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earth_n great_a part_n water_n 5,914 5 6.2806 4 true
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ID Title Author Corrected Date of Publication (TCP Date of Publication) STC Words Pages
A60281 The hydrostaticks, or, The weight, force, and pressure of fluid bodies, made evident by physical, and sensible experiments together vvith some miscellany observations, the last whereof is a short history of coal, and of all the common, and proper accidents thereof, a subject never treated of before / by G.S. Sinclair, George, d. 1696. 1672 (1672) Wing S3854; ESTC R38925 208,492 331

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that_o be_v specifical_o or_o natural_o light_a than_o water_n i_o say_v then_o it_o must_v ascend_v to_o the_o top_n b_o and_o the_o reason_n be_v because_o the_o quadrat_fw-la foot_n of_o water_n k_o be_v more_o press_v upward_o than_o the_o quadrat_fw-la foot_n of_o water_n i_o or_o l_o be_v but_o this_o can_v be_v i●_n fluid_a body_n unless_o motion_n follow_v thereupon_o i_o say_v it_o be_v more_o press_v up_o because_o r_o be_v light_a than_o n_o or_o saint_n it_o must_v press_v with_o great_a force_n upon_o k_o than_o saint_n can_v do_v upon_o l_o or_o n_o upon_o i._o it_o be_v still_o to_o be_v remember_v that_o fluids_n press_v with_o as_o much_o strength_n upward_o as_o downward_o according_a to_o the_o six_o theorem_n and_o that_o a_o horizontal_n surface●doth_a as_o real_o suffer_v unequal_a pressure_n from_o below_o as_o from_o above_z theorem_fw-la fourteen_o body_n natural_o light_a than_o water_n swim_v upon_o the_o surface_n and_o top_n figure_n 1._o the_o reason_n of_o this_o proposition_n must_v be_v take_v from_o the_o nature_n of_o a_o equipondium_fw-la or_o equal_a weight_n for_o without_o doubt_n there_o be_v a_o counterbalance_n between_o the_o pressure_n of_o the_o water_n and_o the_o weight_n of_o the_o body_n that_o swim_v to_o make_v this_o probable_a let_v we_o suppose_v there_o be_v a_o piece_n of_o timber_n in_o form_n of_o a_o cube_n six_o inch_n thick_a every_o way_n without_o weight_n in_o this_o case_n the_o undersurface_n of_o that_o foursquared_a body_n be_v apply_v to_o the_o surface_n of_o the_o water_n a_o will_v lie_v close_o upon_o it_o as_o one_o plain_a table_n lie_v upon_o the_o face_n of_o another_o without_o any_o pressure_n and_o it_o be_v void_a of_o weight_n the_o part_n of_o the_o surface_n a_o will_v be_v no_o more_o burden_v than_o the_o next_o part_n b_o adjacent_a whence_o no_o motion_n will_v follow_v here_o be_v no_o equipondium_fw-la or_o counterbalance_n second_o let_v we_o suppose_v the_o say_a body_n to_o acquire_v two_o ounce_n of_o weight_n than_o it_o follow_v that_o it_o must_v subside_o and_o sink_v two_o inch_n below_o the_o surface_n a_o b_o c_o d_o and_o that_o so_o far_o till_o it_o come_v by_o virtue_n of_o its_o new_a acquire_v weight_n to_o a_o counterbalance_n with_o the_o pressure_n of_o the_o water_n which_o pressure_n be_v nothing_o else_o but_o as_o much_o force_n or_o weight_n as_o be_v equivalent_a to_o the_o weight_n of_o water_n that_o be_v thrust_v out_o of_o its_o own_o place_n by_o the_o subside_v and_o sink_v of_o that_o body_n two_o inch_n three_o let_v we_o suppose_v the_o same_o body_n to_o acquire_v other_o two_o ounce_n of_o weight_n then_o must_v it_o subside_o other_o two_o inch_n last_o let_v we_o suppose_v that_o it_o acquire_v six_o ounce_n of_o weight_n than_o it_o follow_v that_o the_o whole_a body_n sink_v so_o far_o i_o mean_v till_o its_o upmost_a surface_n be_v in_o a_o horizontal_n line_n with_o the_o surface_n of_o the_o water_n a_o b_o 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b_o c_o d._n i_o say_v then_o if_o it_o be_v press_v down_o to_o r_o it_o shall_v arise_v thence_o and_o never_o rest_n till_o it_o be_v where_o it_o be_v namely_o in_o f._n the_o reason_n seem_v to_o be_v this_o because_o the_o foursquared_a body_n of_o water_n r_o be_v real_o heavy_a than_o the_o foursquared_a piece_n of_o timber_n f._n if_o this_o be_v true_a it_o follow_v of_o necessity_n that_o it_o must_v ascend_v for_o if_o the_o timber_n exist_v in_o r_o be_v light_a than_o the_o water_n r_o the_o water_n t_o must_v be_v less_o press_v than_o the_o water_n o_o or_o the_o water_n v_o whence_o according_a to_o the_o twelve_o theorem_n motion_n must_v follow_v again_o if_o the_o timber_n r_o exist_v in_o the_o water_n r_o be_v light_a than_o the_o same_o water_n be_v then_o must_v the_o water_n k_o be_v more_o press_v up_o then_o the_o water_n i_o or_o l_o whence_o yet_o according_a to_o the_o same_o theorem_fw-la motion_n must_v follow_v if_o it_o be_v say_v that_o the_o timber_n 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age_n have_v reject_v the_o old_a opinion_n of_o the_o earth_n nourish_v of_o plant_n or_o be_v convert_v into_o their_o aliment_n have_v make_v many_o laudable_a experiment_n for_o find_v out_o the_o material_n and_o mean_n of_o their_o growth_n and_o vegetation_n such_o as_o sir_n francis_n bacon_n observe_v of_o germination_n helmont_n of_o a_o willow_n and_o the_o noble_a mr._n boyl_n of_o a_o gourd_n etc._n etc._n for_o though_o a_o tree_n be_v cut_v down_o and_o the_o root_n thereof_o wax_v old_a in_o the_o earth_n and_o the_o stock_n die_v in_o the_o ground_n yet_o through_o the_o send_v of_o water_n it_o will_v bud_v as_o job_n speak_v chap._n 14._o 7_o 8_o 9_o i_o shall_v add_v a_o short_a remark_n of_o a_o willow_n grow_v without_o earth_n upon_o the_o 13_o of_o april_n 1662._o i_o set_v a_o top_n branch_n of_o the_o peach-leafed_a willow_n in_o a_o glass-viol_n among_o 12_o ounce_n of_o pure_a spring_n water_n with_o three_o small_a bud_n upon_o the_o top_n thereof_o 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open_a orifice_n of_o the_o tub_n d_o a_o to_o the_o bottom_n and_o you_o shall_v see_v the_o water_n ascend_v in_o it_o as_o high_z as_o d_o according_a to_o the_o first_o experiment_n when_o this_o be_v do_v recline_v the_o say_a pipe_n till_o it_o lie_v as_o b_o e_z and_o you_o shall_v find_v the_o pipe_n complete_o full_a of_o water_n next_o erect_v the_o same_o tub_n again_o as_o d_o a_o and_o you_o shall_v see_v the_o cylinder_n of_o water_n fall_v down_o and_o become_v short_a as_o at_o first_o for_o salve_v this_o phenomenon_n and_o such_o like_a i_o must_v suppose_v this_o water_n to_o be_v 50_o inch_n deep_a and_o the_o tub_n i_o a_o and_o b_o e_z 90_o inch_n long_o and_o the_o say_a tub_n in_o recline_v to_o describe_v the_o quadrant_a of_o a_o circle_n f_o e_o g._n now_o the_o question_n be_v why_o there_o be_v but_o 50_o inch_n of_o water_n in_o the_o tub_n while_o erect_v there_o shall_v be_v 60_o in_o it_o when_o it_o be_v recline_v second_o why_o there_o shall_v be_v 90_o inch_n of_o water_n in_o the_o tub_n b_o e_o and_o but_o 50_o in_o it_o when_o it_o stand_v perpendicular_a as_o d_o a_o if_o you_o reply_v because_o there_o be_v 90_o inch_n in_o recta_fw-la linea_fw-la between_o the_o point_n b_o and_o the_o point_n e_o and_o but_o 50_o between_o a_o and_o d._n but_o this_o will_v not_o answer_v the_o case_n because_o if_o you_o stop_v the_o orifice_n e_o with_o the_o pulp_n of_o your_o finger_n before_o it_o be_v erect_v you_o will_v find_v the_o tub_n remain_v full_a of_o water_n even_o while_o it_o stand_v perpendicular_a and_o fall_v down_o when_o the_o orifice_n be_v open_v or_o while_o the_o tub_n stand_v perpendicular_a stop_v the_o orifice_n i_o and_o recline_v it_o as_o b_o e_z yet_o no_o more_o water_n will_v be_v find_v in_o it_o than_o 50_o inch_n but_o by_o unstop_v the_o say_a orifice_n the_o water_n climb_v up_o from_o r_z to_z e_z and_o become_v 90_o inch_n now_o what_o be_v the_o reason_n why_o it_o run_v up_o from_o r_z to_z e_z and_o why_o it_o fall_v down_o from_o i_o to_o d_o i_o answer_v then_o the_o water_n must_v run-up_v from_o r_z to_z e_z because_o of_o the_o inequality_n that_o be_v between_o the_o pondus_fw-la of_o the_o cylinder_n b_o r_o and_o the_o potentia_fw-la of_o the_o surface_n of_o water_n a_o b_o c_o that_o support_v the_o say_v cylinder_n for_o understand_v this_o know_v while_o the_o tub_n be_v erect_v there_o be_v a_o perfect_a equality_n between_o the_o weight_n of_o the_o pillar_n a_o d_o and_o the_o force_n or_o power_n of_o the_o surface_n that_o sustain_v it_o see_v a_o surface_n 50_o inch_n deep_a support_v a_o pillar_n 50_o inch_n
k_o p_o n_o make_v a_o just_a equipondium_fw-la with_o the_o water_n e_o h_o r_o n._n three_o that_o fluid_v not_o only_o of_o the_o same_o kind_n but_o of_o different_a kind_n do_v counterpoise_v one_o another_o according_a to_o altitude_n and_o not_o according_a to_o thickness_n because_o though_o the_o mercury_n k_o p_o n_o be_v far_o thick_a than_o the_o water_n e_o h_n yet_o they_o counterbalance_v one_o another_o because_o a_o proportion_n be_v keep_v according_a to_o their_o altitude_n four_o that_o a_o fluid_a natural_o light_a may_v move_v a_o fluid_a natural_o heavy_a and_o thrust_v it_o out_o of_o its_o own_o place_n because_o the_o water_n come_v in_o at_o h_n thrust_v down_o the_o mercury_n to_o r_o and_o from_o r_z to_z n_o and_o so_o forth_o five_o that_o of_o two_o f●uids_n unequal_a in_o strength_n debate_v together_o the_o weak_a of_o necessity_n must_v yield_v to_o the_o strong_a though_o the_o weak_a be_n far_o heavy_a natural_o than_o the_o strong_a as_o be_v evident_a in_o the_o mercu●y_n that_o yield_v to_o the_o water_n six_o that_o it_o be_v impossible_a for_o two_o fluid_n so_o long_o as_o they_o be_v unequal_a in_o strength_n to_o cease_v from_o motion_n till_o they_o come_v to_o a_o equipondium_fw-la because_o the_o water_n always_o spring_v up_o through_o the_o mercury_n till_o a_o equal_a balance_n happen_v seven_o that_o one_o fluid_a of_o this_o kind_n can_v counterpoise_v another_o fluid_n of_o the_o same_o kind_n though_o there_o be_v divers_a fluids_n interveening_a because_o the_o air_n f_o e_o counterpoise_v the_o air_n i_o k_o or_o i_o s_o notwithstanding_o of_o water_n and_o mercury_n interveen_v eight_o that_o there_o may_v be_v as_o much_o pressure_n in_o one_o inch_n of_o a_o fluid_a as_o in_o a_o million_o because_o the_o 29_o inch_n of_o air_n i_o saint_n have_v as_o much_o bensil_n in_o they_o as_o be_v in_o the_o whole_a pillar_n of_o air_n e_o f_o that_o go_v up_o from_o the_o top_n of_o the_o water_n to_o the_o top_n of_o the_o atmosphere_n nine_o that_o when_o one_o fluid_a be_v under_o pressure_n the_o next_o must_v be_v under_o the_o same_o degree_n of_o pressure_n though_o they_o be_v not_o of_o the_o same_o kind_n but_o of_o different_a sort_n because_o the_o air_n i_o s_o the_o water_n s_o k_n and_o mercury_n k_o p_o be_v sure_o under_o the_o same_o degree_n of_o pressure_n otherwise_o the_o motion_n can_v not_o end_v ten_o that_o when_o two_o fluid_n of_o divers_a kind_n do_v press_v one_o another_o that_o which_o be_v natural_o light_a ascend_v always_o to_o the_o high_a place_n and_o the_o heavy_a to_o the_o low_a because_o the_o air_n i_o s_o be_v above_o the_o water_n s_o k_n and_o the_o water_n s_o k_n be_v above_o the_o mercury_n note_v that_o this_o be_v not_o universal_a but_o only_o happen_v when_o the_o light_a cylinder_n be_v slendere_a than_o the_o other_o for_o if_o the_o mercury_n k_o p_o be_v no_o thick_a than_o the_o water_n p_o n_o r_o h_n this_o will_v raise_v it_o entire_o eleven_o that_o the_o compression_n of_o air_n to_o less_o space_n be_v not_o according_a to_o arithmetical_a progression_n 1_o 2_o 3_o 4_o 5_o but_o according_a to_o some_o other_o proportion_n which_o may_v be_v call_v uniform-difform_a note_v here_o that_o though_o this_o be_v true_a of_o the_o air_n while_o it_o be_v compress_v from_o a_o more_o quantity_n to_o a_o less_o as_o here_o or_o in_o a_o windgun_n yet_o it_o be_v not_o true_a of_o the_o pressure_n of_o the_o element_n of_o air_n which_o be_v more_o and_o more_o from_o the_o top_n of_o the_o atmosphere_n to_o the_o earth_n according_a to_o arithmetical_a progression_n as_o in_o water_n we_o see_v last_o that_o the_o heavy_a of_o fluid_n such_o as_o mercury_n press_v upward_o as_o well_o as_o downward_o because_o the_o top_n of_o the_o mercury_n k_o thrust_v up_o the_o water_n k_o s_o as_o well_o as_o it_o thrust_v down_o the_o water_n p_o n_o r_o h._n it_o may_v be_v inquire_v here_o how_o far_o this_o glass_n will_v go_v down_o before_o the_o 29_o inch_n of_o air_n i_o k_o be_v reduce_v to_o one_o inch_n i_o answer_v its_o hard_a to_o determine_v but_o it_o seem_v it_o ought_v to_o go_v down_o more_o than_o 300_o fathom_n in_o this_o case_n there_o will_v be_v 28_o inch_n of_o water_n above_o k._n let_v we_o suppose_v the_o orifice_n h_n to_o be_v stop_v at_o that_o deepness_n and_o the_o glass_n bring_v above_o the_o water_n then_o when_o the_o say_a orifice_n be_v open_v in_o the_o air_n you_o will_v find_v the_o whole_a water_n p_o n_o r_o h_n thrust_v out_o and_o not_o only_o this_o but_o the_o whole_a mercury_n p_o k_n spring_v out_o at_o the_o orifice_n h_n likewise_o except_o a_o little_a that_o remain_v between_o n_o and_o h_n the_o reason_n be_v because_o the_o 29_o inch_n of_o air_n be_v reduce_v to_o one_o will_v be_v under_o a_o very_a great_a bensil_n therefore_o the_o weight_n be_v take_v away_o that_o beget_v it_o of_o its_o own_o accord_n it_o will_v expand_v itself_o to_o its_o old_a dimension_n which_o it_o can_v not_o do_v unless_o both_o the_o 28_o inch_n of_o water_n that_o be_v suppose_v to_o be_v above_o k_o and_o the_o mercury_n k_o p_o be_v thrust_v out_o of_o their_o place_n experiment_n xvi_o figure_n 22._o this_o schematism_n represent_v a_o vessel_n full_a of_o water_n 84_o inch_n deep_a namely_o from_o l_o n_o the_o first_o surface_n to_o m_o r_o the_o bottom_n from_o m_n to_o r_o in_o breadth_n be_v 20_o inch_n there_o be_v here_o also_o two_o glass-pipe_n open_a at_o both_o end_n the_o one_o two_o inch_n wide_a the_o other_o half_o a_o inch_n wide_a both_o of_o they_o be_v 85_o inch_n long_o x_o in_n o_o be_v a_o surface_n of_o stagnant_a mercury_n among_o which_o the_o two_o end_n of_o the_o pipe_n be_v drown_v e_o c_o be_v a_o pillar_n of_o mercury_n six_o inch_n in_o height_n and_o so_o be_v g_o d_o both_o of_o they_o raise_v to_o that_o altitude_n by_o the_o pressure_n of_o the_o water_n upon_o the_o surface_n x_o y_o o._n the_o pillar_n e_o c_o at_fw-fr be_v support_v by_o and_o rest_v upon_o the_o imaginary_a pillar_n a_o p._n and_o so_o be_v the_o pillar_n g_o d_o b_o support_v by_o the_o pillar_n b_o q._n there_o be_v three_o thing_n that_o occur_v here_o from_o this_o operation_n of_o nature_n to_o be_v inquire_v after_o first_o why_o ought_v the_o mercury_n to_o rise_v in_o the_o two_o tub_n after_o the_o vessel_n be_v fill_v with_o water_n second_o why_o rather_o six_o inch_n than_o seven_o or_o eight_o three_o what_o be_v the_o reason_n why_o it_o rise_v as_o high_a in_o the_o wide_a t●b_n as_o in_o the_o narrow_a i_o answer_v the_o mercury_n rise_v from_o c_o to_z e_z and_o from_o d_o to_z g_z by_o the_o pressure_n of_o the_o water_n that_o rest_v upon_o the_o surface_n x_o y_o o._n before_o that_o the_o water_n be_v pour_v into_o the_o vessel_n there_o be_v here_o a_o most_o equal_a and_o uniform_a pressure_n upon_o the_o surface_n x_o in_n o_o both_o without_o and_o within_o the_o tub_n namely_o from_o the_o air_n that_o rest_v upon_o it_o but_o no_o soon_o be_v the_o water_n pour_v in_o but_o as_o soon_o the_o pressure_n become_v unequal_a the_o part_n of_o the_o surface_n without_o the_o tub_n be_v more_o burden_v than_o the_o part_n c_o and_o d_o within_o therefore_o the_o part_n that_o be_v less_o press_v must_v rise_v and_o climb_v up_o till_o the_o pressure_n become_v equal_a for_o it_o be_v impossible_a that_o a_o fluid_a can_v cease_v from_o motion_n so_o long_o as_o there_o be_v inequality_n of_o weight_n between_o the_o pondus_fw-la and_o the_o potentia_fw-la if_o any_o doubt_n let_v he_o pierce_v the_o side_n of_o the_o vessel_n and_o when_o the_o whole_a water_n be_v run_v out_o he_o will_v find_v e_o c_o and_o g_o d_o to_n have_v fall_v down_o which_o clear_o prove_v the_o climb_n up_o of_o the_o mercury_n to_o depend_v upon_o the_o inpouring_a of_o the_o water_n for_o understand_v the_o reason_n of_o the_o second_o remember_v that_o mercury_n as_o we_o have_v often_o note_v be_v count_v 14_o time_n heavy_a than_o water_n therefore_o e_z c_z must_v be_v six_o inch_n see_v x_o in_n o_o be_v press_v with_o the_o altitude_n of_o 84_o inch_n of_o water_n it_o will_v be_v judge_v no_o marvel_n to_o see_v the_o mercury_n rise_v from_o c_o to_z e_z and_o from_o d_o to_z g_z provide_v the_o face_n of_o the_o stagnant_a mercury_n be_v as_o high_a as_o z_o f._n no_o more_o strange_a it_o be_v to_o see_v the_o two_o mercury_n rise_v with_o the_o pressure_n of_o the_o water_n for_o in_o effect_n and_o real_o the_o say_a water_n be_v the_o just_a weight_n of_o as_o
a_o magnitude_n of_o water_n 34_o foot_n in_o height_n 12_o inch_n in_o length_n and_o six_o inch_n in_o breadth_n though_o the_o weight_n of_o any_o pillar_n of_o air_n may_v be_v know_v by_o know_v only_o the_o dimension_n of_o it_o in_o breadth_n and_o length_n yet_o the_o weight_n of_o a_o pillar_n of_o water_n can_v be_v know_v unless_o all_o the_o three_o common_a dimension_n of_o it_o be_v first_o know_v the_o reason_n be_v this_o the_o pillar_n of_o air_n be_v all_o of_o the_o same_o height_n but_o the_o pillar_n of_o water_n in_o the_o ocean_n be_v of_o different_a height_n therefore_o not_o only_o must_v they_o be_v know_v secundum_fw-la longitudinem_fw-la &_o latitudinem_fw-la in_o length_n and_o breadth_n but_o secundum_fw-la profunditatem_fw-la that_o be_v according_a to_o deepness_n it_o be_v easy_a to_o know_v then_o what_o each_o particular_a pillar_n weigh_v first_o then_o try_v how_o much_o weight_n be_v in_o a_o cubical_a foot_n of_o water_n and_o have_v find_v this_o to_o be_v v_o g._n 56_o pound_n you_o may_v determine_v that_o a_o pillar_n of_o water_n 34_o foot_n high_a and_o 12_o inch_n thick_a weigh_v 1904_o pound_n a_o pillar_n 34_o foot_n high_a and_o six_o inch_n thick_a weigh_v 476_o pound_n note_v that_o in_o a_o cube_n of_o water_n six_o inch_n thick_a there_o be_v 216_o inch_n which_o weigh_v seven_o pound_n in_o a_o pillar_n 12_o inch_n thick_a and_o 20_o fathom_n or_o 100_o foot_n high_a you_o will_v find_v 5600_o pound_n weight_n in_o one_o of_o the_o same_o thickness_n but_o 200_o fathom_n high_a there_o be_v 56000_o fifty_o six_o thousand_o pound_n weight_n in_o a_o pillar_n three_o foot_n square_a and_o 20_o fathom_n deep_a there_o be_v 50400_o fifty_o thousand_o and_o four_o hundred_o pound_n weight_n make_v it_o 800_o fathom_n high_a with_o that_o thickness_n and_o it_o will_v weigh_v 504000_o five_o hundred_o and_o four_o thousand_o pound_n but_o if_o according_a to_o the_o theorem_fw-la 25_o you_o consider_v the_o 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