we_o sometime_o swift_a and_o at_o other_o time_n more_o slow_a nor_o be_v the_o day_n themselves_o account_v from_o noon_n to_o noon_n of_o equal_a length_n some_o day_n contain_v more_o time_n than_o some_o and_o other_o less_o there_o be_v a_o natural_a necessity_n that_o the_o unequal_a motion_n of_o the_o sun_n shall_v produce_v such_o inequality_n in_o the_o length_n of_o those_o natural_a day_n that_o be_v bound_v by_o it_o for_o a_o natural_a day_n be_v compose_v of_o that_o space_n of_o time_n in_o which_o any_o one_o place_n or_o point_n of_o the_o earth_n be_v move_v in_o its_o diurnal_a motion_n eastward_o from_o the_o meridian_n sun_n of_o any_o one_o day_n to_o that_o of_o the_o next_o it_o will_v follow_v that_o these_o day_n can_v never_o be_v equal_a unless_o the_o sun_n in_o that_o space_n of_o time_n be_v so_o move_v in_o her_o annual_a orb_n as_o to_o cut_v out_o equal_a division_n on_o the_o aequinoctial_a upon_o the_o meridian_n of_o every_o day_n which_o 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those_o intersection_n that_o be_v make_v by_o the_o sun_n on_o the_o aequinox_a upon_o every_o meridian_n so_o that_o there_o will_v by_o this_o mean_n be_v find_v nothing_o but_o a_o almost_o continual_a unequalness_n in_o the_o right_a ascension_n which_o will_v be_v the_o more_o apparent_a if_o you_o make_v a_o estimation_n of_o the_o right_a ascension_n of_o about_o 10_o day_n together_o and_o compare_v that_o with_o those_o of_o the_o same_o number_n the_o like_a will_v appear_v plain_o if_o try_v on_o the_o globe_n for_o if_o you_o mark_v out_o on_o the_o ecliptic_a any_o 10_o or_o more_o day_n be_v motion_n of_o the_o sun_n according_a to_o his_o true_a place_n find_v out_o in_o a_o exact_a ephimeris_n and_o pass_v these_o 10_o or_o more_o day_n motion_n under_o the_o meridian_n note_v what_o degree_n on_o the_o aequmoctial_a be_v then_o trace_v out_o which_o compare_v with_o the_o degree_n trace_v out_o by_o make_v the_o same_o number_n of_o day_n be_v motion_n in_o some_o other_o part_n of_o the_o ecliptic_a to_o pass_v the_o meridian_n and_o the_o difference_n of_o right_a ascension_n include_v between_o those_o two_o equal_a number_n of_o day_n will_v plain_o appear_v all_o which_o irregularity_n or_o difference_n in_o right_a ascension_n proceed_v from_o two_o principal_a cause_n 1._o from_o the_o different_a position_n and_o 2._o from_o the_o different_a centre_n of_o those_o orb_n in_o which_o and_o according_a to_o which_o the_o sun_n and_o earth_n do_v move_v from_o whence_o arise_v a_o natural_a necessity_n that_o between_o two_o such_o regular_a and_o equal_a motion_n who_o position_n be_v thus_o oblique_a those_o appear_a difference_n shall_v still_o arise_v for_o though_o both_o sun_n and_o earth_n the_o one_o in_o his_o annual_a the_o other_o in_o its_o diurnal_a revolution_n be_v rational_o suppose_v to_o be_v regular_a and_o equal_a in_o their_o own_o motion_n yet_o in_o regard_n of_o the_o different_a position_n of_o their_o sphere_n the_o right_a ascension_n that_o be_v make_v by_o they_o can_v be_v equal_a it_o be_v impossible_a that_o the_o sun_n when_o near_o aries_n and_o libra_n where_o he_o move_v cross_v the_o equinoctial_a shall_v then_o in_o any_o particular_a number_n of_o day_n make_v so_o great_a a_o alteration_n in_o right_a ascension_n as_o he_o must_v do_v near_o the_o two_o tropic_n where_o both_o equinoctial_a and_o ecliptic_a run_v parallel_v one_o to_o the_o other_o and_o according_o by_o the_o best_a table_n of_o right_a ascension_n it_o be_v find_v that_o the_o right_a ascension_n of_o 10_o day_n motion_n of_o the_o sun_n near_o the_o tropic_a of_o capricorn_n shall_v arise_v to_o above_o 11_o degree_n 30_o minute_n whereas_o that_o of_o the_o same_o number_n of_o day_n near_o the_o equinoctial_a point_n of_o aries_n shall_v scarce_o amount_v to_o 9_o degree_n moreover_o from_o the_o eccentricity_n of_o these_o orb_n another_o irregularity_n do_v happen_v in_o the_o right_a ascension_n for_o the_o centre_n of_o the_o earth_n upon_o which_o it_o turn_v round_o in_o its_o daily_a revolution_n be_v not_o the_o same_o with_o the_o centre_n of_o the_o sun_n orb_n it_o follow_v that_o the_o apparent_a equinox_n point_v out_o by_o a_o imaginary_a line_n draw_v through_o the_o centre_n of_o the_o earth_n and_o intersect_v the_o ecliptic_a shall_v divide_v that_o circle_n into_o two_o unequal_a part_n from_o whence_o it_o arise_v that_o the_o sun_n must_v spend_v more_o day_n in_o pass_v through_o one_o half_a of_o the_o ecliptic_a than_o he_o do_v in_o pass_v through_o the_o other_o and_o according_o by_o experience_n he_o be_v find_v to_o move_v through_o that_o part_n between_o libra_n and_o aries_n in_o 179_o day_n but_o in_o pass_v between_o aries_n and_o libra_n he_o take_v up_o 186_o which_o be_v 7_o day_n more_o so_o that_o in_o that_o part_n of_o the_o year_n between_o september_n and_o march_n he_o seem_v to_o we_o to_o be_v swift_a in_o motion_n but_o in_o the_o other_o part_n between_o march_n and_o september_n his_o apparent_a course_n be_v more_o slow_a which_o seem_v swiftness_n and_o slowness_n of_o the_o sun_n motion_n be_v the_o cause_n that_o the_o right_a ascension_n near_o both_o the_o tropic_n be_v not_o alike_o but_o differ_v much_o as_o do_v also_o those_o that_o be_v nigh_o the_o equinox_n for_o the_o right_a ascension_n of_o 10_o day_n motion_n near_o the_o winter_n tropic_n be_v more_o by_o 60_o minute_n than_o that_o of_o the_o same_o number_n of_o day_n near_o that_o of_o the_o summer_n one_o so_o also_o the_o right_a ascension_n of_o 10_o day_n time_n near_o libra_n amount_v to_o above_o 30_o minute_n more_o than_o those_o of_o the_o same_o number_n of_o day_n near_o aries_n do_v have_v thus_o plain_o demonstrate_v that_o natural_a day_n must_v needs_o be_v unequal_a and_o lay_v down_o the_o cause_n from_o whence_o those_o unequality_n do_v still_o arise_v i_o suppose_v it_o may_v now_o be_v conclude_v to_o be_v extreme_o unreasonable_a for_o those_o that_o be_v so_o nice_a and_o curious_a as_o some_o be_v to_o expect_v a_o exact_a correspondence_n between_o the_o time_n give_v by_o the_o motion_n of_o a_o clock_n and_o those_o division_n of_o it_o that_o be_v make_v by_o these_o unsteady_a motion_n of_o the_o sun_n on_o the_o line_n of_o a_o dial_n for_o if_o from_o the_o reason_n before_o lay_v down_o there_o be_v in_o nature_n a_o necessity_n for_o those_o difference_n of_o right_a ascension_n before_o assert_v and_o that_o the_o day_n which_o they_o bind_v must_v differ_v also_o in_o length_n correspondent_a to_o what_o those_o difference_n in_o right_a ascension_n do_v amount_v to_o how_o then_o be_v it_o possible_a that_o those_o exact_a and_o regular_a motion_n of_o a_o pendulum_n to_o what_o pitch_n soever_o it_o be_v set_v shall_v agree_v with_o these_o motion_n of_o the_o sun_n and_o true_o divide_v those_o day_n that_o be_v not_o so_o regular_a as_o itself_o be_v for_o suppose_v a_o clock_n shall_v be_v adjust_v to_o the_o hour_n at_o a_o time_n when_o natural_a day_n be_v short_a as_o about_o the_o middle_n of_o march_n this_o clock_n with_o the_o same_o pitch_n of_o motion_n shall_v in_o june_n or_o december_n finish_v its_o diurnal_a revolution_n soon_o than_o the_o day_n shall_v do_v by_o reason_n the_o natural_a day_n be_v now_o long_o than_o those_o of_o march_n to_o which_o the_o clock_n have_v be_v former_o adjust_v and_o by_o consequence_n it_o shall_v now_o gain_v upon_o every_o day_n just_o so_o much_o time_n as_o these_o day_n in_o december_n be_v long_o than_o those_o of_o march_n so_o on_o the_o contrary_a if_o a_o clock_n be_v adjust_v to_o go_v true_a with_o the_o sun_n in_o the_o month_n of_o december_n at_o which_o time_n the_o natural_a day_n be_v always_o long_a this_o clock_n when_o natural_a day_n be_v
short_a as_o in_o march_n or_o september_n shall_v not_o finish_v it_o be_v daily_a revolution_n so_o soon_o as_o the_o day_n itself_o shall_v be_v accomplish_v and_o by_o consequence_n go_v each_o day_n so_o much_o too_o slow_a as_o those_o day_n of_o march_n or_o september_n be_v more_o short_a than_o they_o to_o which_o the_o clock_n before_o have_v be_v exact_o adjust_v since_o therefore_o there_o be_v no_o tolerable_a exactness_n in_o thus_o adjust_v clock_n to_o the_o sun_n itself_o because_o be_v thus_o adjust_v at_o time_n when_o day_n be_v either_o short_a or_o long_a their_o gain_n or_o lose_v will_v be_v the_o more_o extreme_a in_o the_o contrary_a part_n of_o the_o year_n for_o example_n clock_n adjust_v to_o the_o sun_n in_o march_n shall_v upon_o most_o day_n in_o december_n gain_v almost_o 50_o second_o which_o in_o the_o month_n time_n shall_v amount_v to_o near_o half_a a_o hour_n and_o on_o the_o contrary_a if_o adjust_v to_o go_v true_a with_o the_o sun_n in_o december_n it_o shall_v in_o march_n lose_v the_o same_o time_n and_o so_o for_o any_o other_o according_a as_o day_n do_v differ_v in_o length_n that_o clock_n therefore_o may_v be_v reduce_v to_o a_o more_o exact_a pitch_n of_o motion_n that_o their_o gain_n or_o loss_n may_v never_o be_v so_o extreme_a it_o will_v be_v necessary_a to_o adjust_a they_o so_o as_o that_o their_o motion_n may_v be_v agreeable_a to_o that_o of_o a_o middle_a day_n or_o such_o a_o one_o as_o be_v a_o mean_a between_o natural_a day_n that_o be_v most_o long_o and_o those_o other_o that_o be_v most_o short_a to_o which_o pitch_n if_o a_o clock_n be_v once_o adjust_v it_o be_v gain_n or_o loss_n shall_v then_o be_v the_o less_o sensible_a for_o gain_n and_o lose_v it_o will_v still_o amount_v in_o december_n but_o to_o about_o 15_o minute_n in_o the_o whole_a month_n and_o in_o march_n to_o but_o about_o 9_o which_o be_v vast_o more_o exact_a than_o when_o it_o shall_v happen_v to_o be_v adjust_v to_o the_o long_a or_o short_a of_o natural_a day_n or_o to_o any_o other_o that_o be_v not_o equal_a to_o a_o mean_a or_o middle_a day_n of_o which_o there_o be_v but_o few_o which_o in_o the_o table_n be_v express_v by_o the_o character_n ☉_o sol._n but_o to_o this_o exact_a pitch_n of_o motion_n that_o may_v thus_o correspond_v to_o a_o mean_a day_n the_o great_a exactness_n that_o a_o pendulum_n be_v capable_a of_o be_v bring_v to_o there_o be_v no_o way_n certain_o to_o adjust_a a_o clock_n without_o the_o help_n and_o assistance_n of_o a_o table_n of_o equation_n that_o give_v the_o daily_a difference_n between_o a_o mean_a day_n and_o those_o which_o be_v either_o long_o or_o short_a than_o the_o mean_a day_n be_v which_o equation_n have_v former_o be_v compute_v by_o the_o worthy_a and_o ingenious_a mr._n christian_n hugens_fw-la de_fw-fr zulechim_n who_o be_v report_v to_o be_v the_o first_o that_o ever_o apply_v the_o pendulum_n to_o regulate_v the_o motion_n of_o a_o clock_n and_o not_o long_o since_o print_v in_o number_n 49._o philos_fw-la trans_fw-la i_o have_v make_v bold_a in_o regard_n of_o its_o exactness_n to_o transcribe_v in_o its_o more_o natural_a form_n of_o a_o equation_n by_o only_o express_v the_o equation_n themselves_o without_o add_v they_o together_o and_o substract_v as_o mr._n hugens_n have_v do_v for_o a_o particular_a use_n to_o show_v the_o nature_n of_o a_o pendulum_n go_v when_o set_v right_o the_o first_o of_o february_n and_o let_v go_v the_o whole_a year_n round_o without_o set_v afterward_o now_o for_o their_o sake_n that_o desire_v to_o know_v the_o manner_n of_o compose_v such_o a_o table_n themselves_o that_o thereby_o they_o may_v the_o better_o understand_v the_o nature_n of_o it_o they_o may_v note_n that_o the_o equation_n be_v to_o be_v find_v out_o and_o a_o table_n compose_v in_o the_o manner_n follow_v first_o find_v out_o a_o mean_a right_a ascension_n by_o divide_v the_o 360_o degree_n of_o the_o equinox_n into_o 365_o part_n and_o a_o quarter_n equal_a to_o the_o day_n of_o a_o year_n and_o the_o product_n shall_v be_v the_o mean_a right_a ascension_n desire_v which_o will_v be_v find_v to_o be_v about_o three_o minute_n 56_o second_o according_a to_o sir_n ionas_n moor_n account_n of_o it_o in_o his_o mathematical_a compendium_n then_o by_o the_o help_n of_o a_o exact_a ephemerides_n here_o lie_v the_o difficulty_n let_v the_o natural_a right_a ascension_n of_o the_o sun_n be_v compute_v by_o calculation_n for_o the_o meridian_n position_n of_o the_o sun_n for_o every_o day_n to_o minute_n and_o second_o which_o have_v do_v compare_v the_o daily_a difference_n of_o these_o natural_a right_a ascension_n with_o the_o mean_a one_o by_o still_o substract_v the_o lesser_a from_o the_o great_a and_o what_o remain_v shall_v be_v the_o equation_n desire_v still_o note_v down_o either_o the_o excess_n or_o defect_n that_o be_v whether_o the_o natural_a be_v more_o than_o the_o mean_a or_o less_o as_o for_o example_n suppose_v the_o right_a ascension_n between_o the_o meridian_n of_o the_o 1_o st_z and_o 2_o d._n of_o january_n be_v find_v to_o amount_v to_o 4_o minute_n 20_o second_o this_o compare_v with_o the_o mean_a right_a ascension_n 3_o minute_n 56_o second_o and_o by_o substract_v the_o lesser_a from_o the_o great_a the_o remainder_n will_v be_v find_v to_o be_v 24_o second_o and_o so_o much_o the_o natural_a right_a ascension_n do_v then_o exceed_v the_o mean_a one_o this_o 24_o second_o be_v the_o equation_n for_o that_o day_n it_o be_v from_o noon_n to_o noon_n 24_o second_o long_o than_o a_o mean_a day_n be_v and_o show_v you_o that_o a_o clock_n when_o well_o adjust_v to_o a_o mean_a day_n shall_v then_o gain_v 24_o second_o because_o it_o finish_v its_o diurnal_a revolution_n soon_o by_o 24_o second_o than_o the_o day_n itself_o do_v on_o the_o contrary_a when_o the_o right_a ascension_n of_o natural_a day_n be_v less_o than_o the_o mean_a one_o as_o they_o be_v about_o the_o middle_n of_o march_n by_o almost_o 20_o second_o this_o 20_o second_o be_v the_o equation_n belong_v to_o such_o a_o day_n shall_v show_v you_o that_o upon_o such_o a_o like_a day_n a_o well_o adjust_v clock_n shall_v then_o lose_v 20_o second_o for_o the_o mean_a day_n to_o which_o it_o be_v adjust_v being_n long_o than_o the_o natural_a one_o by_o 20_o second_o the_o natural_a day_n shall_v be_v finish_v soon_o by_o 20_o second_o than_o the_o clock_n at_o that_o time_n shall_v accomplish_v it_o be_v diurnal_a or_o daily_a revolution_n and_o by_o consequence_n it_o shall_v then_o lose_v 20_o second_o the_o equation_n thus_o find_v for_o every_o particular_a day_n and_o a_o table_n compose_v of_o they_o shall_v resemble_v that_o which_o be_v here_o insert_v who_o use_n we_o now_o come_v to_o show_v more_o particular_a in_o some_o case_n for_o explanation_n take_v notice_n that_o the_o first_o column_n contain_v the_o day_n common_a to_o every_o month_n the_o other_o 12_o column_n that_o belong_v to_o the_o several_a month_n themselves_o contain_v those_o second_o of_o time_n that_o all_o natural_a day_n be_v either_o long_o or_o short_a than_o the_o mean_a day_n note_v that_o in_o four_o part_n of_o the_o table_n be_v place_v this_o character_n ☉_o which_o denote_v the_o time_n wherein_o natural_a day_n have_v before_o be_v long_a than_o the_o mean_a day_n do_v then_o begin_v to_o be_v short_a or_o have_v before_o be_v short_a do_v then_o begin_v to_o grow_v more_o long_o note_v also_o that_o those_o day_n upon_o which_o this_o character_n ☉_o be_v affix_v have_v no_o equation_n they_o be_v equal_a in_o their_o length_n to_o the_o mean_a day_n as_o for_o the_o word_n insert_v among_o the_o column_n they_o be_v at_o sight_n to_o inform_v you_o that_o the_o equation_n in_o those_o part_n of_o the_o table_n be_v either_o more_o or_o else_o less_o than_o the_o mean_a day_n as_o the_o word_n themselves_o do_v full_o express_v they_o also_o note_v that_o where_o the_o equation_n be_v more_o there_o clock_n shall_v gain_v each_o day_n so_o much_o as_o the_o equation_n belong_v to_o it_o do_v then_o express_v but_o if_o the_o equation_n be_v less_o they_o then_o shall_v lose_v and_o how_o much_o this_o gain_n or_o loss_n for_o every_o particular_a month_n time_n shall_v amount_v to_o be_v by_o continual_a addition_n of_o the_o equation_n belong_v to_o each_o day_n sum_v up_o and_o the_o quantity_n of_o time_n it_o amount_v to_o set_z down_z apart_z at_o the_o bottom_n of_o every_o column_n note_v also_o that_o since_o clock_n do_v either_o gain_v or_o lose_v during_o the_o whole_a number_n of_o day_n include_v between_o those_o day_n on_o who_o this_o character_n ☉_o be_v affix_v the_o whole_a quantity_n of_o
of_o the_o unequality_n of_o natural_a time_n with_o its_o reason_n and_o cause_n together_o with_o a_o table_n of_o the_o true_a aequation_n of_o natural_a day_n draw_v up_o chief_o for_o the_o use_v of_o the_o gentry_n in_o order_n to_o their_o more_o true_a adjust_n and_o right_a manage_n of_o pendulum_n clock_n and_o watch_n by_o john_n smith_n c._n m._n london_n print_v for_o joseph_n watts_n at_o the_o half-moon_n in_o st._n paul_n churchyard_n 1686._o a_o table_n of_o equation_n for_o reduce_v the_o unequality_n of_o natural_a day_n to_o a_o mean_a and_o equal_a time_n design_v chief_o in_o order_n to_o the_o more_o true_a adjust_n and_o right_a manage_n of_o pendulum_n clock_n and_o watch_n by_o john_n smith_n c._n m._n day_n janua_n sec_n febru_n sec._n march_n sec._n april_n sec._n may._n sec._n june_n sec._n july_n sec._n aug._n sec._n sept._n sec._n octob._n sec._n nou._n sec._n dec._n sec._n 1_o natural_a day_n long_o than_o the_o mean_a day_n and_o clock_n gain_v 24_o ☉_o 0_o natural_a day_n short_a than_o the_o mean_a day_n and_o clock_n lose_v 17_o natural_a day_n short_a than_o the_o mean_a day_n and_o clock_n lose_v 17_o  _fw-fr 3_o natural_a day_n long_o than_o the_o mean_a day_n and_o clock_n gain_v 11_o natural_a day_n long_o 7_o nat._n day_n short_a than_o the_o mean_a and_o clock_n lose_v 9_o nat._n day_n short_a than_o the_o mean_a and_o clock_n lose_v 20_o nat._n day_n short_a clock_n lose_v 14_o natural_a day_n long_o than_o the_o mean_a and_o clock_n gain_v 9_o natural_a day_n long_o than_o the_o mean_a and_o clock_n gain_v 29_o 2_o 23_o natural_a day_n short_a than_o the_o mean_a day_n and_o clock_n lose_v 2_o 17_o 16_o 3_o 11_o 7_o 9_o 20_o 14_o 10_o 30_o 3_o 22_o 2_o 18_o 16_o 1_o 12_o 7_o 9_o 21_o 13_o 10_o 30_o 4_o 21_o 4_o 18_o 15_o ☉_o 0_o 12_o 6_o 11_o 21_o 13_o 10_o 30_o 5_o 20_o 4_o 18_o 15_o ☉_o 0_o 12_o 6_o 12_o 21_o 13_o 11_o 30_o 6_o 19_o 4_o 18_o 14_o nat._n day_n long_o than_o the_o mean_a day_n and_o clock_n gain_v 1_o 13_o 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19_o 7_o 8_o 11_o 4_o 19_o 19_o ☉_o 0_o 24_o 30_o 23_o 8_o 15_o 19_o 7_o 9_o 10_o 4_o 19_o 19_o ☉_o 0_o 25_o 30_o 24_o 6_o 15_o 19_o 7_o 10_o 10_o 5_o 19_o 18_o long_o 1_o 25_o 29_o 25_o 5_o 15_o 19_o 6_o 10_o 10_o 5_o 20_o 17_o 2_o 25_o 28_o 26_o 4_o 15_o 19_o 5_o 11_o 10_o 5_o 20_o 17_o 2_o 25_o 28_o 27_o 3_o 16_o 19_o 5_o 11_o 10_o 5_o 20_o 16_o 3_o 26_o 28_o 28_o 3_o 17_o 19_o 5_o 11_o 9_o 6_o 20_o 16_o 4_o 26_o 27_o 29_o 2_o  _fw-fr 19_o 4_o 11_o 9_o 7_o 20_o 15_o 6_o 27_o 27_o 30_o 1_o 18_o 4_o 11_o 8_o 8_o 20_o 15_o 7_o 27_o 25_o 31_o ☉_o 0_o 17_o  _fw-fr 11_o  _fw-fr 9_o 20_o  _fw-fr 8_o  _fw-fr 24_o  _fw-fr clock_n gain_v this_o month_n clock_n lose_v this_o month_n clock_n lose_v this_o month_n clock_n lose_v this_o month_n clock_n gain_v this_o month_n clock_n gain_v this_o month_n clock_n lose_v this_o month_n clock_n lose_v this_o month_n clock_n lose_v this_o month_n clock_n lose_v this_o month_n clock_n gain_v this_o month_n clock_n gain_v this_o month_n sum_n min._n sec._n min._n sec._n min._n sec._n min._n sec._n min._n sec._n min._n sec._n min._n sec._n min._n sec._n min._n sec._n min._n sec._n min._n sec._n min._n sec._n 6_o 26_o 4_o 29_o 9_o 37_o 5_o 16_o 2_o 47_o 5_o 43_o 0_o 6_o 8_o 23_o 9_o 41_o 2_o 20_o 9_o 38_o 15_o 9_o this_o table_n contain_v those_o second_o of_o time_n that_o each_o natural_a day_n be_v either_o long_o or_o short_a than_o the_o mean_a or_o equal_a day_n or_o such_o a_o one_o as_o contain_v in_o length_n the_o just_a time_n of_o 24_o hour_n from_o which_o mean_a day_n the_o natural_a one_o differ_v almost_o continual_o in_o length_n this_o table_n shall_v still_o give_v you_o the_o difference_n between_o they_o and_o by_o inspection_n only_o inform_v you_o what_o quantity_n of_o time_n each_o natural_a day_n be_v either_o more_o than_o 24_o hour_n long_o or_o less_o note_v that_o upon_o each_o particular_a day_n a_o clock_n that_o be_v well_o adjust_v to_o a_o mean_a or_o 24_o hour_n day_n shall_v then_o either_o gain_v or_o lose_v just_a so_o much_o time_n as_o that_o natural_a day_n be_v either_o long_o or_o short_a than_o the_o mean_a day_n therefore_o if_o a_o clock_n have_v be_v first_o set_v right_o to_o the_o sun_n the_o first_o day_n of_o any_o particular_a month_n shall_v either_o gain_v or_o lose_v in_o that_o whole_a month_n so_o much_o in_o time_n as_o the_o whole_a sum_n of_o equation_n for_o that_o month_n amount_v to_o which_o you_o shall_v find_v note_v down_o at_o the_o bottom_n of_o every_o particular_a column_n then_o be_v it_o well_o adjust_v to_o the_o mean_a equal_a or_o 24_o hour_n day_n but_o if_o it_o have_v not_o either_o get_v or_o lose_v so_o much_o as_o the_o whole_a sum_n of_o equation_n for_o the_o whole_a time_n it_o have_v go_v in_o do_v amount_v to_o then_o must_v its_o motion_n be_v regulate_v as_o occasion_n require_v by_o screw_v up_o the_o bob_n to_o make_v it_o go_v fast_o in_o case_n it_o have_v not_o get_v enough_o or_o else_o let_v the_o bob_n down_o 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and_o curious_a hand_n and_o after_o all_o this_o be_v adjust_v by_o the_o utmost_a care_n and_o diligence_n of_o man_n yet_o shall_v not_o the_o motion_n of_o it_o correspond_v so_o continual_o with_o the_o hour_n give_v by_o the_o sun_n but_o that_o in_o some_o considerable_a quantity_n of_o time_n you_o shall_v be_v sensible_a of_o gain_n or_o loss_n in_o the_o motion_n of_o it_o the_o true_a reason_n of_o which_o variation_n proceed_v not_o from_o any_o defect_n that_o may_v be_v attribute_v to_o the_o motion_n of_o the_o pendulum_n of_o who_o exactness_n we_o be_v by_o many_o curious_a experiment_n sufficient_o sensible_a but_o rather_o from_o a_o unequality_n legible_a and_o easy_a enough_o to_o be_v discover_v in_o the_o diurnal_a motion_n of_o the_o sun_n vulgar_o for_o the_o most_o part_n the_o sun_n be_v indeed_o account_v to_o be_v the_o standard_n and_o measure_n of_o all_o equal_a time_n and_o man_n general_o esteem_v natural_a day_n to_o be_v all_o of_o one_o length_n as_o contain_v the_o just_a time_n of_o 24_o hour_n but_o upon_o a_o more_o exact_a and_o curious_a scrutiny_n these_o vulgar_a supposition_n be_v find_v to_o be_v false_a for_o neither_o be_v the_o sun_n motion_n find_v to_o be_v exact_a be_v in_o appearance_n to_o
time_n either_o get_v or_o lose_v do_v amount_v to_o the_o sum_n that_o follow_v viz._n between_o the_o one_a of_o february_n and_o the_o four_o of_o may_n the_o time_n that_o a_o well_o adjust_v clock_n shall_v lose_v amount_v by_o continual_a add_v the_o equation_n together_o to_o about_o 19_o minute_n 29_o second_o between_o this_o four_o of_o may_n and_o the_o 15_o of_o july_n it_o shall_v gain_v about_o 9_o minute_n 43_o second_o from_o the_o 15_o of_o july_n to_o the_o 23d_o of_o october_n it_o shall_v lose_v 22_o minute_n 9_o second_o from_o the_o 23d_o of_o october_n to_o the_o last_o of_o january_n it_o shall_v gain_v 31_o minute_n 55_o second_o all_o this_o be_v to_o be_v understand_v of_o a_o well_o adjust_v clock_n set_v right_o to_o the_o sun_n at_o the_o begin_n of_o each_o time_n of_o either_o gain_n or_o lose_v by_o this_o table_n if_o you_o will_v adjust_a a_o clock_n to_o a_o mean_a time_n which_o be_v the_o great_a exactness_n to_o which_o its_o possible_a to_o be_v bring_v do_v thus_o first_o set_v it_o true_a to_o the_o sun_n and_o note_v the_o day_n then_o let_v its_o motion_n be_v continue_v without_o set_v a_o new_a for_o about_o 30_o or_o more_o day_n observe_v then_o the_o time_n that_o it_o have_v get_v or_o lose_v by_o the_o sun_n then_o sum_v up_o the_o whole_a number_n of_o second_o include_v in_o the_o table_n between_o those_o two_o day_n of_o first_o set_v and_o last_v observation_n allow_v 60_o second_o to_o a_o minute_n and_o if_o the_o gain_n or_o loss_n of_o your_o clock_n be_v equal_a to_o the_o sum_n of_o time_n that_o it_o shall_v have_v gain_v or_o lose_v by_o the_o table_n then_o be_v it_o well_o adjust_v but_o if_o it_o have_v not_o then_o must_v its_o motion_n be_v reduce_v to_o a_o more_o near_a agreement_n by_o shorten_v the_o pendulum_n in_o case_n the_o clock_n have_v go_v too_o slow_a or_o let_v the_o bob_n down_o long_o in_o case_n it_o have_v go_v too_o fast_o then_o set_v it_o anew_o and_o try_v it_o for_o about_o 30_o day_n more_o and_o then_o compare_v its_o loss_n or_o gain_n with_o the_o sum_n of_o those_o equation_n contain_v in_o the_o table_n as_o before_o you_o do_v let_v the_o bob_n be_v again_o rectify_v as_o the_o nature_n of_o its_o motion_n require_v and_o continue_v to_o do_v thus_o till_o you_o find_v its_o gain_n or_o loss_n exact_o to_o correspond_v with_o the_o sum_n of_o time_n give_v by_o the_o equation_n contain_v in_o the_o table_n for_o the_o time_n that_o the_o clock_n have_v go_v when_o it_o be_v thus_o well_o adjust_v to_o a_o mean_a time_n it_o will_v be_v so_o exact_a as_o that_o be_v set_v right_o at_o any_o time_n of_o the_o year_n and_o so_o let_v go_v the_o whole_a year_n about_o it_o shall_v come_v right_a with_o the_o same_o dial_n by_o which_o it_o be_v set_v the_o same_o day_n twelvemonth_n but_o â—n_o all_o other_o part_n of_o the_o year_n it_o shall_v still_o differ_v from_o the_o same_o dial._n for_o example_n if_o set_v right_o the_o first_o of_o 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have_v get_v by_o about_o 12_o minute_n 26_o second_o it_o shall_v still_o be_v too_o fast_o by_o 12_o minute_n 26_o second_o then_o from_o the_o four_o of_o may_n to_o the_o 15_o of_o july_n it_o shall_v gain_v anew_o to_o the_o quantity_n of_o about_o 9_o minute_n 43_o second_o which_o add_v to_o the_o time_n it_o be_v too_o fast_o before_o shall_v amount_v to_o 22_o minute_n 9_o second_o and_o so_o much_o it_o shall_v be_v too_o fast_o on_o the_o 15_o of_o july_n from_o which_o time_n till_o the_o 23d_o of_o october_n it_o shall_v lose_v this_o 22_o minute_n 9_o second_o and_o by_o consequence_n come_v right_a to_o the_o same_o dial_n with_o which_o it_o be_v set_v twelve_o month_n before_o thus_o shall_v one_o and_o the_o same_o clock_n with_o the_o same_o pitch_n of_o motion_n go_v always_o too_o slow_a if_o set_v at_o one_o time_n of_o the_o year_n and_o always_o too_o fast_o if_o set_v at_o another_o time_n if_o it_o be_v let_v go_v the_o whole_a year_n about_o moreover_o if_o set_v at_o some_o other_o time_n and_o then_o continue_v in_o its_o motion_n for_o a_o year_n without_o set_v anew_o it_o shall_v both_o gain_v and_o lose_v be_v sometime_o too_o fast_o and_o sometime_o too_o slow_a for_o if_o a_o well_o adjust_v pendulum_n be_v set_v right_a to_o the_o sun_n the_o four_o of_o may_n by_o the_o 15_o of_o july_n it_o shall_v be_v 9_o minute_n 43_o second_o too_o fast_o from_o this_o 15_o of_o july_n to_o the_o 23d_o of_o october_n have_v lose_v 22_o minute_n 9_o second_o from_o which_o substract_v the_o 9_o minute_n 43_o second_o that_o it_o be_v before_o too_o fast_o there_o remain_v 12_o minute_n 26_o second_o and_o so_o much_o it_o shall_v be_v too_o slow_a on_o the_o 23d_o of_o october_n from_o which_o day_n it_o shall_v begin_v to_o gain_v and_o continue_v so_o to_o do_v till_o the_o first_o of_o january_n by_o which_o time_n the_o clock_n have_v get_v 31_o minute_n 55_o second_o which_o amount_v to_o about_o 19_o minute_n 29_o second_o above_o what_o it_o be_v too_o slow_a on_o the_o 23d_o of_o october_n it_o shall_v by_o consequence_n be_v now_o 19_o minute_n 29_o second_o too_o fast_o from_o whence_o to_o the_o four_o of_o may_n it_o shall_v lose_v what_o now_o it_o be_v too_o fast_o and_o so_o come_v right_a to_o the_o same_o dial_n with_o which_o it_o be_v before_o set_v again_o set_v a_o clock_n to_o the_o sun_n the_o 15_o of_o july_n and_o if_o it_o be_v well_o adjust_v it_o shall_v by_o the_o 23d_o of_o october_n be_v 22_o minute_n 9_o second_o too_o slow_a from_o whence_o to_o the_o last_o of_o january_n it_o be_v to_o gain_v 31_o minute_n 55_o second_o it_o shall_v be_v then_o 9_o minute_n 46_o second_v too_o fast_a from_o which_o time_n to_o the_o four_o of_o may_n it_o lose_v 19_o minute_n 29_o second_o it_o shall_v then_o be_v 9_o minute_n 29_o second_o too_o slow_a which_o time_n by_o the_o 15_o of_o july_n shall_v again_o be_v get_v and_o so_o the_o clock_n shall_v come_v right_a to_o the_o same_o dial._n thus_o by_o this_o table_n be_v these_o great_a variety_n discoverable_a in_o the_o motion_n of_o the_o best_a adjust_v pendulum_n according_a to_o the_o different_a time_n of_o the_o year_n that_o it_o be_v set_v in_o that_o the_o same_o pendulum_n set_v right_a upon_o the_o first_o of_o february_n shall_v go_v always_o too_o slow_a till_o the_o same_o day_n twelvemonth_n but_o if_o set_v right_o the_o 23d_o of_o october_n it_o shall_v the_o whole_a year_n round_o be_v still_o too_o fast_o till_o the_o same_o day_n on_o which_o it_o be_v