Selected quad for the lemma: earth_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
earth_n	body_n	moon_n	sun_n	6,017	5	7.8244	4	true

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
B03739	May it please the King's most excellent Majesty	Halley, Edmond, 1656-1742.	1687 (1687)	Wing H451A; ESTC R177810	7,193	14

may_v it_o please_v the_o king_n be_v most_o excellent_a majesty_n i_o can_v not_o have_v presume_v to_o approach_v your_o majesty_n royal_a presence_n with_o a_o book_n of_o this_o nature_n have_v i_o not_o be_v assure_v that_o when_o the_o weighty_a affair_n of_o your_o government_n permit_v it_o your_o majesty_n have_v frequent_o show_v yourself_o incline_v to_o favour_v mechanical_a and_o philosophical_a discovery_n and_o i_o may_v be_v bold_a to_o say_v that_o if_o ever_o book_n be_v worthy_a the_o favourable_a acceptance_n of_o a_o prince_n this_o wherein_o so_o many_o and_o so_o great_a discovery_n concern_v the_o constitution_n of_o the_o visible_a world_n be_v make_v out_o and_o put_v past_a dispute_n must_v needs_o be_v grateful_a to_o your_o majesty_n especial_o be_v the_o labour_n of_o a_o worthy_a subject_n of_o your_o own_o and_o a_o member_n of_o that_o royal_a society_n found_v by_o your_o late_a royal_a brother_n for_o the_o advancement_n of_o natural_a knowledge_n and_o which_o now_o flourish_v ●nder_v your_o majesty_n most_o gracious_a protection_n but_o be_v sensible_a of_o the_o little_a leisure_n which_o care_n of_o the_o public_a leaf_n to_o prince_n i_o believe_v it_o necessary_a to_o present_v with_o the_o book_n a_o short_a extract_n of_o the_o matter_n contain_v together_o with_o a_o specimen_fw-la thereof_o in_o the_o genuine_a solution_n of_o the_o cause_n of_o the_o tide_n in_o the_o ocean_n a_o thing_n frequent_o attempt_v but_o till_o now_o without_o success_n whereby_o your_o majesty_n may_v judge_v of_o the_o rest_n of_o the_o performance_n of_o the_o author_n the_o sole_a principle_n upon_o which_o this_o author_n proceed_v to_o explain_v most_o of_o the_o great_a and_o surprise_a appearance_n of_o nature_n be_v no_o other_o than_o that_o of_o gravity_n whereby_o in_o the_o earth_n all_o body_n have_v a_o tendency_n towards_o its_o centre_n as_o be_v most_o evident_a and_o from_o undoubted_a argument_n it_o be_v prove_v that_o there_o be_v such_o a_o gravitation_n towards_o the_o centre_n of_o the_o sun_n moon_n and_o all_o the_o planet_n from_o this_o principle_n as_o a_o necessary_a consequence_n follow_v the_o spherical_a figure_n of_o the_o earth_n and_o sea_n and_o of_o all_o the_o other_o celestial_a body_n and_o though_o the_o tenacity_n and_o firmness_n of_o the_o solid_a part_n support_v the_o inequality_n of_o the_o land_n above_o the_o level_n yet_o the_o fluid_n press_v equal_o and_o easy_o yield_v to_o each_o other_o soon_o restore_v the_o aequilibrium_fw-la if_o disturb_v and_o maintain_v the_o exact_a figure_n of_o the_o globe_n now_o this_o force_n of_o descent_n of_o body_n towards_o the_o centre_n be_v not_o in_o all_o place_n alike_o but_o be_v still_o less_o and_o less_o as_o the_o distance_n from_o the_o centre_n increase_v and_o in_o this_o book_n it_o be_v demonstrate_v that_o this_o force_n decrease_v as_o the_o square_n of_o the_o distance_n increase_v that_o be_v the_o weight_n of_o body_n and_o the_o force_n of_o their_o fall_n be_v less_o in_o part_n more_o remove_v from_o the_o centre_n in_o the_o proportion_n of_o the_o square_n of_o the_o distance_n so_o as_o for_o example_n a_o tun_n weight_n on_o the_o surface_n of_o the_o earth_n if_o it_o be_v raise_v to_o the_o height_n of_o 4000_o mile_n which_o i_o suppose_v the_o semidiameter_n of_o the_o earth_n will_v weigh_v but_o ¼_n of_o a_o tun_n or_o 5_o hundred_o weight_n if_o to_o 12000_o mile_n or_o 3_o semidiameter_n from_o the_o surface_n that_o be_v 4_o from_o the_o centre_n it_o will_v weigh_v but_o 1_o 16_o part_n of_o the_o weight_n on_o the_o surface_n or_o a_o hundred_o and_o quarter_n so_o that_o it_o will_v be_v as_o easy_a for_o the_o strength_n of_o a_o man_n at_o that_o height_n to_o carry_v a_o tun_n weight_n as_o here_o to_o carry_v a_o hundred_o and_o quarter_n and_o in_o the_o same_o proportion_n do_v the_o velocity_n of_o the_o fall_n of_o body_n decrease_v for_o whereas_o on_o the_o surface_n of_o the_o earth_n all_o thing_n fall_v 16_o foot_n in_o a_o second_o at_o one_o semidiameter_n above_o this_o fall_n be_v but_o 4_o foot_n and_o at_o 3_o semidiameter_n or_o 4_o from_o the_o centre_n it_o be_v but_o 1_o 16_o of_o the_o fall_n at_o the_o surface_n or_o but_o one_o foot_n in_o a_o second_o and_o at_o great_a distance_n both_o weight_n and_o fall_v become_v very_o small_a but_o yet_o at_o all_o give_v distance_n be_v still_o some_o thing_n though_o the_o effect_n become_v insensible_a at_o the_o distance_n of_o the_o moon_n which_o i_o will_v suppose_v 60_o semidiameter_n of_o the_o earth_n 3600_o pound_n weigh_v but_o one_o pound_n and_o the_o fall_n of_o body_n be_v but_o 16_o 3600_o of_o a_o foot_n in_o a_o second_o or_o 16_o foot_n in_o a_o minute_n that_o be_v a_o body_n so_o far_o off_o descend_v in_o a_o minute_n no_o more_o than_o the_o same_o at_o the_o surface_n of_o the_o earth_n will_v do_v in_o a_o second_o of_o time._n as_o be_v say_v before_o the_o same_o force_n decrease_v after_o the_o same_o manner_n be_v evident_o find_v in_o the_o sun_n moon_n and_o all_o the_o planet_n but_o more_o especial_o in_o the_o sun_n who_o force_n be_v prodigious_a become_v sensible_a even_o in_o the_o immense_a distance_n of_o saturn_n this_o give_v room_n to_o suspect_v that_o the_o force_n of_o gravity_n be_v in_o the_o celestial_a globe_n proportional_a to_o the_o quantity_n of_o matter_n in_o each_o of_o they_o and_o the_o sun_n be_v at_o least_o ten_o thousand_o time_n as_o big_a as_o the_o earth_n its_o gravitation_n or_o attract_v force_n be_v find_v to_o be_v at_o least_o ten_o thousand_o time_n as_o much_o as_o that_o of_o the_o earth_n act_v on_o body_n at_o the_o same_o distance_n this_o law_n of_o the_o decrease_n of_o gravity_n be_v demonstrative_o prove_v and_o put_v past_a contradiction_n the_o author_n with_o great_a sagacity_n inquire_v into_o the_o necessary_a consequence_n of_o this_o supposition_n whereby_o he_o find_v the_o genuine_a cause_n of_o the_o several_a appearence_n in_o the_o theory_n of_o the_o moon_n and_o planet_n and_o discover_v the_o hitherto_o unknown_a law_n of_o the_o motion_n of_o comet_n and_o of_o the_o ebb_a and_o flow_v of_o the_o sea._n each_o of_o which_o be_v subject_n that_o have_v heretofore_o take_v up_o much_o large_a volume_n but_o truth_n be_v uniform_a and_o always_o the_o same_o it_o be_v admirable_a to_o observe_v how_o easy_o and_o how_o satisfactory_o solution_n be_v give_v in_o very_o abstruse_a and_o difficult_a matter_n when_o once_o true_a and_o genuine_a principle_n be_v obtain_v and_o on_o the_o other_o hand_n it_o may_v be_v wonder_v that_o notwithstanding_o the_o great_a facility_n of_o truth_n and_o the_o perplexity_n and_o nonconsequence_n that_o always_o attend_v erroneous_a supposition_n these_o great_a discovery_n shall_v have_v escape_v the_o acute_a disquisition_n of_o the_o best_a philosophical_a head_n of_o all_o past_a age_n and_o be_v reserve_v to_o be_v record_v to_o posterity_n among_o the_o glorious_a acquisition_n your_o nation_n just_o promise_v themselves_o during_o the_o course_n of_o your_o majesty_n happy_a reign_n over_o we_o the_o theory_n of_o the_o motion_n of_o the_o primary_n planet_n be_v here_o show_v to_o be_v nothing_o else_o but_o the_o contemplation_n of_o the_o curve_v line_n which_o body_n cast_v with_o a_o give_v velocity_n in_o a_o give_v direction_n and_o at_o the_o same_o time_n draw_v towards_o the_o sun_n by_o its_o gravitating_a power_n will_v describe_v or_o which_o be_v all_o one_o that_o the_o orb_n of_o the_o planet_n be_v such_o curve_v line_n as_o a_o shot_n from_o a_o gun_n describe_v in_o the_o air_n be_v cast_v according_a to_o the_o direction_n of_o the_o piece_n but_o bend_v into_o a_o crooked_a line_n by_o the_o superven_a tendency_n towards_o the_o earth_n centre_n and_o the_o planet_n be_v suppose_v to_o be_v project_v with_o a_o give_v force_n and_o attract_v towards_o the_o sun_n after_o the_o aforesaid_a manner_n be_v here_o prove_v to_o describe_v such_o figure_n as_o answer_v punctual_o to_o all_o that_o the_o industry_n of_o this_o and_o the_o last_o age_n have_v observe_v in_o the_o planetary_a motion_n so_o that_o it_o appear_v that_o there_o be_v no_o need_n of_o solid_a orb_n and_o intelligence_n as_o the_o ancient_n imagine_v nor_o yet_o of_o vortices_fw-la or_o whirlpool_n of_o the_o celestial_a matter_n as_o des_n cartes_n suppose_v but_o the_o whole_a affair_n be_v simple_o and_o mechanical_a perform_v upon_o the_o sole_a supposition_n of_o a_o gravitation_n towards_o the_o sun_n which_o can_v be_v deny_v the_o motion_n of_o comet_n be_v here_o show_v to_o be_v compound_v of_o the_o same_o element_n and_o not_o to_o differ_v from_o planet_n but_o in_o their_o great_a swiftness_n whereby_o overpower_v the_o gravity_n that_o

shall_v hold_v they_o to_o the_o sun_n as_o it_o do_v the_o planet_n they_o fly_v off_o again_o and_o distance_n themselves_o from_o the_o sun_n and_o earth_n so_o that_o they_o soon_o be_v out_o of_o sight_n and_o the_o fewness_n and_o inaccuracy_n of_o the_o observation_n antiquity_n have_v leave_v we_o be_v not_o sufficient_a to_o determine_v whether_o the_o same_o comet_n ever_o return_v again_o but_o this_o author_n have_v show_v how_o geometrical_o to_o determine_v the_o orb_n of_o a_o comet_n from_o observation_n and_o to_o find_v his_o distance_n from_o the_o earth_n and_o sun_n which_o be_v never_o before_o do_v the_o three_o thing_n here_o do_v be_v the_o theory_n of_o the_o moon_n all_o the_o inequality_n of_o who_o motion_n be_v prove_v to_o arise_v from_o the_o same_o principle_n only_o here_o the_o effect_n of_o two_o centre_n operate_n on_o or_o attract_v a_o project_v body_n come_v to_o be_v consider_v for_o the_o moon_n though_o principal_o attract_v by_o the_o earth_n and_o move_v round_o it_o do_v together_o with_o the_o earth_n move_v round_o the_o sun_n once_o in_o a_o year_n and_o be_v according_a as_o she_o be_v near_a or_o far_o from_o the_o sun_n draw_v by_o he_o more_o or_o less_o than_o the_o centre_n of_o the_o earth_n about_o which_o she_o move_v whence_o arise_v several_a irregularity_n in_o her_o motion_n of_o all_o which_o the_o author_n in_o this_o book_n with_o no_o less_o subtlety_n than_o industry_n have_v give_v a_o full_a account_n and_o though_o by_o reason_n of_o the_o great_a complication_n of_o the_o problem_n he_o have_v not_o yet_o be_v able_a to_o make_v it_o pure_o geometrical_a it_o be_v to_o be_v hope_v that_o in_o some_o far_a essay_n he_o may_v surmount_v the_o difficulty_n and_o have_v perfect_v the_o theory_n of_o the_o moon_n the_o long_a desire_a discovery_n of_o the_o longitude_n which_o at_o sea_n be_v only_o practicable_a this_o way_n may_v at_o length_n be_v bring_v to_o light_v to_o the_o great_a honour_n of_o your_o majesty_n and_o advantage_n of_o your_o subject_n all_o the_o surprise_v phenomena_n of_o the_o flux_n and_o reflux_n of_o the_o sea_n be_v in_o like_a manner_n show_v to_o proceed_v from_o the_o same_o principle_n which_o i_o design_n more_o large_o to_o insist_v on_o since_o the_o matter_n of_o fact_n be_v in_o this_o case_n much_o better_o know_v to_o your_o majesty_n than_o in_o the_o forego_n if_o the_o earth_n be_v alone_o that_o be_v to_o say_v not_o affect_v by_o the_o action_n of_o the_o sun_n and_o moon_n it_o be_v not_o to_o be_v doubt_v but_o the_o ocean_n be_v equal_o press_v by_o the_o force_n of_o gravity_n towards_o the_o centre_n will_v continue_v in_o a_o perfect_a stagnation_n always_o at_o the_o same_o height_n without_o ebb_v or_o flow_v but_o it_o be_v not_o to_o be_v deny_v that_o the_o sun_n and_o moon_n have_v a_o like_a principle_n of_o gravitation_n towards_o their_o centre_n and_o that_o the_o earth_n be_v within_o the_o activity_n of_o their_o attraction_n it_o will_v plain_o follow_v that_o the_o equality_n of_o the_o pressure_n of_o gravity_n towards_o the_o centre_n will_v thereby_o be_v disturb_v and_o though_o the_o smallness_n of_o these_o force_n in_o respect_n of_o the_o gravitation_n towards_o the_o earth_n centre_n render_v they_o altogether_o imperceptible_a by_o any_o experiment_n we_o can_v devise_v yet_o the_o ocean_n be_v fluid_a and_o yield_n to_o the_o least_o force_n by_o its_o rise_n show_v where_o it_o be_v less_o press_v and_o where_o it_o be_v more_o press_v by_o its_o sink_n now_o if_o we_o suppose_v the_o force_n of_o the_o moon_n attraction_n to_o decrease_v as_o the_o square_n of_o the_o distance_n from_o its_o centre_n increase_v as_o in_o the_o earth_n and_o other_o celestial_a body_n we_o shall_v find_v that_o where_o the_o moon_n be_v perpendicular_o either_o above_o or_o below_o the_o horizon_n either_o in_o zenith_n or_o nadir_n there_o the_o force_n of_o gravity_n be_v most_o of_o all_o diminish_v and_o consequent_o that_o there_o the_o ocean_n must_v necessary_o swell_v by_o the_o come_n in_o of_o the_o water_n from_o those_o part_n where_o the_o pressure_n be_v great_a viz._n in_o those_o place_n where_o the_o moon_n be_v near_o the_o horizon_n but_o that_o this_o may_v be_v the_o better_o understand_v i_o think_v it_o needful_a to_o add_v the_o follow_a figure_n where_o m_n be_v the_o moon_n e_o the_o earth_n c_o its_o centre_n and_o z_o the_o place_n where_o the_o moon_n be_v in_o the_o zenith_n n_o where_o in_o the_o nadir_n now_o by_o the_o hypothesis_n it_o be_v evident_a that_o the_o water_n in_o z_o being_n near_o be_v more_o draw_v by_o the_o moon_n than_o the_o centre_n of_o the_o earth_n c_o and_o that_o again_o more_o than_o the_o water_n in_o n_o wherefore_o the_o water_n in_o z_o have_v a_o tendency_n towards_o the_o moon_n contrary_a to_o that_o of_o gravity_n be_v equal_a to_o the_o excess_n of_o the_o gravitation_n in_o z_o above_o that_o in_o c_o and_o in_o the_o other_o case_n the_o water_n in_o n_o tend_v less_o towards_o the_o moon_n that_o the_o centre_n c_o be_v leave_v behind_o by_o as_o much_o as_o be_v the_o difference_n of_o the_o gravitation_n towards_o the_o moon_n in_o c_o and_o n._n this_o right_o understand_v it_o follow_v plain_o that_o the_o sea_n which_o otherwise_o will_v be_v spherical_a upon_o the_o pressure_n of_o the_o moon_n must_v form_v itself_o into_o a_o spheroidal_a or_o oval_a figure_n who_o long_a diameter_n be_v where_o the_o moon_n be_v vertical_a and_o short_a where_o she_o be_v in_o the_o horizon_n and_o that_o the_o moon_n shift_v her_o position_n as_o she_o turn_v round_o the_o earth_n once_o a_o day_n this_o oval_a of_o water_n shift_n with_o she_o occasion_v thereby_o the_o two_o flood_n and_o ebb_n observable_a in_o each_o 25_o hour_n and_o this_o may_v suffice_v as_o to_o the_o general_a cause_n of_o the_o tide_n it_o remain_v now_o to_o show_v how_o natural_o this_o notion_n account_v for_o all_o the_o particular_n that_o have_v be_v observe_v about_o they_o so_o that_o there_o can_v be_v no_o room_n leave_v to_o doubt_v but_o that_o this_o be_v the_o true_a cause_n thereof_o the_o spring_n tide_n upon_o the_o new_a and_o full_a moon_n and_o neap_n tide_n on_o the_o quarter_n be_v occasion_v by_o the_o attractive_a force_n of_o the_o sun_n in_o the_o new_a and_o full_o conspire_v with_o the_o attraction_n of_o the_o moon_n and_o produce_v a_o tide_n by_o their_o unite_a force_n whereas_o in_o the_o quarter_n the_o sun_n raise_v the_o water_n where_o the_o moon_n depress_n it_o and_o the_o contrary_a so_o as_o the_o tide_n be_v make_v only_o by_o the_o difference_n of_o their_o attraction_n that_o the_o force_n of_o the_o sun_n be_v no_o great_a in_o this_o case_n proceed_v from_o the_o very_a small_a proportion_n the_o semidiameter_n of_o the_o earth_n bear_v to_o the_o vast_a distance_n of_o the_o sun._n it_o be_v also_o observe_v that_o caeteris_fw-la paribus_fw-la the_o aequinoctial_a spring_n tide_n in_o march_n and_o september_n or_o near_o they_o be_v the_o high_a and_o the_o neap_n tide_v the_o low_a which_o proceed_v from_o the_o great_a agitation_n of_o the_o water_n when_o the_o fluid_a sphaeroid_fw-fr revolve_v about_o a_o great_a circle_n of_o the_o earth_n than_o when_o it_o turn_v about_o in_o a_o lesser_a circle_n it_o be_v plain_a that_o if_o the_o moon_n be_v constitute_v in_o the_o pole_n and_o there_o stand_v that_o the_o spheroid_fw-fr will_v have_v a_o fix_a position_n and_o that_o it_o will_v be_v always_o high_a water_n under_o the_o pole_n and_o low_a water_n every_o where_o under_o the_o aequinoctial_a and_o therefore_o the_o near_a the_o moon_n approach_v the_o pole_n the_o less_o be_v the_o agitation_n of_o the_o ocean_n which_o be_v always_o great_a where_o the_o moon_n be_v in_o the_o aequinoctial_a or_o far_a distant_a from_o the_o pole_n whence_o the_o sun_n and_o moon_n be_v either_o conjoin_v or_o opposite_a in_o the_o aequinoctial_a produce_v the_o great_a spring_n tide_n and_o the_o subsequent_a neap_n tide_n be_v produce_v by_o the_o tropical_a moon_n in_o the_o quarter_n be_v always_o the_o least_o tide_n whereas_o in_o june_n and_o december_n the_o spring_n tide_n be_v make_v by_o the_o tropical_a sun_n and_o moon_n and_o therefore_o less_o vigorous_a and_o the_o neap_n tide_n by_o the_o aequinoctial_a moon_n which_o therefore_o be_v the_o strong_a hence_o it_o happen_v that_o the_o difference_n between_o the_o spring_n and_o neap_n tide_n in_o these_o month_n be_v much_o less_o considerable_a than_o in_o march_n and_o september_n and_o the_o reason_n why_o the_o very_o high_a spring_n tide_n be_v find_v to_o be_v rather_o before_o the_o vernal_a and_o after_o the_o autumnal_a equinox_n viz._n in_o