Selected quad for the lemma: day_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
day_n	clock_n	minute_n	south_n	4,253	5	12.0152	5	false

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A52487	The seaman's companion being a plain guide to the understanding of arithmetick, geometry, trigonometry, navigation, and astronomy. Applied chiefly to navigation: and furnished with a table of meridional parts, to every third minute: with excellent and easie ways of keeping a reckoning at sea, never in print before. Also, a catalogue of the longitude and latitude of the principal places in the world with other useful things. The third edition corrected and amended. By Matthew Norwood, mariner.	Norwood, Matthew.	1678 (1678)	Wing N1345A; ESTC R218969	104,181	203

rise_v at_o 6_o of_o the_o clock_n and_o so_o there_o be_v no_o difference_n of_o ascension_n for_o he_o be_v then_o in_o the_o aequinoctial_a which_o cut_v the_o horizon_n in_o the_o two_o opposite_a point_n of_o east_n and_o west_n in_o this_o question_n the_o difference_n of_o ascension_n be_v o_o p_o and_o be_v a_o distance_n upon_o a_o line_n that_o go_v not_o through_o the_o centre_n therefore_o take_v half_a the_o length_n of_o the_o parallel_n i_o d_o and_o proceed_v as_o you_o do_v in_o the_o three_o question_n and_o after_o you_o have_v find_v it_o in_o degree_n and_o minute_n convert_v it_o into_o hour_n and_o minute_n of_o time_n and_o set_v it_o down_o i_o find_v it_o to_o be_v here_o 16_o deg_fw-la 18_o min._n which_o be_v 1_o hour_n 5′_n 3_o 15._o by_o the_o difference_n of_o ascension_n thus_o find_v you_o may_v find_v the_o length_n of_o the_o day_n or_o night_n the_o hour_n of_o sun_n rise_v or_o the_o hour_n of_o uns_fw-fr set_v question_n vii_o for_o the_o time_n of_o the_o sun_n rise_v or_o set_v in_o this_o example_n i_o consider_v as_o much_o as_o the_o sun_n rise_v before_o 6_o so_o much_o he_o set_v after_o 6_o here_o he_o rise_v before_o 6_o of_o the_o clock_n 1_o hour_n 5′_n subtract_v that_o from_o 6_o hour_n and_o you_o have_v the_o hour_n of_o the_o sun_n rise_v 4_o h._n 55′_n add_v it_o to_o 6_o hour_n and_o you_o have_v the_o time_n the_o sun_n set_v 7_o h._n 5′_n double_a that_o and_o it_o be_v the_o length_n of_o the_o whole_a day_n which_o be_v here_o 14_o deg_fw-la 10_o min._n subtract_v the_o length_n of_o the_o day_n from_o 24_o hour_n and_o it_o leave_v the_o length_n of_o the_o night_n 9_o h._n 50′_n i_o omit_v the_o fraction_n but_o if_o the_o sun_n rise_v after_o 6_o of_o the_o clock_n and_o you_o have_v a_o desire_n to_o find_v these_o thing_n as_o he_o do_v when_o he_o be_v south_n declination_n add_v the_o difference_n of_o ascension_n to_o 6_o hour_n and_o it_o give_v the_o time_n of_o the_o sun_n rise_v subtract_v it_o from_o 6_o and_o it_o give_v the_o time_n of_o sun_n set_v and_o that_o double_a be_v the_o length_n of_o the_o whole_a day_n again_o that_o subtract_v from_o 24_o hour_n be_v the_o length_n of_o the_o night_n question_v viii_o to_o find_v the_o hour_n of_o the_o sun_n be_v due_a east_n or_o west_n the_o sun_n be_v due_a east_n in_o this_o example_n or_o any_o other_o when_o he_o go_v by_o the_o east_n point_n of_o the_o horizon_n or_o west_n when_o he_o go_v by_o the_o west_n point_fw-fr in_o this_o example_n the_o sun_n parallel_n of_o declination_n cut_v the_o east_n and_o west_n azimuth_n in_o s_n which_o be_v late_a in_o the_o morning_n than_o 6_o of_o the_o clock_n by_o the_o distance_n s_o p_o therefore_o see_v what_o s_n p_o be_v by_o the_o three_o way_n of_o measure_v and_o convert_v it_o into_o time_n and_o add_v it_o to_o 6_o hour_n it_o shall_v give_v the_o hour_n of_o the_o sun_n be_v due_a east_n i_o find_v it_o in_o this_o example_n to_o be_v 6_o h._n 46′_n subtract_v this_o from_o 12_o hour_n and_o it_o give_v the_o time_n of_o the_o sun_n be_v due_a west_n that_o day_n for_o as_o many_o hour_n and_o minute_n as_o the_o sun_n be_v due_a east_n before_o 12_o of_o the_o clock_n so_o many_o hour_n and_o minute_n must_v it_o be_v due_a west_n after_o 12_o according_a to_o this_o example_n the_o sun_n be_v due_a west_n at_o 5_o of_o the_o clock_n 14_o min._n if_o the_o sun_n have_v south_n declination_n he_o pass_v the_o point_n of_o east_n before_o he_o rise_v and_o be_v set_v as_o long_o before_o he_o come_v to_o the_o point_n of_o west_n provide_v the_o latitude_n be_v northerly_a as_o this_o be_v but_o if_o the_o latitude_n and_o declination_n be_v both_o one_o way_n the_o sun_n be_v always_o up_o before_o he_o come_v to_o the_o point_n of_o east_n and_o the_o work_n be_v as_o i_o have_v show_v question_n ix_o to_o find_v the_o time_n of_o day_n break_v and_o twilight_n end_v it_o be_v a_o ancient_a observation_n and_o conclude_v opinion_n that_o the_o sun_n make_v some_o show_n of_o day_n when_o he_o be_v 17_o degree_n under_o the_o horizon_n therefore_o take_v 17_o deg_fw-la from_o your_o scale_n of_o chord_n and_o set_v it_o from_o both_o end_n of_o the_o horizon_n downward_o and_o draw_v the_o line_n t_o r_o then_o fix_v your_o compass_n in_o r_o the_o place_n where_o the_o sun_n parallel_n of_o declination_n intersect_v that_o line_n and_o extend_v they_o to_o 6_o of_o the_o clock_n set_v it_o off_o by_o the_o three_o way_n of_o measure_v and_o convert_v it_o into_o time_n subtract_v that_o from_o 6_o of_o the_o clock_n and_o it_o give_v the_o time_n of_o day_n break_v i_o find_v in_o this_o example_n day_n break_v at_o 3_o of_o the_o clock_n 6_o min._n ●8_o 15._o add_v it_o to_o 6_o hour_n and_o it_o give_v the_o time_n of_o twilight_n end_v 8_o of_o the_o clock_n 3_o 53_o 14_o 13._o it_o may_v happen_v so_o sometime_o that_o it_o may_v be_v past_o 6_o of_o the_o clock_n before_o the_o day_n break_v in_o such_o a_o case_n you_o must_v add_v in_o the_o morning_n for_o break_v of_o day_n and_o subtract_v for_o night_n from_o 6_o hour_n which_o be_v the_o contrary_a these_o thing_n your_o own_o reason_n will_v give_v you_o after_o you_o be_v use_v to_o it_o which_o make_v i_o forbear_v to_o give_v any_o more_o reason_n of_o it_o question_n x._o to_o find_v the_o continuance_n of_o twilight_n the_o continuance_n of_o twilight_n be_v the_o time_n between_o the_o day_n break_v and_o sun_n rise_v which_o be_v r_o o_o take_v it_o off_o by_o the_o three_o way_n of_o measure_v and_o convert_v it_o into_o time_n i_o find_v it_o to_o be_v 1_o hour_n 48_o min._n question_n xi_o to_o find_v the_o length_n of_o the_o long_a day_n in_o that_o latitude_n when_o the_o sun_n be_v near_a the_o zenith_n in_o any_o latitude_n that_o day_n must_v be_v the_o long_a now_o in_o place_n near_o the_o aequinoctial_a as_o between_o the_o tropic_n there_o be_v but_o little_a difference_n all_o the_o year_n long_o but_o in_o place_n near_o the_o pole_n there_o be_v more_o the_o sun_n be_v near_a the_o zenith_n in_o this_o latitude_n when_o he_o be_v in_o the_o tropic_a of_o cancer_n so_o that_o then_o must_v be_v the_o long_a day_n imagine_v the_o tripick_n of_o cancer_n to_o be_v the_o parallel_n of_o the_o sun_n declination_n as_o indeed_o it_o be_v that_o day_n take_v the_o distance_n between_o y_z and_z r_z which_o be_v between_o sun_n rise_v and_o 6_o of_o the_o clock_n that_o day_n and_o set_v it_o off_o by_o the_o three_o way_n of_o measure_v the_o number_n of_o degree_n and_o minute_n convert_v into_o time_n and_o add_v it_o to_o 6_o hour_n which_o make_v the_o length_n of_o the_o forenoon_n and_o that_o double_a be_v the_o length_n of_o the_o whole_a day_n as_o in_o quest_n 7._o which_o be_v equal_a to_o the_o long_a night_n in_o that_o latitude_n i_o find_v it_o here_o to_o be_v 16_o hour_n 10_o minute_n subtract_v the_o length_n of_o this_o long_a day_n from_o 24_o h._n 00_o min._n and_o it_o leave_v the_o length_n of_o the_o short_a night_n 7_o h._n 50_o min._n equal_a to_o which_o be_v the_o length_n of_o the_o short_a day_n 7_o h._n 50_o min._n but_o you_o may_v measure_v the_o length_n of_o the_o short_a day_n and_o subtract_v that_o from_o 24_o hour_n and_o it_o will_v be_v the_o length_n of_o the_o long_a night_n which_o be_v equal_a to_o the_o long_a day_n now_o the_o short_a day_n be_v when_o the_o sun_n be_v in_o the_o tropic_a of_o capricorn_n for_o than_o it_o be_v late_a before_o he_o rise_v now_o to_o measure_v it_o take_v the_o distance_n from_o 6_o of_o the_o clock_n which_o be_v t_n and_o the_o sun_n rise_v which_o be_v u_o and_o set_v it_o off_o by_o the_o three_o way_n of_o measure_v convert_v the_o degree_n into_o time_n and_o subtract_v that_o time_n from_o 6_o hour_n it_o leave_v the_o length_n of_o the_o forenoon_n which_o double_v be_v the_o length_n of_o the_o short_a day_n as_o in_o quest_n 7._o i_o have_v speak_v to_o that_o purpose_n i_o need_v say_v no_o more_o that_o 7_o the_o question_n be_v light_a sufficient_a i_o may_v do_v a_o example_n of_o what_o be_v before_o do_v in_o a_o south_n latitude_n but_o reason_n give_v that_o the_o same_o which_o the_o south_n pole_n or_o southern_a part_n of_o the_o heaven_n be_v depress_v in_o a_o northern_a latitude_n the_o same_o will_v the_o northern_a part_n of_o the_o heaven_n be_v depress_v in_o a_o latitude_n as_o far_o southerly_a so_o that_o there_o will_v be_v no_o difference_n

a_o great_a circle_n for_o by_o great_a circle_n be_v the_o sphere_n measure_v question_n i._o to_o find_v the_o meridian_n altitude_n of_o the_o sun_n in_o this_o or_o any_o other_o sphere_n m_o g_o e_o be_v that_o part_n of_o the_o heaven_n that_o be_v visible_a the_o other_o half_o invisible_a to_o we_o for_o it_o be_v part_v from_o our_o sight_n by_o the_o earth_n and_o sea_n and_o the_o further_a part_n of_o it_o which_o seem_v to_o mix_v as_o it_o be_v with_o the_o heaven_n we_o call_v the_o horizon_n which_o be_v the_o great_a circle_n m_o e_o for_o it_o be_v a_o great_a circle_n though_o here_o we_o be_v force_v to_o represent_v it_o by_o a_o straight_a line_n m_n be_v the_o south_n point_n of_o the_o horizon_n now_o the_o sun_n meridian_n altitude_n be_v his_o distance_n between_o that_o point_n and_o the_o place_n he_o cut_v the_o meridian_n that_o day_n which_o be_v m_n i_o fix_v your_o compass_n in_o m_n and_o extend_v the_o other_o foot_n to_o i_o and_o apply_v it_o to_o your_o scale_n of_o chord_n and_o as_o many_o degree_n as_o you_o find_v it_o there_o so_o many_o degree_n be_v the_o sun_n high_a when_o he_o be_v upon_o the_o meridian_n that_o day_n which_o be_v the_o thing_n require_v note_v that_o at_o o_o the_o sun_n rise_v at_z p_o it_o be_v 6_o of_o the_o clock_n and_o p_o i_o be_v equal_a to_o ♈_o k_n when_o it_o be_v extend_v to_o a_o great_a circle_n and_o both_o the_o sine_fw-la of_o 90_o deg_fw-la which_o be_v extend_v to_o a_o chord_n must_v be_v the_o chord_n of_o as_o many_o degree_n which_o be_v 6_o hour_n in_o time_n the_o time_n between_o 6_o a_o clock_n and_o 12_o which_o prove_v that_o m_o i_o be_v the_o meridian_n altitude_n of_o the_o sun_n and_o this_o measure_n any_o distance_n from_o the_o meridian_n be_v call_v the_o first_o way_n of_o measure_v question_n ii_o to_o find_v the_o sun_n amplitude_n of_o rise_v and_o set_v fix_v one_o foot_n of_o your_o compass_n in_o the_o place_n of_o the_o sun_n rise_v which_o be_v o_o and_o extend_v the_o other_o foot_n to_o the_o centre_n of_o the_o sphere_n which_o be_v term_v the_o east_n point_n of_o the_o horizon_n and_o this_o distance_n apply_v to_o your_o line_n of_o sines_n if_o you_o have_v any_o but_o if_o you_o have_v no_o line_n of_o sines_n extend_v it_o to_o the_o chord_n of_o the_o same_o arch_n thus_o fix_v your_o compass_n with_o that_o distance_n one_o foot_n in_o the_o meridian_n so_o that_o the_o other_o may_v just_o sweep_v a_o line_n that_o go_v through_o the_o centre_n of_o the_o sphere_n then_o say_v i_o the_o arch_n between_o that_o foot_n of_o your_o compass_n that_o stand_v in_o the_o circle_n and_o the_o place_n where_o this_o line_n you_o sweep_v cut_v the_o circle_n be_v the_o chord_n of_o the_o thing_n require_v and_o will_v be_v the_o same_o number_n of_o degree_n upon_o the_o line_n of_o chord_n as_o o_o r_n will_v be_v upon_o the_o line_n of_o sines_n and_o after_o this_o manner_n be_v the_o chord_n of_o any_o distance_n take_v from_o a_o line_n that_o go_v through_o the_o centre_n of_o the_o sphere_n find_v and_o this_o be_v call_v the_o second_o way_n of_o measure_v i_o find_v that_o the_o sun_n rise_v 20_o deg_fw-la 53_o min._n to_o the_o northwards_o of_o the_o east_n for_o she_o have_v north_n declination_n and_o the_o latitude_n be_v northerly_a or_o set_v so_o much_o to_o the_o northwards_o of_o the_o west_n question_n iii_o to_o find_v the_o sun_n azimuth_n at_o six_o of_o the_o clock_n the_o sun_n azimuth_n at_o 6_o of_o the_o clock_n be_v the_o near_a distance_n between_o the_o sun_n at_o 6_o of_o the_o clock_n and_o the_o east_n and_o west_n azimuth_n which_o be_v p_o z_o now_o if_o you_o mind_v it_o p_o z_o be_v take_v off_o from_o a_o circle_n which_o be_v not_o so_o great_a as_o the_o horizon_n and_o yet_o be_v parallel_n to_o it_o as_o the_o line_n n_o which_o be_v parallel_n to_o the_o line_n m_o e_o and_o as_o many_o degree_n as_o the_o sun_n be_v from_o the_o near_a part_n of_o the_o east_n and_o west_n azimuth_n in_o the_o little_a circle_n so_o many_o he_o be_v from_o it_o if_o a_o azimuth_n where_o draw_v in_o the_o great_a circle_n for_o p_o z_o be_v as_o many_o degree_n in_o the_o little_a circle_n as_o n_o ♈_o be_v in_o the_o great_a one_o now_o because_o your_o scale_n be_v make_v by_o the_o great_a circle_n therefore_o extend_v the_o distance_n take_v from_o the_o lesser_a circle_n to_o the_o measure_n of_o the_o great_a which_o be_v do_v thus_o take_v half_o the_o length_n of_o the_o prick_a line_n which_o be_v z_o w_o and_o fix_v one_o foot_n of_o your_o compass_n in_o the_o centre_n of_o the_o sphere_n describe_v a_o arch_n from_o some_o line_n that_o go_v through_o the_o centre_n of_o the_o sphere_n as_o the_o arch_n m_o l_o n_z then_o set_v the_o distance_n z_o p_o as_o a_o sine_fw-la upon_o that_o arch_n for_o it_o be_v a_o sine_fw-la upon_o that_o arch_n as_o well_o as_o o_o ♈_o be_v a_o sine_fw-la upon_o the_o meridian_n i_o find_v the_o sine_fw-la of_o it_o be_v the_o sine_fw-la of_o the_o arch_n l_o m_o lay_v your_o scale_n from_o the_o centre_n of_o the_o sphere_n by_o l_o and_o draw_v the_o line_n l_o q_o than_o shall_v q_o m_o be_v the_o same_o quantity_n of_o degree_n upon_o the_o great_a circle_n as_o l_o m_n be_v upon_o the_o little_a one_o therefore_o take_v m_n q_o and_o apply_v it_o to_o the_o scale_n of_o chord_n and_o it_o answer_v your_o desire_n and_o thus_o be_v the_o sun_n azimuth_n at_o 6_o of_o the_o clock_n p_o z_o sound_v to_o be_v 8_o deg_fw-la 36_o min._n to_o the_o northwards_o of_o the_o east_n and_o this_o be_v call_v the_o three_o way_n of_o measure_v to_o measure_v any_o distance_n from_o a_o line_n that_o do_v not_o go_v through_o the_o centre_n which_o must_v represent_v a_o small_a circle_n and_o thus_o you_o may_v find_v the_o sun_n azimuth_n at_o any_o time_n of_o the_o day_n question_n iv_o to_o find_v the_o sun_n height_n at_o six_o of_o the_o clock_n the_o sun_n be_v at_o p_o at_o 6_o of_o the_o clock_n fix_v one_o foot_n of_o your_o compass_n in_o p_o and_o extend_v the_o other_o to_o sweep_v the_o horizon_n which_o be_v the_o same_o as_o though_o you_o let_v fall_v the_o perpendicular_a p_o n_z set_v it_o off_o by_o the_o second_o way_n of_o measure_v as_o be_v show_v in_o quest_n 2._o and_o apply_v it_o to_o your_o line_n of_o chord_n and_o the_o reason_n be_v because_o p_o n_z represent_v a_o part_n of_o a_o great_a circle_n and_o so_o be_v to_o be_v understand_v to_o be_v of_o the_o nature_n of_o those_o line_n that_o go_v through_o the_o centre_n of_o the_o sphere_n for_o all_o azimuth_n pass_v through_o the_o zenith_n and_o nadir_n which_o be_v two_o opposite_a point_n i_o find_v the_o sun_n be_v 10_o deg_fw-la 7_o min_fw-mi high_a at_o 6_o of_o the_o clock_n question_n v._o to_o find_v the_o sun_n height_n be_v due_a east_n or_o west_n where_o the_o sun_n parallel_n of_o declination_n cut_v the_o east_n and_o west_n azimuth_n be_v the_o place_n the_o sun_n be_v in_o when_o he_o be_v due_a east_n in_o the_o morning_n for_o you_o see_v he_o be_v then_o over_o the_o point_n of_o east_n in_o the_o horizon_n which_o be_v ♈_o or_o the_o centre_n therefore_o take_v the_o distance_n between_o that_o place_n and_o the_o centre_n which_o be_v s_n ♈_o and_o apply_v it_o to_o the_o line_n of_o sines_n but_o if_o you_o have_v no_o line_n of_o sines_n extend_v it_o to_o a_o chord_n after_o the_o manner_n of_o the_o second_o question_n which_o i_o call_v the_o the_o second_o way_n of_o measure_v for_o it_o be_v the_o distance_n of_o a_o line_n which_o go_v through_o the_o centre_n i_o find_v the_o sun_n height_n be_v due_a east_n or_o west_n be_v 17_o deg_fw-la 25_o m._n note_v that_o the_o same_o height_n that_o the_o sun_n be_v be_v over_o the_o east_n point_n so_o high_a he_o be_v be_v over_o the_o west_n point_n in_o the_o afternoon_n question_n vi_o to_o find_v the_o difference_n of_o ascension_n the_o difference_n of_o ascension_n be_v the_o portion_n of_o time_n that_o be_v between_o the_o sun_n rise_v and_o six_o of_o the_o clock_n if_o the_o day_n be_v long_o than_o the_o night_n the_o sun_n rise_v before_o 6_o but_o if_o short_a after_o 6_o but_o whether_o it_o be_v before_o or_o after_o 6_o that_o he_o rise_v so_o many_o hour_n and_o minute_n as_o it_o be_v from_o 6_o so_o much_o be_v the_o half_a day_n or_o night_n long_o or_o short_a than_o 6_o hour_n from_o whence_o it_o be_v evident_a that_o if_o the_o sun_n rise_v due_a east_n he_o

but_o in_o any_o case_n take_v this_o in_o general_a that_o if_o the_o difference_n of_o ascension_n be_v before_o 6_o of_o the_o clock_n subtract_v it_o if_o after_o 6_o add_v it_o to_o 6_o hour_n and_o you_o have_v the_o time_n of_o sun_n rise_v this_o stand_v to_o good_a reason_n forasmuch_o as_o the_o difference_n of_o ascension_n be_v the_o portion_n of_o time_n that_o the_o sun_n rise_v before_o or_o after_o 6_o of_o the_o clock_n in_o this_o example_n you_o see_v the_o difference_n of_o ascension_n be_v before_o 6_o of_o the_o clock_n 1_o hour_n 5′_n 3_o 15_o we_o will_v omit_v the_o part_n of_o a_o part_n of_o a_o minute_n i_o will_v know_v the_o time_n of_o the_o sun_n rise_v example_n subtract_v the_o difference_n of_o ascension_n 1_o h._n 5_o m._n 3_o 15_o from_o 6_o hour_n 5_o 60_o the_o remainder_n be_v the_o time_n of_o sun_n rise_v 4_o 54_o 12_o 15_o or_o ⅘_n thus_o i_o conclude_v the_o sun_n rise_v at_o 4_o a_o clock_n 54_o min._n ⅘_n if_o you_o have_v a_o desire_n to_o 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add_v there_o you_o subtract_v from_o 6_o hour_n to_o find_v the_o hour_n of_o the_o sun_n be_v due_a east_n or_o add_v to_o 6_o hour_n for_o the_o time_n of_o its_o be_v due_a west_n but_o your_o own_o reason_n if_o you_o look_v well_o on_o the_o scheme_n will_v guide_v you_o to_o know_v this_o and_o also_o to_o know_v that_o it_o be_v useless_a in_o such_o case_n for_o than_o he_o be_v not_o above_o the_o horizon_n latitude_n 50_o deg_fw-la 0_o min._n declination_n 13_o deg_fw-la 15_o min._n i_o demand_v the_o continuance_n of_o twilight_n as_o i_o have_v note_v before_o the_o sun_n be_v account_v 17_o deg_fw-la under_o the_o horizon_n when_o the_o day_n break_v therefore_o in_o the_o follow_a scheme_n let_v 17_o i_o be_v a_o arch_a parallel_n to_o the_o horizon_n 17_o deg_fw-la under_o it_o let_v d_o b_o c_o at_fw-fr be_v a_o azimuth_n cut_v the_o aequinoctial_a and_o the_o line_n of_o 17_o deg_fw-la in_o the_o place_n of_o their_o intersection_n which_o be_v at_o c_o then_o in_o the_o triangle_n r_o b_o c_o right_o angle_v at_o b_o you_o have_v give_v b_o c_o 17_o deg_fw-la the_o angle_n b_o r_o c_o the_o compliment_n of_o the_o pole_n elevation_n 40_o deg_fw-la to_o find_v c_o r_o the_o continuance_n of_o twilight_n for_o c_o r_o and_o b_o you_o be_v equal_a i_o leave_v it_o to_o your_o own_o practice_n i_o find_v the_o continuance_n of_o twilight_n to_o be_v 27_o deg_fw-la 4_o min._n which_o convert_v into_o time_n be_v 1_o h._n 48_o min._n 4_o 13_o near_a so_o i_o conclude_v that_o between_o the_o day_n break_v and_o sun_n rise_v it_o be_v 1_o h._n 48_o min._n 4_o 15_o which_o be_v u._fw-mi b_o now_o if_o you_o add_v this_o to_o the_o difference_n of_o ascension_n before_o find_v b_o 6_o which_o be_v 1_o h._n 5_o min._n 3_o 15_o of_o a_o minute_n i_o omit_v the_o small_a fraction_n you_o have_v the_o time_n between_o break_n of_o day_n and_o 6_o of_o the_o clock_n which_o may_v be_v term_v u._fw-mi b_o 6_o 2_o h._n 53_o min._n 7_o 15._o and_o because_o the_o day_n break_v so_o much_o before_o 6_o of_o the_o clock_n if_o you_o subtract_v it_o from_o 6_o hour_n you_o have_v the_o hour_n and_o minute_n of_o day_n break_v which_o be_v at_o 3_o of_o the_o clock_n 6_o min._n ●8_o 15._o add_v it_o to_o 6_o of_o the_o clock_n and_o you_o have_v the_o time_n of_o twilight_n end_v which_o be_v at_o 8_o h._n 53_o min._n 7_o 15._o to_o find_v the_o sun_n place_n and_o right_a ascension_n provide_v the_o latitude_n and_o declination_n be_v give_v latitude_n 50_o

in_o the_o work_n at_o all_o and_o indeed_o my_o desire_n to_o be_v brief_a make_v i_o omit_v thing_n that_o i_o think_v may_v be_v understand_v without_o treat_v of_o they_o i_o will_v only_o touch_v upon_o a_o example_n in_o a_o sphere_n which_o have_v south_n declination_n latitude_n northerly_a 50_o deg_fw-la 00_o min._n declination_n 13_o deg_fw-la 15_o min._n southerly_a also_o if_o you_o subtract_v this_o amplitude_n v_o ♈_o from_o ♈_o h_o 90_o deg_fw-la the_o remainder_n be_v the_o sun_n azimuth_n from_o the_o south_n v_o h_n or_o if_o you_o add_v v_z ♈_o to_o ♈_o a_o 90_o deg_fw-la it_o be_v v._o a_o the_o sun_n azimuth_n of_o rise_v from_o the_o north_n forasmuch_o as_o five_o a_o be_v as_o much_o above_o 90_o deg_fw-la as_o v_z h_n want_v of_o it_o the_o same_o be_v to_o be_v understand_v in_o any_o sphere_n that_o the_o amplitude_n and_o azimuth_n of_o the_o sun_n be_v compliment_n one_o of_o a_o other_o to_o 90_o deg_fw-la in_o that_o quarter_n when_o the_o sun_n declination_n be_v southerly_a in_o any_o northern_a latitude_n the_o day_n be_v not_o so_o long_o as_o the_o night_n so_o that_o the_o sun_n can_v be_v up_o at_o 6_o of_o the_o clock_n which_o be_v at_o r_n therefore_o the_o sun_n azimuth_n at_o 6_o of_o the_o clock_n be_v of_o no_o use_n neither_o be_v he_o up_o when_o he_o pass_v the_o east_n point_n of_o the_o horizon_n which_o be_v at_o p_o so_o that_o you_o can_v take_v his_o height_n but_o you_o may_v measure_v how_o far_o he_o be_v under_o the_o horizon_n at_o either_o of_o those_o time_n or_o you_o may_v find_v his_o true_a azimuth_n at_o 6_o which_o be_v of_o no_o value_n to_o we_o that_o be_v seaman_n because_o we_o can_v have_v a_o magnetical_a azimuth_n they_o be_v measure_v as_o before_o the_o difference_n of_o ascension_n be_v here_o after_o 6_o of_o the_o clock_n as_o much_o as_o it_o be_v before_o 6_o in_o the_o last_o example_n and_o the_o reason_n be_v because_o the_o latitude_n be_v the_o same_o and_o the_o 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it_o into_o time_n and_o subtract_v it_o from_o 6_o of_o the_o clock_n and_o it_o leave_v the_o time_n of_o day_n break_v namely_o the_o time_n in_o the_o morning_n that_o the_o sun_n be_v in_o p_o you_o subtract_v because_o the_o day_n break_v so_o long_o before_o 6_o of_o the_o clock_n if_o it_o where_o so_o that_o the_o sun_n be_v in_o the_o tropic_a of_o capricorn_n you_o must_v take_v the_o distance_n s_o q._n you_o see_v the_o sun_n be_v pass_v the_o hour_n of_o 6_o before_o it_o be_v break_v of_o day_n now_o in_o this_o case_n you_o must_v add_v whereas_o before_o you_o subtract_v for_o the_o continuance_n of_o twilight_n it_o be_v measure_v as_o before_o from_o the_o place_n where_o the_o parallel_n of_o the_o sun_n declination_n cut_v the_o circle_n of_o 17_o deg_fw-la to_o the_o place_n where_o it_o cut_v the_o horizon_n convert_v it_o into_o time_n and_o set_v it_o down_o in_o this_o example_n it_o be_v p_o v._n what_o i_o have_v not_o mention_v here_o i_o have_v give_v sufficient_a instruction_n about_o in_o the_o other_o example_n before_o this_o latitude_n 51_o deg_fw-la 30_o min._n northerly_a declination_n 11_o deg_fw-la 10_o min._n northerly_a i_o demand_v the_o sun_n place_n and_o right_a ascension_n before_o we_o can_v find_v the_o sun_n place_n in_o the_o ecliptic_a you_o be_v to_o consider_v that_o the_o ecliptic_a be_v divide_v into_o 12_o equal_a part_n by_o the_o 12_o sign_n six_o of_o these_o sign_n divide_v that_o half_a of_o the_o ecliptic_a which_o be_v to_o the_o northwards_o of_o the_o aequinoctial_a and_o be_v call_v northern_a sign_n and_o the_o other_o 6_o divide_v the_o half_a that_o be_v to_o the_o southwaad_n of_o the_o aequinoctial_a and_o be_v call_v southern_a sign_n as_o i_o have_v set_v they_o down_o in_o this_o book_n before_o with_o their_o name_n and_o month_n to_o their_o character_n and_o have_v set_v the_o northern_a sign_n by_o themselves_o and_o the_o southern_a sign_n by_o themselves_o this_o plain_a superficies_n can_v show_v but_o one_o part_n of_o the_o globous_a body_n but_o you_o must_v know_v it_o be_v round_o which_o make_v the_o ecliptic_a to_o be_v divide_v on_o both_o side_n from_o ♈_o to_o ♋_o be_v 90_o deg_fw-la from_o ♋_o to_o ♎_o be_v 90_o deg_fw-la from_o ♎_o to_o ♑_o be_v 90_o deg_fw-la and_o from_o ♑_o to_o ♈_o be_v 90_o deg_fw-la every_o one_o of_o these_o quarter_n contain_v 3_o sign_n the_o ecliptic_a be_v thus_o divide_v into_o sign_n we_o may_v find_v the_o sun_n place_n and_o right_a ascension_n the_o sun_n place_n in_o the_o ecliptic_a be_v the_o near_a distance_n between_o the_o next_o aequinoctial_a point_n and_o the_o sun_n in_o the_o ecliptic_a by_o aequinoctial_a point_n be_v mean_v ♈_o and_o ♎_o the_o two_o point_n of_o intersection_n that_o the_o aequinoctial_a and_o the_o ecliptic_a make_n now_o in_o this_o case_n the_o sun_n must_v be_v near_a the_o equinoctial_a point_n at_o ♈_o because_o the_o month_n be_v belong_v to_o a_o sign_n near_o ♈_o than_o ♎_o therefore_o fix_v your_o compass_n in_o the_o point_n of_o ♈_o and_o extend_v the_o other_o foot_n to_o the_o sun_n in_o the_o ecliptic_a which_o be_v i_o and_o apply_v it_o to_o the_o line_n of_o sines_n or_o if_o you_o have_v no_o line_n of_o sines_n convert_v it_o to_o a_o chord_n by_o the_o second_o way_n of_o measure_v and_o as_o many_o degree_n as_o it_o be_v so_o far_o be_v the_o sun_n distant_a from_o the_o near_a aequinoctial_a point_n if_o it_o exceed_v 30_o deg_fw-la the_o sun_n must_v be_v in_o that_o degree_n of_o ♉_o that_o be_v above_o 30_o deg_fw-la if_o it_o exceed_v 60_o deg_fw-la the_o sun_n must_v be_v in_o that_o degree_n of_o ♊_o above_o 60_o but_o here_o i_o find_v it_o in_o less_o than_o 30_o namely_o 29_o deg_fw-la 3_o min._n therefore_o i_o conclude_v the_o sun_n be_v in_o 20_o deg_fw-la 3_o min._n of_o ♈_o but_o suppose_v it_o be_v time_n of_o year_n that_o the_o sun_n be_v return_v from_o the_o tropic_a towards_o the_o aequinoctial_a and_o be_v the_o same_o declination_n then_o will_v the_o sun_n place_n be_v the_o same_o from_o enter_v into_o ♎_o that_o it_o now_o be_v in_o ♈_o namely_o in_o 57_o min._n of_o ♍_o which_o want_v 29_o deg_fw-la 3_o min._n of_o enter_v into_o ♎_o thus_o much_o for_o the_o sun_n place_n the_o sun_n right_a ascension_n be_v measure_v from_o the_o place_n where_o the_o sun_n parallel_n of_o declination_n cut_v the_o ecliptic_a to_o 6_o of_o the_o clock_n which_o be_v i_o 6_o set_v it_o off_o by_o the_o three_o way_n of_o measure_v to_o extend_v it_o to_o a_o great_a circle_n for_o the_o sine_fw-la of_o i_o

the_o difference_n of_o latitude_n in_o the_o whole_a run_v 13_o league_n 3_o 10_o if_o you_o have_v west_n longitude_n you_o must_v have_v subtract_v thus_o likewise_o and_o that_o which_o be_v great_a the_o remainder_n belong_v to_o of_o a_o reckon_a from_o what_o have_v be_v already_o show_v you_o understand_v that_o if_o the_o latitude_n of_o two_o place_n be_v know_v and_o the_o difference_n of_o longitude_n between_o they_o you_o may_v find_v the_o bear_n of_o they_o one_o from_o the_o other_o their_o distance_n asunder_o or_o any_o thing_n you_o desire_v and_o this_o be_v all_o so_o plain_a that_o if_o i_o set_v from_o a_o place_n and_o be_o bind_v to_o a_o place_n who_o latitude_n be_v know_v and_o the_o difference_n of_o longitude_n also_o know_v between_o they_o and_o keep_v a_o reckon_n of_o the_o departure_n both_o east_n and_o west_n that_o i_o make_v set_v they_o down_o in_o two_o distinct_a column_n it_o be_v but_o subtract_v one_o from_o the_o other_o and_o the_o remainder_n will_v be_v the_o east_n or_o west_n longitude_n that_o i_o have_v make_v that_o of_o the_o two_o which_o be_v most_o also_o if_o i_o know_v what_o latitude_n i_o be_o in_o and_o what_o latitude_n the_o place_n lie_v in_o it_o be_v but_o subtract_v the_o lesser_a from_o the_o great_a and_o the_o remainder_n will_v be_v the_o difference_n of_o latitude_n between_o your_o ship_n and_o that_o place_n provide_v the_o latitude_n be_v both_o one_o way_n also_o subtract_v the_o difference_n of_o longitude_n that_o you_o have_v make_v provide_v that_o it_o be_v that_o way_n which_o shorten_v your_o longitude_n between_o the_o place_n you_o set_v from_o and_o be_v bind_v to_o from_o the_o whole_a difference_n of_o longitude_n between_o the_o two_o place_n and_o the_o remainder_n will_v be_v what_o be_v still_o between_o you_o and_o the_o place_n you_o be_v bind_v to_o but_o if_o your_o departure_n which_o you_o have_v make_v have_v increase_v the_o difference_n of_o longitude_n between_o the_o place_n you_o set_v from_o and_o be_v bind_v to_o add_v the_o remainder_n after_o your_o subtract_v the_o column_n one_o from_o the_o other_o to_o the_o whole_a difference_n of_o longitude_n between_o the_o place_n the_o like_a for_o latitude_n example_n in_o the_o reckon_a follow_v suppose_v the_o island_n of_o ditiatha_n lie_v so_o that_o it_o have_v be_v find_v to_o have_v 950_o league_n departure_n west_n from_o the_o meridian_n of_o the_o lizard_n according_a to_o the_o course_n that_o be_v ordinary_o sail_v by_o plano_n the_o latitude_n of_o it_o be_v 16_o deg_fw-la 16_o min._n north_n latitude_n the_o lizard_n lie_v in_o the_o latitude_n of_o 50_o deg_fw-la 00_o min._n now_o upon_o some_o occasion_n that_o fall_v in_o the_o term_n of_o our_o voyage_n namely_o the_o 29_o of_o january_n on_o tuesday_n the_o captain_n demand_v of_o i_o what_o distance_n ditiatha_n be_v from_o i_o by_o plano_n how_o it_o bear_v what_o league_n of_o departure_n i_o have_v to_o it_o and_o the_o like_a i_o look_v in_o my_o reckon_a and_o i_o find_v in_o the_o west_n column_n 434_o league_n i_o look_v in_o the_o east_n column_n and_o see_v 60_o league_n i_o subtract_v 60_o my_o whole_a east_n column_n from_o 434_o the_o whole_a west_n column_n and_o the_o remainder_n be_v 374_o league_n which_o signify_v the_o ship_n have_v depart_v from_o the_o meridian_n of_o the_o lizard_n 374_o league_n west_n for_o the_o west_n column_n be_v great_a subtract_v this_o west_n departure_n 374_o league_n from_o 950_o the_o whole_a departure_n and_o i_o find_v there_o be_v still_o want_v 576_o league_n this_o 576_o league_n be_v the_o departure_n that_o be_v from_o the_o meridian_n that_o my_o ship_n be_v in_o and_o ditiatha_n subtract_v also_o the_o latitude_n one_o from_o the_o other_o namely_o the_o latitude_n your_o ship_n be_v in_o and_o the_o latitude_n of_o ditiatha_n and_o the_o remainder_n be_v the_o difference_n of_o latitude_n in_o degree_n and_o minute_n between_o the_o ship_n and_o the_o place_v you_o be_v bind_v to_o which_o in_o this_o example_n i_o find_v to_o be_v 6_o degree_n 24_o minute_n take_v the_o latitude_n out_o of_o the_o column_n of_o latitude_n for_o that_o day_n in_o the_o reckon_a and_o you_o will_v find_v it_o so_o if_o you_o subtract_v 16_o deg_fw-la 16_o min._n from_o it_o thus_o you_o have_v the_o difference_n of_o latitude_n between_o you_o that_o day_n and_o your_o port_n and_o the_o departure_n that_o the_o port_n have_v from_o the_o meridian_n that_o you_o be_v in_o that_o day_n give_v you_o to_o find_v the_o thing_n demand_v i_o will_v not_o work_v it_o for_o it_o have_v beeen_n show_v sufficient_o already_o i_o have_v here_o follow_v set_v down_o a_o reckon_a and_o afterward_o how_o i_o work_v it_o and_o last_o the_o reason_n that_o make_v i_o use_v this_o way_n of_o keep_v my_o whole_a reckon_a in_o the_o last_o line_n so_o that_o i_o be_o not_o trouble_v to_o add_v it_o up_o when_o i_o give_v account_n of_o it_o january_n the_o 3_o anno_fw-la dom._n 1655_o we_o depart_v from_o the_o lizard_n lie_v in_o the_o latitude_n of_o 50_o d._n 00_o m._n be_v bind_v for_o ditiatha_n which_o lie_v in_o the_o latitude_n of_o 16_o d._n 16_o m._n it_o have_v west_n departure_n from_o the_o meridian_n of_o the_o lizard_n 950_o league_n according_a to_o the_o course_n which_o we_o then_o steer_v at_o 4_o of_o the_o clock_n the_o lizard_n bear_v from_o we_o n_z n_o e_o about_z 6_o league_n distance_n by_o estimation_n every_o day_n at_o sea_n you_o set_v down_o at_o noon_n that_o 24_o hour_n work_n now_o i_o advise_v you_o to_o set_v it_o down_o as_o it_o be_v here_o in_o the_o first_o column_n on_o the_o left_a hand_n i_o set_v the_o day_n of_o the_o month_n in_o the_o next_o the_o day_n of_o the_o week_n in_o the_o three_o the_o latitude_n i_o be_o in_o by_o dead_a reckon_a or_o by_o observation_n only_o i_o make_v a_o distinction_n between_o they_o by_o the_o letter_n e_o which_o stand_v for_o estimation_n and_o be_v set_v down_o only_o when_o i_o do_v not_o observe_v that_o so_o you_o may_v know_v where_o to_o begin_v to_o correct_v in_o the_o 4_o the_o column_n i_o set_v down_o the_o ea_n in_o the_o five_o column_n the_o westing_n the_o manner_n that_o i_o set_v my_o ea_n and_o westing_n down_o be_v thus_o every_o day_n there_o be_v the_o ship_n course_n mind_v and_o a_o observation_n whereby_o you_o have_v the_o difference_n of_o latitude_n and_o course_n to_o find_v the_o departure_n or_o else_o if_o you_o can_v observe_v you_o have_v the_o distance_n run_v guess_v at_o and_o the_o course_n to_o help_v your_o d._n m._n week_n day_n latitude_n dep._n e._n in_o leag_n dep._n w._n in_o leag_n deg_fw-la min._n 4_o friday_n 49_o 00_o 000_o 021_o 5_o saturday_n 47_o 55_o 000_o 059_o 6_o sunday_n 46_o 20_o 000_o 085_o 7_o monday_n 45_o 00_o 000_o 088_o 8_o tuesday_n 43_o e_z 54_o 000_o 108_o 9_o wednesday_n 42_o 4_o 000_o 147_o 10_o thursday_n 41_o e_z 19_o 000_o 262_o 11_o friday_n 41_o 10_o 000_o 264_o 12_o saturday_n 40_o 46_o 000_o 274_o 13_o sunday_n 40_o 45_o 000_o 178_o 14_o monday_n 39_o e_z 49_o 000_o 179_o 15_o tuesday_n 37_o e_z 24_o 000_o 200_o 16_o wednesday_n 35_o 59_o 000_o 229_o 17_o thursday_n 34_o 42_o 000_o 249_o 18_o friday_n 33_o 15_o 000_o 278_o 19_o saturday_n 31_o 15_o 000_o 322_o 20_o sunday_n 29_o 5_o 000_o 364_o 21_o monday_n 28_o e_z 20_o 000_o 400_o 22_o tuesday_n 27_o 5_o 012_o 400_o 23_o wednesday_n 27_o 30_o 022_o 400_o 24_o thursday_n 27_o 22_o 031_o 400_o 25_o friday_n 26_o e_z 49_o 049_o 400_o 26_o saturday_n 25_o 36_o 060_o 400_o 27_o sunday_n 24_o 31_o 060_o 406_o 28_o monday_n 23_o 28_o 060_o 406_o 29_o tuesday_n 22_o e_z 40_o 060_o 434_o 30_o wednesday_n 22_o 08_o 060_o 434_o 31_o thursday_n 21_o 53_o 060_o 444_o february_n 1_o friday_n 21_o 40_o 060_o 450_o 2_o saturday_n 20_o 47_o 060_o 456_o 3_o sunday_n 19_o 22_o 060_o 460_o 4_o monday_n 19_o 53_o 060_o 472_o 5_o tuesday_n 18_o 23_o 060_o 485_o d._n m._n week_n day_n latitude_n dep._n e._n in_o leag_n dep._n w._n in_o leag_n deg_fw-la min._n 6_o wednesday_n 17_o 19_o 060_o 518_o 7_o thursday_n 16_o 47_o 060_o 556_o 8_o friday_n 16_o 54_o 060_o 606_o 9_o saturday_n 16_o 29_o 060_o 643_o 10_o sunday_n 16_o 19_o 060_o 678_o 11_o monday_n 16_o 21_o 060_o 726_o 12_o tuesday_n 16_o 28_o 060_o 784_o 13_o wednesday_n 16_o 35_o 060_o 840_o 14_o thursday_n 16_o 27_o 060_o 889_o 15_o friday_n 16_o 24_o 060_o 929_o 16_o saturday_n 16_o 2_o 060_o 973_o 17_o sunday_n 16_o 44_o 060_o 1003_o guess_n be_v the_o log-line_n every_o 2_o hour_n your_o course_n and_o distance_n be_v set_v

down_o upon_o the_o logboard_n every_o 2_o hour_n whereby_o you_o may_v see_v it_o and_o work_v it_o every_o 24_o hour_n to_o find_v the_o departure_n and_o difference_n of_o latitude_n now_o whatsoever_o i_o find_v the_o departure_n to_o be_v i_o add_v it_o from_o the_o first_o day_n all_o along_o thus_o the_o departure_n when_o i_o set_v the_o lizard_n which_o be_v n_n n_o e_o 6_o league_n off_o be_v 2_o league_n west_n i_o keep_v mind_n of_o that_o till_o the_o next_o day_n at_o noon_n and_o i_o find_v what_o departure_n i_o have_v make_v from_o the_o meridian_n that_o i_o be_v in_o the_o day_n before_o at_o noon_n by_o the_o thing_n i_o have_v give_v i_o and_o here_o i_o find_v it_o be_v 19_o league_n i_o add_v it_o to_o my_o departure_n from_o the_o meridian_n west_n yesterday_o 2_o league_n and_o it_o make_v my_o whole_a departure_n west_n 21_o league_n again_o the_o next_o day_n at_o noon_n i_o work_v my_o ship_n travis_n as_o have_v be_v show_v and_o i_o find_v that_o she_o have_v depart_v from_o the_o meridian_n she_o be_v in_o yesterday_o 38_o league_n west_n which_o i_o add_v to_o what_o i_o have_v before_o which_o be_v 21_o and_o it_o make_v 59_o league_n and_o thus_o i_o go_v forward_o add_v my_o last_o day_n departure_n in_o its_o true_a column_n to_o all_o the_o rest_n which_o be_v in_o one_o sum_n and_o by_o this_o mean_v the_o last_o line_n be_v the_o whole_a reckon_a 21_o 38_o 59_o in_o the_o east_n column_n i_o set_v cipher_n to_o fill_v it_o up_o till_o i_o have_v some_o east_n departure_n to_o put_v in_o it_o and_o as_o that_o increase_v so_o i_o add_v it_o as_o the_o other_o every_o day_n also_o i_o carry_v the_o west_n departure_n along_o in_o its_o full_a number_n of_o league_n in_o the_o same_o line_n without_o increase_n or_o decrease_v till_o such_o time_n as_o i_o have_v more_o to_o increase_v it_o and_o then_o i_o increase_v that_o and_o carry_v the_o whole_a ea_n with_o it_o in_o the_o same_o line_n and_o thus_o you_o have_v need_n to_o look_v upon_o nothing_o but_o the_o last_o line_n to_o resolve_v you_o any_o thing_n that_o you_o desire_v either_o of_o your_o course_n make_v good_a since_o you_o set_v out_o your_o distance_n upon_o a_o straight_a line_n that_o you_o have_v fail_v your_o port_n bear_v from_o you_o what_o departure_n be_v yet_o between_o you_o and_o your_o port_n your_o distance_n to_o it_o upon_o a_o straight_a line_n for_o there_o you_o have_v your_o whole_a westing_n and_o your_o whole_a ea_n and_o the_o latitude_n you_o be_v in_o as_o also_o the_o latitude_n of_o the_o place_n you_o be_v bind_v to_o whereby_o as_o i_o have_v former_o show_v you_o may_v find_v they_o if_o there_o be_v longitude_n but_o one_o way_n you_o will_v see_v nothing_o but_o cipher_n in_o the_o other_o column_n this_o way_n you_o see_v be_v do_v without_o a_o plat._n i_o hold_v a_o plat_v to_o be_v necessary_a only_o to_o show_v what_o danger_n lie_v in_o your_o way_n that_o so_o you_o may_v shape_v a_o course_n clear_a by_o it_o and_o i_o shall_v use_v a_o plat_v for_o nothing_o else_o except_o it_o be_v for_o coast_v where_o it_o be_v real_o useful_a i_o common_o set_v down_o the_o ea_n or_o westing_n between_o the_o place_n i_o set_v and_o the_o place_n i_o be_o bind_v to_o at_o the_o begin_n of_o my_o reckon_n as_o also_o the_o latitude_n of_o each_o place_n as_o i_o have_v do_v here_o you_o may_v ask_v why_o i_o do_v not_o set_v down_o the_o course_n that_o i_o make_v good_a every_o day_n indeed_o that_o be_v not_o unnecessary_a but_o the_o reason_n why_o i_o omit_v it_o be_v first_o because_o i_o find_v it_o of_o little_a use_n in_o my_o reckon_a and_o second_o i_o find_v it_o can_v be_v better_o express_v in_o a_o journal_n which_o be_v keep_v with_o my_o reckon_a and_o indeed_o there_o i_o set_v it_o with_o the_o wind_n and_o the_o reason_n for_o steer_v upon_o such_o course_n but_o i_o leave_v every_o one_o to_o their_o own_o judgement_n for_o that_o as_o also_o for_o distance_n and_o wind_n for_o difference_n and_o variation_n it_o will_v have_v be_v necessary_a here_o to_o have_v set_v down_o some_o table_n to_o have_v work_v triangle_n by_o for_o as_o i_o have_v say_v sometime_o in_o 24_o hour_n you_o have_v a_o travis_n of_o 4_o or_o 5_o several_a course_n and_o to_o work_v they_o this_o way_n may_v seem_v tedious_a i_o commend_v you_o to_o my_o father_n practice_n where_o there_o be_v as_o good_a table_n as_o can_v be_v to_o every_o degree_n of_o the_o compass_n its_o use_n be_v easy_a and_o work_n to_o the_o ten_o part_n of_o a_o mile_n or_o league_n concern_v the_o variation_n of_o the_o compass_n there_o be_v always_o two_o thing_n give_v to_o find_v the_o variation_n of_o the_o compass_n that_o be_v the_o true_a amplitude_n of_o the_o sun_n rise_v and_o the_o magnetical_a amplitude_n of_o the_o sun_n rise_v or_o set_v the_o true_a amplitude_n of_o the_o sun_n rise_v be_v as_o i_o have_v say_v before_o in_o another_o place_n the_o true_a and_o absolute_a quantity_n of_o degree_n that_o the_o sun_n rise_v from_o the_o east_n either_o northwards_o or_o southwards_o or_o set_v from_o the_o west_n and_o be_v find_v as_o i_o have_v before_o show_v in_o the_o use_n of_o the_o sphere_n the_o magnetical_a amplitude_n of_o the_o sun_n be_v what_o the_o sun_n rise_v from_o the_o east_n or_o set_v from_o the_o west_n by_o the_o compass_n now_o because_o the_o first_o give_v the_o truth_n how_o far_o the_o sun_n rise_v from_o the_o east_n or_o set_v from_o the_o west_n therefore_o whatsoever_o difference_n there_o be_v between_o they_o so_o much_o be_v the_o variation_n as_o now_o suppose_v i_o find_v in_o a_o certain_a latitude_n such_o a_o day_n of_o the_o month_n by_o the_o sphere_n that_o the_o sun_n rise_v to_o the_o northwards_o of_o the_o east_n 17_o degree_n that_o be_v the_o true_a amplitude_n but_o i_o observe_v the_o sun_n at_o her_o rise_n with_o a_o azimuth_n compass_n which_o be_v make_v for_o that_o purpose_n and_o find_v that_o she_o rise_v but_o east_n 10_o degree_n northerly_a then_o i_o conclude_v the_o variation_n be_v 7_o deg_fw-la 0_o min._n or_o the_o compass_n be_v false_a so_o much_o so_o that_o whereas_o if_o i_o direct_v my_o course_n east_n 10_o degree_n northerly_a by_o the_o compass_n i_o do_v not_o go_v on_o that_o course_n but_o i_o go_v east_n and_o by_o north_n 5_o deg_fw-la 45_o min._n northerly_a which_o be_v just_a 7_o d._n from_o my_o expectation_n or_o east_n 17_o deg_fw-la northerly_a the_o true_a amplitude_n now_o that_o be_v a_o gross_a error_n and_o in_o long_a run_n may_v deceive_v a_o man_n much_o and_o perhaps_o be_v a_o mean_n to_o lose_v a_o ship_n when_o one_o little_a think_v of_o it_o and_o therefore_o it_o ought_v to_o be_v look_v to_o a_o azimuth_n compass_n be_v no_o other_o in_o effect_n but_o a_o compass_n fit_v for_o the_o exact_a take_n of_o the_o sun_n at_o her_o rise_n or_o set_v or_o upon_o other_o certain_a time_n of_o the_o day_n as_o you_o may_v have_v occasion_n in_o like_a manner_n you_o may_v find_v the_o variation_n of_o the_o compass_n at_o other_o time_n by_o take_v the_o sun_n azimuth_n at_o any_o time_n of_o the_o day_n example_n suppose_v i_o be_v in_o the_o latitude_n of_o 33_o deg_fw-la 20_o min._n northerly_a and_o upon_o the_o 8_o the_o day_n of_o november_n the_o sun_n declination_n be_v southerly_a 19_o deg_fw-la 20_o min._n i_o demand_v the_o sun_n azimuth_n at_o 8_o of_o the_o clock_n the_o sun_n azimuth_n at_o her_o rise_n as_o i_o have_v show_v be_v the_o compliment_n of_o the_o sun_n amplitude_n but_o after_o the_o sun_n be_v up_o it_o may_v be_v also_o the_o distance_n of_o the_o sun_n from_o the_o east_n and_o west_n azimuth_n now_o in_o this_o proposition_n you_o desire_v to_o know_v how_o many_o degree_n the_o sun_n be_v from_o the_o east_n and_o west_n azimuth_n which_o be_v that_o part_n of_o the_o heaven_n that_o be_v distant_a from_o the_o sun_n parallel_n to_o the_o horizon_n over_o the_o east_n point_v of_o it_o or_o if_o it_o have_v be_v at_o 4_o of_o the_o clock_n in_o the_o afternoon_n it_o will_v have_v be_v require_v from_o the_o west_n point_n for_o the_o resolve_v this_o question_n project_v a_o sphere_n as_o have_v be_v teach_v for_o the_o latitude_n propose_v with_o the_o parallel_n of_o the_o sun_n declination_n draw_v as_o it_o be_v give_v divide_v this_o parallel_n of_o declination_n into_o the_o hour_n of_o the_o day_n from_o 6_o to_o 12_o or_o which_o serve_v from_o 12_o to_o 6_o in_o the_o afternoon_n the_o way_n to_o divide_v it_o be_v thus_o from_o 6_o of_o the_o

clock_n set_v off_o 15_o degree_n by_o the_o three_o way_n of_o measure_v which_o will_v be_v 7_o than_o because_o 30_o degree_n be_v two_o hour_n in_o time_n next_o set_v off_o 30_o degree_n by_o the_o three_o way_n of_o measure_v from_o 6_o and_o it_o make_v 8_o a_o clock_n then_o take_v 45_o deg_fw-la which_o be_v three_o hour_n and_o it_o make_v 9_o a_o clock_n than_o 60_o deg_fw-la for_o 10_o a_o clock_n than_o 75_o deg_fw-la for_o 11_o a_o clock_n and_o then_o 90_o deg_fw-la which_o will_v just_o fall_v in_o the_o place_n where_o the_o sun_n come_v to_o the_o meridian_n for_o 12_o a_o clock_n thus_o you_o divide_v the_o parallel_n of_o the_o sun_n declination_n into_o hour_n as_o you_o may_v see_v in_o the_o sphere_n here_o follow_v it_o be_v thus_o divide_v the_o sun_n azimuth_n at_o 8_o of_o the_o clock_n be_v 8_o s_o take_v off_o by_o the_o three_o way_n of_o measure_v i_o find_v it_o to_o be_v 33_o deg_fw-la 0_o min._n by_o the_o scale_n so_o it_o be_v certain_a that_o the_o sun_n shall_v be_v just_a 33_o deg_fw-la 0_o min._n to_o the_o southwards_o of_o the_o east_n at_o 8_o of_o the_o clock_n than_o i_o will_v see_v how_o high_a he_o shall_v be_v at_o that_o time_n and_o i_o find_v he_o to_o be_v 13_o deg_fw-la 50_o min._n equal_a to_o s_o ♈_o take_v off_o s_o ♈_o by_o the_o second_o way_n of_o measure_v i_o will_v observe_v the_o sun_n till_o i_o find_v he_o at_o that_o height_n and_o then_o i_o know_v it_o be_v 8_o of_o the_o clock_n see_v by_o your_o azimuth_n compass_n whether_o he_o be_v 33_o deg_fw-la 0_o min._n from_o the_o east_n or_o no_o and_o if_o not_o what_o it_o differ_v so_o much_o be_v the_o variation_n of_o the_o compass_n i_o have_v wrought_v this_o example_n no_o near_o than_o the_o plain_a scale_n work_v it_o which_o possible_o may_v be_v 15_o min._n or_o half_a a_o degree_n of_o the_o compass_n out_o of_o the_o way_n but_o that_o be_v no_o considerable_a error_n in_o a_o course_n which_o be_v the_o thing_n we_o here_o use_v it_o for_o the_o same_o may_v be_v do_v at_o any_o time_n of_o the_o day_n as_o latitude_n 32_o deg_fw-la 20_o min._n north_n declination_n 19_o deg_fw-la 20_o min._n south_n suppose_v it_o be_v cloudy_a but_o at_o some_o time_n the_o sun_n break_v out_o so_o that_o i_o have_v a_o opportunity_n to_o take_v his_o height_n with_o my_o quadrant_n and_o also_o his_o magnetical_a azimuth_n with_o my_o azimuth_n compass_n now_o i_o find_v his_o height_n to_o be_v r_o t_o equal_a to_o n_n p_o and_o the_o azimuth_n at_o that_o time_n be_v n_n t_o it_o be_v draw_v parallel_n to_o the_o horizon_n this_o n_o t_o set_v off_o by_o the_o three_o way_n of_o measure_v and_o so_o much_o as_o it_o come_v to_o so_o much_o be_v the_o true_a azimuth_n of_o the_o sun_n from_o the_o east_n towards_o the_o south_n take_v your_o magnetical_a azimuth_n at_o the_o same_o time_n and_o as_o much_o as_o they_o differ_v so_o much_o be_v the_o variation_n and_o thus_o much_o for_o the_o variation_n of_o the_o compass_n when_o a_o man_n observe_v the_o sun_n with_o a_o quadrant_n which_o be_v our_o usual_a instrument_n he_o take_v the_o upper_a edge_n which_o be_v to_o the_o northwards_o in_o this_o latitude_n suppose_v then_o i_o set_v from_o the_o lizard_n and_o be_o bind_v to_o barbadoes_n i_o make_v observation_n of_o the_o sun_n as_o often_o as_o i_o can_v all_o the_o way_n till_o i_o bring_v the_o sun_n to_o the_o zenith_n after_o i_o pass_v the_o zenith_n the_o edge_n of_o the_o sun_n that_o be_v high_o be_v low_a now_o he_o that_o do_v not_o consider_v this_o lose_v the_o breadth_n or_o diameter_n of_o the_o sun_n so_o that_o your_o observation_n may_v differ_v from_o your_o expectation_n 30_o mile_n which_o be_v enough_o to_o miss_v a_o island_n therefore_o i_o advise_v you_o always_o to_o allow_v the_o sun_n diameter_n which_o some_o count_v 30_o min._n to_o every_o observation_n you_o make_v in_o place_n where_o the_o sun_n be_v to_o the_o northwards_o of_o you_o that_o be_v make_v your_o meridian_n altitude_n 30_o min._n less_o than_o it_o be_v which_o be_v the_o altitude_n of_o the_o low_a edge_n which_o be_v your_o upper_a edge_n before_o you_o cross_v the_o zenith_n where_o the_o sun_n be_v or_o if_o you_o work_v your_o observation_n by_o the_o compliment_n of_o his_o height_n make_v that_o 30_o min._n more_o i_o confess_v the_o best_a way_n will_v be_v at_o all_o time_n to_o subtract_v the_o semidiameter_n of_o the_o sun_n which_o be_v 15_o min._n from_o your_o meridian_n altitude_n but_o because_o the_o latitude_n of_o place_n be_v not_o set_v down_o with_o this_o consideration_n it_o be_v more_o safe_a to_o do_v as_o before_o unless_o you_o know_v otherwise_o by_o your_o own_o experience_n this_o only_a by_o the_o by_o to_o give_v notice_n example_n for_o the_o lay_v open_a of_o this_o error_n suppose_v i_o observe_v the_o sun_n at_o barbadoes_n the_o 11_o day_n of_o december_n and_o i_o find_v that_o the_o meridian_n altitude_n of_o the_o sun_n upper_a edge_n be_v 53_o deg_fw-la 18_o min._n to_o which_o i_o add_v the_o sun_n declination_n for_o that_o day_n which_o be_v southerly_a 23_o deg_fw-la 30_o min._n and_o it_o give_v the_o height_n of_o the_o aequinoctial_a above_o the_o horizon_n of_o the_o compliment_n of_o the_o latitude_n to_o 90_o degree_n which_o be_v 76_o deg_fw-la 48_o min._n which_o subtract_v from_o 90_o degree_n leave_v the_o latitude_n or_o aequinoctial's_n distance_n from_o the_o zenith_n 13_o deg_fw-la 12_o min._n upon_o the_o 11_o of_o june_n i_o observe_v the_o sun_n again_o in_o the_o same_o place_n and_o i_o find_v the_o meridian_n altitude_n of_o the_o upper_a edge_n of_o the_o sun_n be_v 80_o deg_fw-la 12_o min._n note_n that_o this_o upper_a edge_n be_v opposite_a to_o the_o edge_n before_o for_o the_o sun_n declination_n be_v 23_o deg_fw-la 30_o min._n northerly_a which_o make_v that_o the_o sun_n give_v a_o south_n horizon_n i_o add_v the_o sun_n declination_n to_o the_o meridian_n altitude_n and_o it_o give_v 103_o deg_fw-la 42_o min._n the_o distance_n between_o the_o aequinoctial_a and_o the_o north_n horizon_n from_o which_o subtract_v 90_o deg_fw-la and_o the_o remainder_n be_v the_o aequinoctial's_n distance_n from_o the_o zenith_n or_o the_o latitude_n which_o be_v 13_o deg_fw-la 42_o min._n now_o this_o latitude_n shall_v agree_v with_o the_o other_o for_o the_o place_n stand_v still_o but_o for_o want_v of_o this_o subtract_v the_o semidiameter_n of_o the_o sun_n it_o differ_v 30_o min._n and_o when_o man_n meet_v with_o thing_n thus_o at_o sea_n for_o want_v of_o mind_v of_o this_o they_o run_v 30_o min._n more_o southerly_a than_o they_o shall_v do_v which_o i_o suppose_v may_v be_v the_o great_a reason_n of_o their_o miss_v this_o island_n and_o other_o that_o lie_v near_o the_o aequinoctial_a but_o for_o those_o place_n that_o lie_v far_o from_o the_o bound_n of_o the_o sun_n it_o be_v not_o to_o be_v mind_v yet_o it_o be_v good_a methinks_v if_o all_o place_n have_v be_v lay_v down_o with_o allowance_n for_o the_o sun_n semidiameter_n but_o because_o they_o be_v not_o you_o ought_v to_o be_v careful_a when_o at_o any_o time_n you_o cross_v the_o zenith_n of_o the_o sun_n i_o have_v not_o be_v myself_o in_o a_o time_n of_o year_n to_o cross_v the_o sun_n zenith_n and_o therefore_o i_o only_o set_v this_o down_o by_o way_n of_o caution_n to_o those_o that_o may_v the_o use_n of_o a_o plain_a sea-chart_n most_o plait_n have_v all_o the_o point_n of_o the_o compass_n draw_v out_o from_o several_a centre_n through_o the_o plat_v and_o because_o they_o be_v common_a and_o the_o way_n to_o work_v by_o they_o so_o ordinary_o know_v i_o have_v think_v it_o necessary_a to_o draw_v the_o manner_n of_o a_o plat_v and_o to_o show_v its_o use_n that_o have_v only_a meridian_n and_o parallel_n draw_v in_o it_o which_o be_v the_o plat_v follow_v suppose_v then_o that_o i_o have_v a_o plat_v that_o have_v the_o meridian_n and_o parallel_n draw_v to_o every_o four_o degree_n as_o this_o follow_v be_v you_o see_v this_o plat_v be_v divide_v into_o equal_a square_n throughout_o by_o the_o meridian_n and_o parallel_n so_o draw_v also_o one_o of_o these_o square_n be_v divide_v into_o eight_o point_n of_o the_o compass_n which_o be_v the_o square_a e_o c_o d_o o_o the_o manner_n of_o divide_v it_o we_o will_v show_v anon_o now_o if_o a_o where_o the_o lizard_n and_o b_o be_v the_o island_n madera_n i_o demand_v their_o distance_n asunder_o let_v b_o a_o represent_v the_o edge_n of_o a_o scale_n lie_v between_o they_o take_v the_o distance_n a_o b_o and_o apply_v it_o to_o the_o meridian_n and_o see_v