again_o in_o which_o hypothesis_n indeed_o there_o seem_v to_o be_v much_o more_o reason_n for_o aninequality_n of_o motion_n though_o not_o in_o the_o manner_n as_o he_o have_v place_v it_o it_o be_v very_o rational_a that_o the_o motion_n of_o it_o at_o first_o if_o cast_v out_o of_o the_o sun_n shall_v be_v very_o swift_a but_o than_o it_o ought_v likewise_o to_o have_v accelerate_a its_o motion_n in_o the_o same_o manner_n in_o its_o return_n back_o to_o it_o again_o which_o it_o do_v not_o in_o his_o hypothesis_n for_o a_o stone_n or_o any_o other_o heavy_a body_n be_v shoot_v up_o into_o the_o air_n do_v make_v its_o return_n back_o again_o to_o the_o earth_n almost_o by_o the_o same_o degree_n of_o velocity_n by_o which_o it_o ascend_v from_o it_o almost_o i_o say_v because_o the_o resistance_n of_o the_o air_n do_v so_o far_a impede_fw-la the_o motion_n of_o the_o body_n through_o it_o that_o it_o never_o suffer_v it_o to_o acquire_v the_o same_o degree_n of_o velocity_n with_o which_o it_o be_v first_o shoot_v upward_o this_o be_v sufficient_o evident_a from_o a_o pendulum_n which_o if_o it_o be_v throw_v upward_o and_o be_v suffer_v to_o return_v back_o it_o will_v never_o rise_v again_o on_o the_o opposite_a side_n to_o a_o equal_a height_n with_o that_o it_o descend_v from_o on_o that_o side_n towards_o which_o it_o be_v throw_v but_o beside_o in_o his_o hypothesis_n he_o seem_v to_o take_v no_o notice_n at_o all_o of_o the_o latitude_n of_o the_o comet_n which_o seem_v to_o carry_v it_o much_o far_o off_o from_o the_o sun_n when_o he_o suppose_v it_o to_o be_v return_v near_o and_o indeed_o upon_o the_o whole_a his_o hypothesis_n seem_v rather_o a_o product_n of_o chance_n than_o of_o any_o contrivance_n for_o he_o in_o endeavour_v to_o set_v off_o the_o longitude_n of_o the_o comet_n according_a to_o tycho_n table_n and_o to_o trace_v its_o way_n by_o suppose_v the_o earth_n annual_a motion_n make_v use_n always_o of_o the_o same_o radius_fw-la to_o set_v off_o the_o aspect_n or_o apparent_a angle_n of_o it_o with_o the_o sun_n his_o line_n of_o chord_n he_o make_v use_v of_o do_v always_o direct_a the_o point_n of_o his_o compass_n to_o the_o place_n where_o he_o situate_v the_o comet_n as_o may_v be_v easy_o find_v by_o examine_v the_o nine_o figure_n where_o you_o may_v find_v that_o he_o place_v the_o comet_n always_o equal_o distant_a from_o the_o earth_n and_o that_o distance_n be_v always_o equal_a to_o the_o distance_n of_o the_o sun_n which_o have_v so_o many_o inconvenience_n and_o improbability_n that_o i_o shall_v not_o insist_v far_o on_o it_o especial_o since_o i_o do_v not_o find_v that_o he_o bestow_v any_o far_a pain_n in_o explicate_v or_o cultivate_v this_o his_o hypothesis_n than_o only_o the_o bare_a delineation_n of_o this_o nine_o figure_n but_o to_o return_v to_o tycho_n hypothesis_n if_o that_o be_v true_a why_o do_v not_o the_o comet_n again_o appear_v after_o a_o certain_a space_n of_o time_n and_o why_o can_v not_o he_o have_v foretell_v when_o it_o shall_v again_o appear_v as_o well_o as_o he_o can_v predict_v the_o appearance_n of_o venus_n about_o who_o orb_n he_o suppose_v it_o to_o circulate_v i_o shall_v pass_v by_o several_a other_o very_a material_a objection_n that_o may_v be_v make_v against_o that_o his_o supposition_n because_o many_o of_o they_o may_v be_v make_v also_o against_o his_o hypothefis_n of_o the_o heaven_n in_o general_a which_o i_o shall_v the_o rather_o omit_v because_o i_o do_v not_o find_v he_o have_v many_o follower_n in_o that_o supposition_n the_o generality_n of_o
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
of_o art_n do_v often_o prove_v without_o the_o conjunction_n of_o the_o study_n of_o nature_n and_o upon_o what_o rational_a ground_n it_o be_v that_o sir_n john_n cutler_n the_o patron_n and_o founder_n of_o this_o lecture_n proceed_v in_o join_v the_o contemplation_n of_o they_o both_o together_o the_o next_o thing_n be_v the_o instrument_n for_o the_o make_n of_o this_o observation_n such_o a_o one_o as_o shall_v not_o be_v liable_a to_o any_o of_o the_o former_a exception_n nor_o any_o other_o new_a one_o that_o be_v considerable_a to_o this_o purpose_n i_o pitch_v upon_o a_o telescope_n the_o large_a i_o can_v get_v and_o make_v use_n of_o which_o i_o design_v so_o to_o fix_v upright_o as_o that_o look_v direct_o upward_o i_o can_v be_v able_a certain_o to_o observe_v the_o transit_n of_o any_o star_n over_o or_o near_o the_o zenith_n and_o furnish_v it_o with_o perpendicular_o and_o a_o convenient_a divide_v instrument_n i_o shall_v be_v able_a not_o only_o to_o know_v exact_o when_o the_o star_n come_v to_o cross_v the_o meridian_n but_o also_o how_o far_o it_o cross_v it_o from_o the_o centre_n or_o zenith_n point_n of_o gresham_n college_n either_o towards_o the_o north_n or_o towards_o the_o south_n all_o which_o particular_n how_o i_o perform_v i_o shall_v now_o in_o order_n describe_v and_o this_o somewhat_o the_o more_o distinct_o that_o such_o as_o have_v a_o desire_n to_o do_v the_o like_a may_v be_v the_o more_o ready_a and_o better_o enable_v to_o proceed_v with_o the_o same_o first_o then_o find_v a_o tube_n will_v be_v very_o troublesome_a to_o the_o room_n through_o which_o it_o pass_v especial_o if_o it_o be_v place_v pretty_a far_o in_o the_o room_n and_o that_o one_o want_v so_o free_a a_o access_n as_o be_v necessary_a if_o it_o be_v plant_v nigh_o the_o wall_n and_o that_o there_o be_v no_o absolute_a necessity_n of_o such_o a_o intermediate_v tube_n suppose_v there_o be_v a_o cell_n to_o direct_v the_o eye_n fix_v to_o the_o eye_n glass_n and_o that_o there_o be_v some_o short_a cell_n to_o carry_v the_o object_n glass_n in_o at_o the_o top_n so_o as_o to_o keep_v it_o steady_a when_o raise_v upward_o or_o let_v downward_o the_o light_n in_o the_o intermediate_v room_n not_o at_o all_o hinder_v but_o rather_o prove_v of_o good_a use_n to_o this_o purpose_n for_o see_v the_o mensurator_n i_o open_v a_o passage_n of_o about_o a_o foot_n square_n through_o the_o roof_n of_o my_o lodging_n see_v the_o four_o figure_n and_o there_o in_o fix_v a_o tube_n a_o a_o perpendicular_a and_o upright_a of_o about_o ten_o or_o twelve_o foot_n in_o length_n and_o a_o foot_n square_a so_o as_o that_o the_o low_a end_n thereof_o come_v through_o the_o ceiling_n and_o be_v open_a into_o the_o chamber_n underneath_o this_o tube_n i_o cover_v with_o a_o lid_n at_o the_o top_n q_o house_v so_o as_o to_o throw_v off_o the_o rain_n and_o so_o contrive_v as_o i_o can_v easy_o open_v or_o shut_v it_o by_o a_o small_a string_n n_z o_o p_o which_o come_v down_o through_o the_o tube_n to_o the_o place_n where_o i_o observe_v within_o this_o perpendicular_a tube_n a_o a_o i_o make_v another_o small_a square_a tube_n b_o b_o fit_v so_o as_o to_o slide_v upward_o and_o downward_o as_o there_o be_v occasion_n and_o by_o the_o help_n of_o a_o screw_n to_o be_v fix_v in_o any_o place_n that_o be_v necessary_a within_o this_o tube_n in_o a_o convenient_a cell_n c_o be_v fix_v the_o object_n glass_n of_o the_o telescope_n that_o which_o i_o make_v use_v of_o be_v thirty_o six_o foot_n in_o length_n have_v none_o long_o by_o i_o but_o one_o of_o sixty_o foot_n and_o so_o too_o long_o to_o be_v make_v use_n of_o in_o my_o room_n the_o manner_n of_o fix_v which_o be_v this_o the_o glass_n itself_o be_v fix_v into_o a_o cell_n or_o frame_n of_o brass_n so_o exact_o fit_v to_o it_o that_o it_o go_v in_o stiff_a and_o to_o fill_v up_o all_o the_o interstitia_n there_o be_v melt_v in_o hard_a cement_n this_o cell_n have_v a_o small_a bar_n that_o cross_v under_o the_o centre_n of_o the_o glass_n or_o the_o aperture_n thereof_o in_o which_o bar_n be_v drill_v two_o small_a hole_n at_o equal_a distance_n from_o the_o middle_n of_o the_o glass_n through_o which_o the_o upper_a end_n of_o the_o two_o perpendicular_o do_v d_o be_v fasten_v and_o in_o the_o fix_v this_o brass_n cell_n or_o frame_n into_o the_o square_a tube_n that_o be_v to_o slide_v up_o and_o down_o care_n be_v take_v to_o make_v the_o bar_n lie_v as_o exact_o north_n and_o south_n as_o can_v be_v though_o that_o be_v not_o altogether_o so_o absolute_o necessary_a to_o this_o observation_n these_o perpendicular_o d_o d_o fasten_v to_o the_o bar_n hang_v 36_o foot_n and_o better_o in_o length_n and_o have_v at_o the_o low_a end_n of_o they_o two_o ball_n of_o lead_v e_o e_o as_o big_a as_o the_o silk_n can_v bear_v by_o which_o the_o low_a part_n of_o this_o instrument_n be_v adjust_v as_o i_o shall_v by_o and_o by_o explain_v but_o first_o i_o must_v acquaint_v the_o reader_n that_o i_o open_v a_o so_o perpendicular_o under_o this_o tube_n a_o hole_n r_o r_o a_o foot_n square_n in_o the_o floor_n below_o which_o with_o shutter_n can_v be_v close_v or_o open_v upon_o occasion_n by_o this_o mean_v i_o have_v a_o perpendicular_a well-hole_n of_o about_o forty_o foot_n long_o from_o the_o top_n of_o a_o to_o the_o low_a floor_n s_o s._n upon_o the_o second_o floor_n s_o s_o i_o fix_v the_o frame_n that_o carry_v the_o eye-glass_n and_o the_o other_o apparatus_fw-la fit_a to_o make_v this_o observation_n i_o make_v then_o a_o stool_n or_o table_n such_o as_o be_v describe_v in_o the_o same_o four_o figure_n i_o h_o h_o i_o have_v a_o hole_n through_o the_o top_n or_o cover_v thereof_o h_o h_z of_o about_o nine_o inch_n over_o the_o middle_n of_o which_o i_o place_v as_o near_o as_o i_o can_v perpendicular_o under_o the_o middle_n of_o the_o object_n glass_n in_o the_o cell_n above_o and_o then_o nail_v the_o frame_n fast_o to_o the_o floor_n by_o the_o bracket_n i_o i_o that_o it_o can_v not_o stir_v underneath_o the_o cover_n of_o this_o table_n i_o make_v a_o slider_n g_o g_o in_o which_o be_v fix_v in_o a_o cell_n a_o eye_n glass_n f_o so_o as_o that_o i_o can_v through_o the_o eye_n glass_n move_v to_o and_o fro_o see_v any_o part_n of_o the_o hole_n in_o the_o table_n that_o i_o desire_v without_o stir_v the_o stool_n from_o its_o fixtness_n this_o be_v necessary_a because_o many_o star_n which_o be_v forerunner_n of_o this_o star_n in_o draco_n and_o serve_v as_o warning_n to_o prepare_v for_o the_o approach_a star_n go_v pretty_a wide_a from_o the_o parallel_n that_o pass_v over_o our_o zenith_n by_o this_o mean_n also_o i_o take_v notice_n of_o the_o star_n itself_o at_o above_o half_a a_o degree_n distance_n from_o the_o zenith_n to_o the_o east_n and_o so_o follow_v the_o motion_n of_o it_o with_o my_o eye_n glass_n and_o also_o with_o my_o measure_n clew_n and_o at_o the_o same_o time_n tell_v the_o 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at_o the_o place_n k_o and_o l_o where_o the_o perpendicular_a point_n be_v make_v by_o the_o two_o long_a plumb_n line_n this_o instrument_n be_v produce_v on_o the_o side_n a_o to_z n_z n_z e_z be_v make_v fifteen_o time_n the_o length_n of_o e_o m_o so_o that_o e_z m_z be_v one_o inch_n and_o two_o three_o e_z n_z be_v twenty_o five_o inch_n at_o n_o the_o line_n n_z e_z be_v cross_v by_o a_o rule_n of_o about_o 3½_n foot_n long_o o_o p_o which_o from_o the_o point_n n_z be_v divide_v each_o way_n into_o inch_n and_o part_n each_o inch_n be_v subdivide_v into_o thirty_o part_n which_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 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θ_o and_o from_o γ_n θ_o to_z o_fw-mi the_o focus_n and_o so_o through_o the_o lens_n z_o to_o the_o eye_n x._o this_o i_o take_v to_o be_v the_o best_a by_o reflection_n but_o it_o may_v be_v twenty_o other_o way_n contrive_v which_o i_o shall_v not_o now_o spend_v more_o time_n in_o describe_v it_o be_v so_o easy_a a_o matter_n from_o the_o consideration_n of_o these_o i_o have_v mention_v to_o make_v a_o hundred_o other_o variation_n of_o the_o principle_n to_o this_o helioscope_n may_v be_v fit_v instrument_n for_o measure_v the_o maculae_fw-la faculae_fw-la and_o nebulae_fw-la visible_a in_o the_o body_n of_o the_o sun_n as_o also_o the_o space_n pass_v by_o they_o in_o a_o day_n two_o three_o ten_o etc._n etc._n together_o with_o the_o variation_n of_o their_o figure_n and_o magnitude_n but_o the_o diameter_n of_o the_o body_n of_o the_o sun_n will_v be_v better_o take_v by_o the_o follow_a instrument_n and_o by_o reason_n that_o it_o will_v be_v often_o necessary_a to_o draw_v 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be_v glad_a to_o understand_v i_o will_v willing_o also_o be_v inform_v whether_o my_o letter_n of_o the_o second_o of_o december_n mention_v above_o be_v come_v to_o your_o hand_n and_o how_o those_o observation_n do_v please_v the_o gentleman_n of_o your_o society_n and_o also_o to_o understand_v the_o receipt_n of_o this_o the_o manner_n how_o the_o say_a mr._n leeuwenhoeck_n do_v make_v these_o discovery_n he_o do_v as_o yet_o not_o think_v fit_a to_o impart_v for_o reason_n best_o know_v to_o himself_o and_o therefore_o i_o be_o not_o able_a to_o acquaint_v you_o with_o what_o it_o be_v but_o as_o to_o the_o way_n i_o have_v make_v use_n of_o i_o here_o free_o discover_v that_o all_o such_o person_n as_o have_v a_o desire_n to_o make_v any_o inquiry_n into_o nature_n this_o way_n may_v be_v the_o better_o enable_v so_o to_o do_v first_o for_o the_o manner_n of_o hold_v the_o liquor_n so_o as_o to_o examine_v it_o by_o the_o microscope_n i_o find_v that_o the_o way_n prescribe_v by_o mr._n leeuwenhoeck_n be_v to_o include_v the_o same_o in_o a_o very_a fine_a pipe_n of_o glass_n and_o then_o to_o view_v it_o by_o the_o help_n of_o the_o microscope_n for_o by_o place_v that_o at_o a_o due_a distance_n whatever_o be_v contain_v in_o the_o say_a liquor_n will_v most_o easy_o be_v discover_v the_o liquor_n will_v most_o easy_o insinuate_v itself_o into_o the_o cavity_n of_o the_o say_a pipe_n if_o the_o end_n thereof_o only_o be_v just_o put_v within_o the_o liquor_n this_o as_o it_o be_v exceed_o convenient_a for_o many_o trial_n so_o be_v it_o not_o very_o difficult_a to_o prepare_v but_o because_o every_o one_o be_v not_o instruct_v how_o to_o proceed_v in_o this_o matter_n and_o it_o may_v cause_v he_o more_o trouble_n than_o need_v to_o procure_v they_o i_o will_v here_o describe_v the_o way_n and_o so_o much_o the_o rather_o because_o the_o same_o apparatus_n will_v serve_v for_o the_o prepare_n of_o microscope_n as_o i_o shall_v afterward_o show_v provide_v 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of_o tin_n make_v large_a enough_o to_o contain_v it_o the_o use_n of_o which_o be_v to_o keep_v the_o former_a lamp_n box_n from_o fowl_v the_o board_n or_o table_n on_o which_o it_o stand_v this_o stand_v upon_o a_o board_n about_o one_o foot_n square_a into_o which_o be_v fasten_v a_o standard_n or_o stick_v upright_o cleave_v so_o as_o to_o pinch_v and_o hold_v the_o soder_v pipe_n between_o its_o cleft_n which_o may_v be_v fasten_v with_o a_o screw_n or_o a_o slip_a ring_n through_o which_o pipe_n blow_v with_o your_o breath_n the_o flame_n will_v be_v dart_v forward_o with_o great_a swiftness_n and_o brightness_n if_o then_o into_o this_o flame_n you_o hold_v a_o small_a piece_n of_o a_o glass_n pipe_n make_v of_o white_a glass_n for_o green_a glass_n or_o coarse_a glass_n will_v not_o be_v melt_v easy_o in_o this_o flame_n and_o keep_v it_o turn_v round_o between_o your_o finger_n and_o thumb_n you_o shall_v find_v that_o the_o flame_n will_v in_o a_o very_a short_a time_n melt_v the_o middle_a part_n of_o the_o say_a pipe_n so_o that_o if_o you_o remove_v it_o out_o of_o the_o flame_n and_o draw_v your_o hand_n one_o from_o another_o you_o may_v easy_o draw_v the_o former_a pipe_n into_o a_o very_a small_a size_n which_o will_v yet_o remain_v hollow_a though_o draw_v never_o so_o small_a the_o best_a oil_n for_o this_o purpose_n be_v good_a clean_a salad_n oil_n or_o oil_n olive_n but_o high_o rectify_v spirit_n of_o wine_n be_v yet_o better_a and_o cleanly_a but_o much_o more_o chargeable_a and_o for_o most_o use_v the_o oil_n olive_n will_v serve_v this_o i_o have_v set_v down_o because_o many_o who_o be_v far_o off_o in_o the_o country_n can_v have_v the_o convenience_n of_o go_v to_o a_o lamp-blower_n as_o oft_o as_o they_o have_v occasion_n for_o such_o pipe_n which_o if_o they_o provide_v themselves_o with_o small_a white_a glass_n pipe_n from_o the_o potter_n they_o may_v accommodate_v themselves_o withal_o though_o they_o have_v nothing_o but_o a_o large_a candle_n and_o a_o tobacco-pipe_n instead_o of_o the_o aforesaid_a apparatus_n though_o not_o altogether_o so_o convenient_o but_o i_o will_v rather_o advise_v they_o to_o have_v a_o lamp_n make_v which_o most_o tin-man_n know_v how_o to_o fit_v and_o prepare_v and_o so_o it_o will_v not_o need_n much_o more_o description_n but_o this_o way_n of_o mr._n leeuwenhoeck_n of_o hold_v the_o liquor_n in_o small_a glass_n pipe_n though_o it_o be_v exceed_o ingenious_a and_o very_o convenient_a for_o many_o examination_n yet_o for_o divers_a other_o it_o be_v not_o so_o well_o accommodate_v as_o this_o which_o i_o contrive_v myself_o for_o my_o own_o trial_n at_o least_o for_o those_o microscope_n i_o make_v use_n of_o what_o it_o may_v be_v for_o those_o which_o mr._n leeuwenhoeck_n use_v i_o know_v not_o i_o take_v then_o instead_o of_o a_o glass_n pipe_v a_o very_a thin_a plate_n of_o muscovy_n glass_n this_o serve_v instead_o of_o the_o movable_a plate_n which_o be_v usual_o put_v upon_o the_o pedestal_n of_o microscope_n but_o because_o the_o common_a pedestal_n hitherto_o make_v use_n of_o in_o microscope_n be_v general_o not_o so_o convenient_a for_o trial_n of_o this_o nature_n i_o lay_v those_o by_o and_o instead_o thereof_o i_o fix_v into_o the_o bottom_n of_o the_o tube_n of_o the_o microscope_n a_o cylindrical_a rod_n of_o brass_n or_o iron_n upon_o this_o a_o little_a socket_n be_v make_v to_o slide_v to_o and_o fro_o and_o by_o mean_n of_o a_o pretty_a stiff_a spring_n will_v stand_v fast_o in_o any_o place_n this_o have_v fasten_v to_o it_o a_o joint_v arm_n of_o three_o or_o four_o joint_n and_o at_o the_o end_n a_o plate_n about_o the_o bigness_n of_o a_o half_a crown_n with_o a_o hole_n in_o the_o middle_n of_o it_o about_o three_o quarter_n of_o a_o inch_n wide_a upon_o this_o plate_n i_o lay_v the_o muscovy_n glass_n and_o upon_o that_o i_o spread_v a_o very_a little_a of_o the_o liquor_n to_o be_v examine_v then_o look_v against_o the_o 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and_o the_o liquor_n in_o which_o they_o swim_v appear_v dark_a but_o when_o the_o water_n begin_v to_o dry_v off_o the_o bend_n of_o the_o superficies_n of_o the_o liquor_n over_o their_o back_n and_o over_o the_o top_n of_o other_o small_a mote_n which_o be_v in_o the_o water_n make_v a_o confuse_a appearance_n which_o some_o not_o use_v to_o these_o kind_n of_o examination_n take_v to_o be_v quite_o differ_v thing_n from_o what_o they_o be_v real_o and_o the_o appearance_n here_o be_v so_o very_o strange_a that_o to_o one_o not_o well_o accustom_v to_o the_o phaenomena_fw-la of_o fluid_n of_o differ_v figure_n and_o refraction_n the_o examination_n of_o substance_n this_o way_n will_v be_v very_o apt_a to_o mis
rather_o than_o instruct_v he_o especial_o of_o such_o substance_n as_o be_v not_o perfect_o fluid_a and_o will_v not_o ready_o and_o natural_o smooth_v their_o own_o superficies_n such_o as_o tallow_n concrete_v oil_n marrow_n brain_n fat_a inspissated_a juice_n etc._n etc._n for_o if_o those_o substance_n be_v so_o examine_v by_o spread_v they_o upon_o this_o plate_n and_o be_v look_v upon_o against_o the_o candle_n or_o other_o small_a define_v light_n all_o the_o inequality_n leave_v on_o the_o surface_n by_o the_o spread_a do_v by_o the_o refraction_n of_o the_o ray_n of_o light_n render_v such_o odd_a appearance_n that_o they_o will_v easy_o deceive_v the_o examinator_fw-la and_o make_v he_o to_o conceive_v that_o to_o be_v in_o the_o texture_n of_o the_o part_n which_o be_v real_o no_v where_o but_o in_o the_o make_v of_o the_o superficies_n of_o it_o this_o therefore_o as_o another_o great_a inconvenience_n to_o be_v meet_v with_o in_o microscopical_a observation_n i_o 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the_o experimenter_n that_o he_o provide_v himself_o with_o instrument_n by_o which_o to_o stretch_v and_o pull_v in_o piece_n any_o substance_n whilst_o the_o same_o be_v yet_o in_o view_n of_o the_o microscope_n of_o which_o there_o may_v be_v many_o which_o any_o one_o will_v easy_o contrive_v when_o he_o have_v this_o hint_n give_v he_o of_o the_o usefulness_n thereof_o in_o the_o examination_n of_o the_o texture_n of_o several_a substance_n as_o of_o tendon_n nerve_n muscle_n etc._n etc._n those_o i_o have_v make_v use_n of_o be_v make_v to_o open_v like_o a_o pair_n of_o tobacco_n tongue_n by_o two_o angular_a plate_n of_o thin_a brass_n rivet_v together_o which_o by_o pinch_v the_o opposite_a end_n will_v either_o open_a or_o shut_v at_o the_o other_o as_o i_o have_v occasion_n these_o have_v a_o part_n extend_v between_o the_o two_o top_n be_v fix_v at_o a_o due_a distance_n from_o the_o object-glass_n that_o the_o body_n extend_v between_o they_o may_v be_v distinct_o see_v 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by_o the_o ancient_n which_o be_v once_o find_v and_o table_n thereof_o calculate_v i_o shall_v anon_o show_v a_o way_n how_o to_o calculate_v the_o power_n they_o have_v in_o shoot_v or_o cast_v of_o arrow_n bullet_n stone_n granade_n or_o the_o like_a from_o these_o principle_n also_o it_o will_v be_v easy_a to_o calculate_v the_o proportionate_a strength_n of_o the_o spring_n of_o a_o watch_n upon_o the_o fusey_n thereof_o and_o consequent_o of_o adjust_v the_o fusey_n to_o the_o spring_n so_o as_o to_o make_v it_o draw_v or_o move_v the_o watch_n always_o with_o a_o equal_a force_n from_o the_o same_o also_o it_o will_v be_v easy_a to_o give_v the_o reason_n of_o the_o isochrone_n motion_n of_o a_o spring_n or_o extend_a string_n and_o of_o the_o uniform_a sound_n produce_v by_o those_o who_o vibration_n be_v quick_a enough_o to_o produce_v a_o audible_a sound_n as_o likewise_o the_o reason_n of_o the_o sound_n and_o their_o variation_n in_o all_o manner_n of_o sonorous_a or_o spring_a body_n of_o which_o more_o on_o another_o occasion_n from_o this_o appear_v the_o reason_n as_o i_o shall_v show_v by_o and_o by_o why_o a_o spring_n apply_v to_o the_o balance_n of_o a_o watch_n do_v make_v the_o vibration_n thereof_o equal_a whether_o they_o be_v great_a or_o small_a one_o of_o which_o kind_n i_o show_v to_o the_o right_n honourable_a the_o lord_n viscount_n brounker_n the_o honourable_a robert_n boyle_n esq_n and_o sir_n robert_n morey_n in_o the_o year_n 1660._o in_o order_n to_o have_v get_v letter_n patent_n for_o the_o use_n and_o benefit_n thereof_o from_o this_o it_o will_v be_v easy_a to_o make_v a_o philosophical_a scale_n to_o examine_v the_o weight_n of_o any_o body_n without_o put_v in_o weight_n which_o be_v that_o which_o i_o mention_v at_o the_o end_n of_o my_o description_n of_o helioscope_n the_o ground_n of_o which_o be_v veil_v under_o this_o anagram_n c_o e_o d_o i_o i_o n_z n_z o_o o_o p_o s_o s_o s_o t_o t_o u._fw-mi u._fw-mi namely_o ut_fw-la pondus_fw-la sic_fw-la tensio_fw-la the_o fabric_n of_o which_o see_v in_o the_o three_o first_o figure_n this_o scale_n i_o contrive_v in_o order_n to_o examine_v the_o gravitation_n of_o body_n towards_o the_o centre_n of_o the_o earth_n viz._n to_o examine_v whether_o body_n at_o a_o further_a distance_n from_o the_o centre_n of_o the_o earth_n do_v not_o lose_v somewhat_o of_o their_o power_n or_o tendency_n towards_o it_o and_o propound_v it_o as_o one_o of_o the_o experiment_n to_o be_v try_v at_o the_o top_n of_o the_o pike_n of_o teneriff_n and_o attempt_v the_o same_o at_o the_o top_n of_o the_o tower_n of_o st._n paul_n before_o the_o burn_a of_o it_o in_o the_o late_a great_a fire_n as_o also_o at_o the_o top_n and_o bottom_n of_o the_o abbey_n of_o st._n peter_n in_o westminster_n though_o these_o be_v by_o but_o small_a distance_n remove_v from_o the_o surface_n i_o be_v not_o able_a certain_o to_o perceive_v any_o manifest_a difference_n i_o propound_v the_o same_o also_o to_o be_v try_v at_o the_o bottom_n and_o several_a station_n of_o deep_a mine_n and_o d._n power_n do_v make_v some_o trial_n to_o that_o end_n but_o his_o instrument_n not_o be_v good_a nothing_o can_v be_v certain_o conclude_v from_o they_o these_o be_v the_o phenomena_n of_o spring_n and_o springy_a body_n which_o as_o they_o have_v not_o hitherto_o be_v by_o any_o that_o i_o know_v reduce_v to_o rule_n so_o have_v all_o the_o attempt_n for_o the_o explication_n of_o the_o reason_n of_o their_o power_n and_o of_o springiness_n in_o general_a be_v very_o insufficient_a in_o the_o year_n 1660._o i_o print_v a_o little_a tract_n which_o i_o call_v a_o attempt_n for_o the_o explication_n of_o the_o phenomena_n etc._n etc._n of_o the_o rise_n of_o water_n in_o the_o pore_n of_o very_a small_a pipe_n filtre_n etc._n etc._n and_o be_v unwilling_a then_o to_o publish_v this_o theory_n as_o suppose_v it_o may_v be_v prejudicial_a to_o my_o design_n of_o watch_n which_o i_o be_v then_o procure_v a_o patent_n for_o i_o only_o hint_v the_o principle_n which_o i_o suppose_v to_o be_v the_o cause_n of_o these_o phaenomena_n of_o spring_n in_o the_o 31_o page_n thereof_o in_o the_o english_a edition_n and_o in_o the_o 38_o page_n of_o the_o latin_a edition_n translate_v by_o m._n behem_n and_o print_v at_o amsterdam_n 1662._o but_o refer_v the_o further_a explication_n thereof_o till_o some_o other_o opportunity_n the_o principle_n i_o then_o mention_v i_o call_v by_o the_o name_n of_o congruity_n and_o incongruity_n of_o body_n and_o promise_v a_o further_a explanation_n of_o what_o i_o thereby_o mean_v on_o some_o other_o occasion_n i_o shall_v here_o only_o explain_v so_o much_o of_o it_o as_o concern_v the_o explication_n of_o this_o present_a phaenomenon_n by_o congruity_n and_o incongruity_n than_o i_o understand_v nothing_o else_o but_o a_o agreement_n or_o disagreement_n of_o body_n as_o to_o their_o magnitude_n and_o motion_n those_o body_n than_o i_o suppose_v congruous_a who_o particle_n have_v the_o same_o magnitude_n and_o the_o same_o degree_n of_o velocity_n or_o else_o a_o harmonical_a proportion_n of_o magnitude_n and_o harmonical_a degree_n of_o velocity_n and_o those_o i_o suppose_v incongruous_a which_o have_v neither_o the_o same_o magnitude_n nor_o the_o same_o degree_n of_o velocity_n nor_o a_o harmonical_a proportion_n of_o magnitude_n nor_o of_o velocity_n i_o suppose_v then_o the_o sensible_a universe_n to_o consist_v of_o body_n and_o motion_n by_o body_n i_o mean_v somewhat_o receptive_a and_o communicative_a of_o motion_n or_o progression_n nor_o can_v i_o have_v any_o other_o idea_n thereof_o for_o neither_o extension_n nor_o quantity_n hardness_n nor_o softness_n fluidity_n nor_o fixedness_n rarefaction_n nor_o densation_n be_v the_o propriety_n of_o body_n but_o of_o motion_n or_o somewhat_o move_v by_o motion_n i_o understand_v nothing_o but_o a_o power_n or_o tendency_n progressive_a of_o body_n according_a to_o several_a degree_n of_o velocity_n these_o two_o do_v always_o counterbalance_v each_o other_o in_o all_o the_o effect_n appearance_n and_o operation_n of_o nature_n and_o therefore_o it_o be_v not_o impossible_a but_o that_o they_o may_v be_v one_o and_o the_o same_o for_o a_o little_a body_n with_o great_a motion_n be_v equivalent_a to_o a_o great_a body_n with_o little_a motion_n as_o to_o all_o its_o sensible_a effect_n in_o nature_n i_o do_v further_o suppose_v then_o that_o all_o thing_n in_o the_o universe_n that_o become_v the_o object_n of_o our_o sense_n be_v compound_v of_o these_o two_o which_o we_o will_v for_o the_o present_n suppose_v distinct_a essence_n though_o possible_o they_o may_v be_v find_v hereafter_o to_o be_v only_o differ_v conception_n of_o one_o and_o the_o same_o essence_n namely_o body_n and_o motion_n and_o that_o there_o be_v no_o one_o sensible_a particle_n of_o matter_n but_o owe_v the_o great_a part_n of_o its_o sensible_a extension_n to_o motion_n whatever_o part_n thereof_o it_o owe_v to_o body_n according_a to_o the_o common_a notion_n thereof_o which_o be_v that_o body_n be_v somewhat_o that_o do_v perfect_o fill_v a_o determinate_a quantity_n of_o space_n or_o extension_n so_o as_o necessary_o to_o exclude_v all_o other_o body_n from_o be_v comprehend_v within_o the_o same_o dimension_n i_o do_v therefore_o define_v a_o sensible_a body_n to_o be_v a_o determinate_a space_n or_o extension_n defend_v from_o be_v penetrate_v by_o another_o by_o a_o power_n from_o within_o to_o make_v this_o the_o more_o intelligible_a imagine_v a_o very_a thin_a plate_n of_o iron_n or_o the_o like_a a_o foot_n square_a to_o be_v move_v with_o a_o vibrative_a motion_n forward_o and_o backward_o the_o flat_a way_n the_o length_n of_o a_o foot_n with_o so_o swift_a a_o motion_n as_o not_o to_o permit_v any_o other_o body_n to_o enter_v into_o that_o space_n within_o which_o it_o vibrate_v this_o will_v compose_v such_o a_o essence_n as_o i_o call_v in_o my_o sense_n a_o cubick_a foot_n of_o sensible_a body_n which_o differ_v from_o the_o common_a notion_n of_o body_n as_o this_o space_n of_o a_o cubick_a foot_n thus_o defend_v by_o this_o vibrate_n plate_n do_v from_o a_o cubick_a foot_n of_o iron_n or_o the_o like_a throughout_o solid_a the_o particle_n therefore_o that_o compose_v all_o body_n i_o do_v suppose_v to_o owe_v the_o great_a part_n of_o their_o sensible_a or_o potential_a extension_n to_o a_o vibrative_a motion_n this_o vibrative_a motion_n i_o do_v not_o suppose_v inherent_a or_o inseparable_a from_o the_o particle_n of_o body_n but_o communicate_v by_o impulse_n give_v from_o other_o body_n in_o the_o universe_n this_o only_a i_o suppose_v that_o the_o magnitude_n or_o bulk_n of_o the_o body_n do_v make_v it_o receptive_a of_o this_o or-that_a peculiar_a motion_n that_o be_v communicate_v and_o not_o of_o any_o other_o
line_n of_o the_o motion_n of_o the_o body_n so_o shoot_v shall_v be_v move_v in_o a_o parabola_fw-la or_o a_o line_n very_o near_o it_o i_o say_v very_o near_o it_o by_o reason_n that_o the_o impediment_n of_o the_o medium_n do_v hinder_v the_o exactness_n of_o it_o if_o it_o be_v deliver_v with_o treble_a quadruple_a quintuple_a sextuple_a etc._n etc._n the_o first_o velocity_n it_o shall_v touch_v the_o floor_n at_o almost_o treble_a quadruple_a quintuple_a sextuple_a etc._n etc._n the_o first_o distance_n i_o shall_v not_o need_v to_o show_v the_o reason_n why_o it_o be_v move_v in_o a_o parabola_fw-la it_o have_v be_v sufficient_o demonstrate_v long_o since_o by_o many_o other_o if_o the_o body_n be_v deliver_v by_o the_o spring_n at_o the_o floor_n but_o shoot_v by_o some_o angle_n upward_o know_v withwhat_o velocity_n the_o same_o be_v move_v when_o deliver_v and_o with_o what_o inclination_n to_o the_o perpendicular_a the_o same_o be_v direct_v and_o the_o true_a velocity_n of_o a_o fall_a body_n you_o may_v easy_o know_v the_o length_n of_o the_o jactus_fw-la or_o shot_n and_o the_o time_n it_o will_v spend_v in_o pass_v that_o length_n this_o be_v find_v by_o compare_v the_o time_n of_o its_o ascent_n with_o the_o time_n of_o the_o descent_n of_o heavy_a body_n the_o ascent_n of_o any_o body_n be_v easy_o know_v by_o compare_v its_o velocity_n with_o the_o angle_n of_o inclination_n let_v a_o b_o then_o in_o the_o five_o figure_n represent_v 16_o foot_n or_o the_o space_n descend_v by_o a_o heavy_a body_n in_o a_o second_o minute_n of_o time_n if_o a_o body_n be_v shoot_v from_o b_o in_o the_o line_n b_o f_o with_o a_o velocity_n as_o much_o swift_a than_o that_o equal_a motion_n of_o 16_o foot_n in_o a_o second_o as_o this_o line_n b_o f_o be_v long_o than_o a_o b_o the_o body_n shall_v fall_v at_o e_o for_o in_o the_o same_o space_n of_o time_n that_o the_o oblique_a equal_a motion_n will_v make_v it_o ascend_v from_o b_o d_o to_o a_o c_o will_n the_o accelerate_a direct_a motion_n downward_o move_v it_o from_o a_o c_o to_o b_o d_o and_o therefore_o at_o the_o end_n of_o the_o space_n of_o one_o second_o when_o the_o motion_n do_v equal_a and_o balance_v each_o other_o the_o body_n must_v be_v in_o the_o same_o horizontal_n line_n in_o which_o it_o be_v at_o first_o but_o remove_v asunder_o by_o the_o space_n b_o e_o and_o for_o the_o point_v it_o pass_v through_o in_o all_o the_o intermediate_v space_n this_o method_n will_v determine_v it_o let_v the_o parallelogram_n a_o b_o p_o q_o than_o represent_v the_o whole_a velocity_n of_o the_o ascent_n of_o a_o body_n by_o a_o equal_a motion_n of_o 16_o foot_n in_o a_o second_o and_o the_o triangle_n p_o q_o r_o represent_v the_o whole_a velocity_n of_o the_o accelerate_a descend_v motion_n p_o b_o be_v then_o the_o velocity_n with_o which_o the_o body_n be_v shoot_v and_o p_o be_v the_o point_n of_o rest_n where_o the_o power_n of_o gravity_n begin_v to_o work_v on_o the_o body_n and_o make_v it_o descend_v now_o draw_v line_n parallel_v to_o a_o q_o r_o as_o s_z t_z u._fw-mi s_z t_z gives_z the_o velocity_n of_o the_o point_n to_o ascend_v and_o t_o u._fw-mi the_o velocity_n of_o the_o same_o point_n to_o descend_v again_o p_o b_o s_o t_o signify_v the_o space_n ascend_v and_o p_o t_o u._fw-mi the_o space_n descend_v so_o that_o subtract_v the_o descent_n from_o the_o ascent_n you_o have_v the_o height_n above_o the_o line_n b_o d_o the_o consideration_n of_o this_o and_o the_o equal_a progress_n forward_o will_v give_v the_o intermediate_v velocity_n and_o determine_v the_o point_n of_o the_o parabola_fw-la now_o have_v the_o jactus_fw-la give_v by_o this_o scheme_n or_o scale_n appropriate_v to_o the_o particular_a velocity_n wherewith_o any_o body_n be_v move_v in_o this_o or_o that_o line_n of_o inclination_n it_o will_v be_v easy_a to_o find_v what_o velocity_n in_o any_o inclination_n will_v throw_v it_o to_o any_o length_n for_o in_o any_o inclination_n as_o the_o square_n of_o the_o velocity_n thus_o find_v in_o this_o scale_n for_o any_o inclination_n be_v to_o the_o square_n of_o any_o other_o velocity_n so_o be_v the_o distance_n find_v by_o this_o scale_n to_o the_o distance_n answer_v to_o the_o second_o velocity_n i_o have_v not_o now_o time_n to_o enlarge_v upon_o this_o speculation_n which_o will_v afford_v matter_n enough_o to_o fill_v a_o volume_n by_o which_o all_o the_o difficulty_n about_o impress_v and_o receive_v motion_n and_o the_o velocity_n and_o effect_n result_v will_v be_v easy_o resolve_v nor_o have_v i_o now_o time_n to_o mention_v the_o great_a number_n of_o use_n that_o be_v and_o may_v be_v make_v of_o spring_n in_o mechanic_n contrivance_n but_o shall_v only_o add_v that_o of_o all_o springy_a body_n there_o be_v none_o comparable_a to_o the_o air_n for_o the_o vastness_n of_o its_o power_n of_o extension_n and_o contraction_n upon_o this_o principle_n i_o remember_v to_o have_v see_v long_o since_o in_o wadham_n college_n in_o the_o garden_n of_o the_o learned_a dr._n wilkins_n late_a bishop_n of_o chester_n a_o fountain_n so_o contrive_v as_o by_o the_o spring_n of_o the_o include_v air_n to_o throw_v up_o to_o a_o great_a height_n a_o large_a and_o last_a stream_n of_o water_n which_o water_n be_v first_o force_v into_o the_o leaden_a cistern_n thereof_o by_o two_o force_n pump_n which_o do_v alternate_o work_v and_o so_o condense_a the_o air_n include_v into_o a_o small_a room_n the_o contrivance_n of_o which_o engine_n be_v not_o unknown_a to_o the_o ancient_n as_o hero_n in_o his_o spiritalia_fw-la do_v sufficient_o manifest_a nor_o be_v they_o want_v in_o apply_v it_o to_o very_o good_a use_n namely_o for_o engine_n for_o quench_a fire_n as_o vitruvius_n by_o the_o help_n of_o the_o ingenious_a mounseur_fw-fr clande_n perrault_n interpretation_n have_v acquaint_v we_o in_o the_o twelve_o chapter_n of_o his_o ten_o book_n where_o he_o endeavour_v to_o describe_v ctesibius_n his_o engine_n for_o quench_v fire_n not_o long_o since_o a_o german_a here_o in_o england_n have_v add_v a_o further_a improvement_n thereof_o by_o convey_v the_o constant_a stream_n of_o water_n through_o pipe_n make_v of_o well_o tan_a and_o liquor_v leather_n join_v together_o to_o any_o convenient_a length_n by_o the_o help_n of_o brazen_a screw_n by_o which_o the_o stream_n of_o water_n may_v be_v convey_v to_o any_o convenient_a place_n through_o narrow_a and_o otherwise_o inaccessible_a passage_n the_o ingenious_a dr._n denys_n pappin_n have_v add_v a_o further_a improvement_n that_o may_v be_v make_v to_o this_o ctesibian_a engine_n by_o a_o new_a and_o excellent_a contrivance_n of_o his_o own_o for_o make_v of_o the_o force_a syringe_n or_o pump_n which_o at_o my_o desire_n he_o be_v please_v to_o communicate_v to_o the_o public_a by_o this_o follow_a description_n which_o he_o send_v i_o some_o time_n since_o dr._n pappin_n letter_n contain_v a_o description_n of_o a_o wind-fountain_n and_o his_o own_o particular_a contrivance_n about_o the_o forcer_n of_o its_o syringe_n since_o the_o artificial_a fountain_n you_o have_v see_v at_o mr._n boyles_n which_o be_v of_o my_o make_n upon_o his_o desire_n have_v be_v so_o please_v to_o you_o as_o to_o make_v you_o desire_v to_o see_v my_o description_n thereof_o i_o can_v doubt_v but_o the_o same_o will_v be_v as_o grateful_a also_o and_o well_o receive_v by_o the_o public_a especial_o when_o they_o shall_v therein_o find_v a_o remedy_n for_o one_o of_o the_o great_a inconvenience_n of_o force_a pump_n which_o be_v of_o so_o great_a use_n for_o raise_v of_o water_n and_o quench_v of_o fire_n this_o be_v the_o occasion_n of_o my_o send_v you_o this_o present_a description_n which_o will_v not_o have_v be_v thus_o prolix_a have_v it_o be_v only_o for_o yourself_o in_o the_o figure_n than_o a_o a_o be_v the_o receptacle_n or_o body_n of_o the_o fountain_n careful_a soder_v in_o all_o place_n b_o b_o be_v the_o pump_n c_o c_o the_o plug_n or_o forcer_n d_o a_o pipe_n in_o the_o middle_n of_o the_o plug_n which_o be_v perfect_o shut_v and_o stop_v when_o the_o plate_n e_o e_o be_v force_v down_o upon_o it_o e_z e_z be_v the_o plate_n with_o a_o hole_n in_o the_o middle_n upon_o which_o be_v soder_v a_o pipe_n f_o which_o serve_v for_o a_o handle_n to_o move_v the_o plug_n up_o and_o down_o g_o be_v a_o cock_n at_o the_o top_n of_o the_o pipe_n which_o serve_v to_o moderate_v the_o jetto_n or_o stream_n h_o h_n be_v a_o valve_n at_o the_o bottom_n of_o the_o pump_n which_o open_v outward_a for_o the_o passage_n of_o the_o water_n out_o of_o the_o pump_n into_o the_o fountain_n or_o receptacle_n i_o i_o be_v a_o cross_n at_o the_o top_n of_o the_o plug_n to_o hinder_v