the_o hole_n and_o put_v a_o final_a stop_n to_o the_o course_n of_o the_o water_n nor_o be_v i_o able_a to_o take_v out_o the_o needle_n and_o put_v it_o in_o again_o so_o nimble_o but_o that_o the_o air_n find_v time_n to_o get_v into_o the_o syphon_n and_o till_o the_o hole_n be_v again_o stop_v render_v it_o useless_a notwithstanding_o that_o the_o water_n be_v by_o suction_n endeavour_v to_o be_v set_v a_o run_v paradox_n xi_o that_o a_o solid_a body_n as_o ponderous_a as_o any_o yet_o know_v though_o near_o the_o top_n of_o the_o water_n it_o will_v sink_v by_o its_o own_o weight_n yet_o if_o it_o be_v place_v at_o a_o great_a depth_n then_o that_o of_o twenty_o time_n its_o own_o thickness_n it_o will_v not_o sink_v if_o its_o descent_n be_v not_o assist_v by_o the_o weight_n of_o the_o incumbent_a water_n this_o paradox_n have_v never_o be_v that_o i_o know_v of_o propose_v as_o yet_o by_o any_o have_v seem_v so_o little_a credible_a to_o those_o to_o who_o i_o have_v mention_v it_o without_o except_v mathematician_n themselves_o that_o i_o can_v scarce_o hope_v it_o shall_v be_v ready_o and_o general_o receive_v in_o this_o illustrious_a company_n upon_o less_o clear_a testimony_n then_o that_o of_o experience_n and_o therefore_o though_o if_o i_o mistake_v not_o some_o part_n of_o this_o proposition_n may_v be_v plausible_o deduce_v by_o the_o help_n of_o a_o instrument_n ingenious_o think_v upon_o by_o mounseur_fw-fr paschal_n yet_o i_o shall_v have_v recourse_n to_o my_o own_o method_n for_o the_o make_n of_o it_o out_o for_o these_o two_o reason_n the_o one_o that_o a_o great_a part_n of_o the_o paradox_n must_v be_v explicate_v as_o well_o as_o prove_v by_o the_o doctrine_n already_o settle_v in_o this_o paper_n the_o other_o that_o the_o experiment_n propose_v by_o monsieur_n paschal_n be_v to_o be_v do_v in_o a_o deep_a river_n and_o require_v a_o tube_n 20_o foot_n long_o who_o bottom_n must_v be_v fit_v with_o a_o brass_n cylinder_n make_v with_o a_o exactness_n scarce_o if_o at_o all_o to_o be_v hope_v for_o from_o our_o workman_n if_o i_o shall_v build_v any_o thing_n on_o this_o so_o difficult_a a_o experiment_n which_o himself_o do_v not_o affirm_v to_o have_v ever_o be_v actual_o try_v i_o fear_v most_o man_n will_v rather_o reject_v the_o experiment_n as_o a_o chimaerical_a thing_n then_o receive_v for_o its_o sake_n a_o doctrine_n that_o appear_v to_o they_o very_o extravagant_a let_v we_o then_o to_o employ_v in_o this_o case_n also_o the_o method_n we_o have_v hitherto_o make_v use_n of_o fill_v a_o glass_n vessel_n a_o b_o c_o d_o almost_o full_a of_o water_n 19_o only_o in_o regard_n that_o there_o be_v a_o great_a depth_n of_o water_n requisite_a to_o some_o circumstance_n of_o the_o experiment_n this_o last_o must_v not_o be_v so_o shallow_a as_o those_o hitherto_o employ_v but_o a_o deep_o cylinder_n or_o tube_n seal_v at_o one_o end_n who_o depth_n must_v be_v at_o least_o two_o or_o three_o foot_n though_o its_o breadth_n need_v not_o be_v above_o 2_o or_o 3_o inch_n and_o to_o keep_v it_o upright_o it_o may_v be_v place_v in_o a_o socket_n of_o metal_n or_o wood_n of_o a_o size_n and_o weight_n convenient_a for_o such_o a_o purpose_n this_o glass_n be_v thus_o fit_v in_o water_n let_v we_o suppose_v e_o f_o to_o be_v a_o round_a and_o flat_a piece_n of_o solid_a brass_n have_v about_o a_o inch_n in_o diameter_n and_o a_o four_o or_o six_o part_n of_o a_o inch_n in_o thickness_n this_o cylinder_n be_v immerse_v under_o water_n till_o it_o be_v just_o cover_v by_o the_o uppermost_a surface_n of_o that_o liquor_n and_o be_v let_v go_v must_v necessary_o fall_v downward_o in_o it_o because_o if_o we_o suppose_v the_o imaginary_a superficies_n g_o h_n to_o pass_v along_o the_o circle_n f_o which_o be_v the_o low_a part_n of_o the_o brass_n body_n that_o metal_n be_v in_o specie_fw-la far_o heavy_a than_o water_n the_o brass_n that_o lean_v upon_o the_o part_n f_o must_v far_o more_o gravitate_fw-la upon_o the_o say_a part_n f_o than_o the_o incumbent_a water_n do_v upon_o any_o other_o part_n of_o the_o superficies_n g_o h_n and_o consequent_o the_o subjacent_a water_n at_o f_o will_v be_v thrust_v out_o of_o place_n by_o the_o descend_a body_n and_o because_o that_o in_o what_o part_n soever_o of_o the_o water_n not_o exceed_v nine_o time_n its_o thickness_n measure_v from_o the_o top_n of_o the_o water_n a_o c_o the_o ponderous_a body_n e_o f_o shall_v happen_v to_o be_v there_o will_v be_v still_o by_o reason_n of_o the_o specific_a gravity_n of_o the_o metal_n a_o great_a pressure_n upon_o that_o part_n of_o the_o imaginary_a superficies_n that_o pass_v along_o the_o bottom_n of_o the_o body_n on_o which_o the_o part_n f_o shall_v happen_v to_o lean_v then_o upon_o any_o other_o part_n of_o the_o same_o imaginary_a superficies_n the_o brass_n body_n will_v still_o descend_v by_o virtue_n of_o its_o own_o weight_n though_o it_o be_v not_o assist_v by_o the_o weight_n of_o the_o water_n that_o be_v over_o it_o but_o let_v we_o suppose_v it_o to_o be_v place_v under_o water_n on_o the_o designable_a plain_n i_o k_o and_o let_v this_o plain_a which_o as_o all_o other_o imaginary_a plain_n be_v as_o well_o as_o the_o real_a surface_n of_o the_o water_n to_o be_v conceive_v parallel_n to_o the_o horizon_n and_o let_v the_o depth_n or_o distance_n of_o this_o plain_a from_o the_o uppermost_a surface_n of_o the_o water_n be_v some_o what_o above_o nine_o time_n the_o thickness_n of_o the_o brass_n body_n i_o say_v that_o in_o this_o case_n the_o body_n will_v not_o descend_v if_o it_o be_v not_o press_v downward_o by_o the_o weight_n of_o the_o water_n it_o have_v over_o it_o for_o brass_n be_v but_o about_o nine_o time_n fraction_n as_o heavy_a as_o water_v of_o a_o equal_a bulk_n to_o it_o the_o body_n e_o f_o alone_o will_v press_v upon_o the_o part_n f_o but_o as_o much_o as_o a_o cylinder_n of_o water_n will_v which_o have_v a_o equal_a basis_n be_v 8_o or_o 9_o time_n as_o high_a as_o the_o brass_n be_v thick_a but_o now_o all_o the_o other_o part_n of_o the_o imaginary_a surface_n i_o k_o be_v press_v upon_o by_o the_o incumbent_a water_n which_o be_v as_o high_a above_o they_o as_o the_o new_o mention_v cylinder_n of_o water_n will_v be_v there_o be_v no_o reason_n why_o the_o part_n f_o shall_v be_v depress_v rather_o than_o any_o other_o part_n of_o the_o superficies_n i_o k_o but_o because_o it_o be_v true_a which_o we_o former_o teach_v namely_o that_o water_n retain_v its_o gravity_n in_o water_n and_o that_o too_o though_o a_o body_n heavy_a in_o specie_fw-la then_o it_o be_v place_v immediate_o under_o it_o it_o will_v necessary_o happen_v that_o in_o what_o part_n soever_o the_o solid_a body_n be_v place_v provide_v it_o be_v every_o way_n environ_v with_o the_o water_n it_o must_v for_o the_o reason_n new_o give_v be_v make_v to_o move_v downward_o partly_o by_o its_o own_o weight_n and_o partly_o by_o that_o of_o the_o incumbent_a water_n and_o must_v continue_v to_o sink_v till_o it_o come_v to_o the_o bottom_n or_o some_o other_o body_n that_o hinder_v its_o far_a descent_n but_o in_o case_n the_o water_n above_o the_o solid_a body_n do_v not_o gravitate_fw-la upon_o it_o and_o thereby_o assist_v its_o descent_n or_o in_o case_n that_o the_o incumbent_a water_n be_v by_o some_o artifice_n or_o other_o so_o remove_v that_o none_o of_o the_o lateral_a water_n if_o i_o may_v so_o call_v it_o can_v succeed_v in_o its_o place_n to_o lean_v upon_o the_o solid_a than_o it_o will_v follow_v from_o what_o we_o have_v new_o show_v that_o the_o solid_a will_v be_v keep_v suspend_v and_o in_o case_n it_o be_v place_v much_o deep_a in_o the_o water_n as_o over_z against_o the_o point_n l_o or_o m_o then_o if_o we_o conceive_v the_o incumbent_a water_n to_o be_v remove_v or_o fence_v off_o from_o it_o the_o pressure_n of_o the_o solid_a alone_o upon_o the_o part_n f_o of_o the_o imaginary_a superficies_n l_o m_o be_v very_o much_o inferior_a to_o that_o of_o the_o water_n upon_o the_o other_o part_n of_o the_o same_o surface_n the_o part_n f_o will_v be_v strong_o impel_v upward_o by_o a_o force_n proportionate_a to_o the_o difference_n of_o those_o two_o pressure_n and_o therefore_o since_o i_o have_v find_v by_o trial_n purposely_o make_v in_o scale_n marvellous_o exact_a and_o with_o refine_a gold_n pure_a than_o perhaps_o any_o that_o be_v ever_o weigh_v in_o water_n that_o gold_n though_o much_o the_o ponderouf_a of_o body_n yet_o know_v in_o the_o world_n be_v not_o full_a 20_o time_n as_o heavy_a as_o water_v of_o the_o same_o bulk_n i_o keep_v within_o compass_n as_o well_o
the_o pressure_n of_o the_o ambient_fw-la atmosphaere_n this_o bubble_n be_v like_o a_o pear_n with_o its_o stem_n furnish_v with_o a_o very_a slender_a pipe_n of_o glass_n at_o which_o it_o be_v blow_v that_o it_o may_v be_v ready_o seal_v up_o and_o then_o the_o air_n within_o it_o be_v by_o the_o flame_n of_o the_o lamp_n gradual_o rarify_v as_o much_o as_o convenient_o can_v be_v whilst_o the_o body_n of_o the_o bubble_n be_v exceed_v hot_a the_o new_o mention_v stem_n be_v nimble_o put_v into_o the_o middle_n of_o the_o flame_n where_o by_o reason_n of_o its_o slenderness_n the_o glass_n which_o be_v exceed_v thin_a be_v immediate_o melt_v whereby_o the_o bubble_n be_v hermetical_o seal_v up_o this_o glass_n be_v permit_v leisurely_o to_o cool_v i_o can_v afterward_o keep_v it_o by_o i_o a_o hour_n or_o a_o day_n or_o a_o week_n or_o long_o if_o i_o think_v fit_a and_o when_o i_o have_v a_o mind_n to_o show_v the_o experiment_n i_o put_v it_o in_o one_o of_o the_o scale_n of_o a_o exact_a balance_n that_o will_v turn_v perhaps_o with_o the_o 30_o or_o 50th_o or_o a_o less_o part_n of_o a_o grain_n and_o have_v careful_o counterpoise_v it_o i_o then_o wary_o break_v off_o the_o seal_a end_n place_v a_o sheet_n of_o paper_n just_a under_o the_o scale_n to_o receive_v the_o fragment_n of_o the_o glass_n and_o put_v in_o again_o those_o fragment_n that_o scale_n wherein_o the_o glass_n be_v will_v considerable_o preponderate_v which_o it_o must_v do_v upon_o the_o account_n of_o the_o weight_n of_o air_n there_o be_v no_o other_o cause_n either_o needful_a or_o just_o assignable_a but_o the_o weight_n of_o the_o air_n that_o rush_v into_o the_o cavity_n of_o the_o glass_n as_o find_v less_o resistance_n there_o then_o elsewhere_o by_o reason_n that_o the_o include_v aire_n have_v its_o spring_n much_o weaken_v by_o its_o great_a expansion_n this_o experiment_n i_o many_o time_n try_v sometime_o before_o some_o virtuoso_n and_o sometime_o before_o other_o who_o all_o allow_v it_o to_o be_v conclusive_a for_o here_o it_o can_v not_o be_v object_v as_o against_o the_o weigh_v of_o air_n in_o a_o bladder_n which_o objection_n yet_o i_o can_v easy_o answer_v if_o it_o be_v now_o proper_a that_o the_o air_n which_o ponderate_v it_o stuff_v with_o the_o effluvia_fw-la of_o he_o that_o blow_v the_o bladder_n and_o beside_o that_o be_v not_o air_n in_o its_o natural_a state_n but_o violent_o compress_v for_o here_o it_o be_v the_o free_a air_n and_o in_o its_o wont_a laxity_n that_o make_v the_o glass_n preponderate_a and_o that_o there_o be_v a_o great_a ingress_n of_o the_o external_a air_n be_v evident_a by_o these_o three_o phaenomena_n the_o one_o that_o if_o you_o lend_v a_o attentive_a ear_n you_o shall_v plain_o hear_v a_o kind_n of_o whistle_a noise_n to_o be_v make_v by_o the_o external_a air_n as_o it_o rush_v violent_o in_o upon_o the_o break_n of_o the_o glass_n the_o other_o that_o the_o rarefaction_n of_o the_o air_n seal_v up_o in_o the_o bubble_n be_v very_o great_a there_o be_v a_o great_a deal_n of_o space_n leave_v for_o the_o ambient_fw-la air_n to_o fill_v upon_o its_o admission_n and_o the_o greatness_n of_o this_o rarefaction_n may_v be_v guess_v at_o both_o by_o the_o break_n of_o such_o bubble_n now_o and_o then_o by_o the_o pressure_n of_o the_o external_n air_n which_o be_v not_o competent_o assist_v by_o the_o internal_a to_o resist_v and_o also_o by_o the_o three_o phaenomenon_n i_o intend_v to_o take_v notice_n of_o namely_o that_o if_o instead_o of_o break_v off_o the_o seal_a end_n of_o the_o glass_n in_o the_o air_n you_o break_v it_o under_o water_n that_o liquor_n will_v by_o the_o pressure_n of_o the_o atmosphaere_n be_v force_v to_o spring_v up_o like_o a_o artificial_a fountain_n into_o the_o cavity_n of_o the_o bubble_n and_o fill_v about_o three_o quarter_n of_o it_o by_o which_o last_o circumstance_n i_o gather_v that_o the_o weight_n of_o the_o air_n be_v more_o considerable_a than_o even_o many_o who_o admit_v the_o air_n to_o have_v weight_n seem_v to_o imagine_v for_o we_o must_v not_o suppose_v that_o all_o the_o air_n contain_v in_o the_o bubble_n when_o break_v weigh_v no_o more_o than_o the_o weight_n requisite_a in_o the_o opposite_a scale_n to_o reduce_v the_o balance_n to_o a_o aequilibrium_fw-la since_o this_o additional_a weight_n be_v only_o that_o of_o the_o air_n that_o intrude_v on_o the_o break_n of_o the_o glass_n which_o air_n by_o the_o observation_n new_o mention_v to_o have_v be_v make_v with_o water_n appear_v to_o be_v but_o about_o three_o quarter_n of_o the_o whole_a air_n contain_v in_o the_o break_a bubble_n and_o yet_o according_a both_o to_o our_o estimate_n and_o that_o of_o divers_a virtuoso_n and_o some_o of_o they_o eminent_a mathematician_n when_o the_o capacity_n of_o the_o bubble_n be_v short_a of_o two_o cubical_a inch_n and_o so_o proportionable_o in_o other_o glass_n the_o nice_a balance_n we_o use_v manifest_v the_o new_o admit_v air_n to_o amount_v to_o some_o time_n near_o half_a a_o grain_n and_o sometime_o beyond_o it_o and_o because_o one_o of_o the_o last_o experiment_n that_o i_o make_v to_o this_o purpose_n with_o seal_a bubble_n be_v none_o of_o the_o least_o accurate_a i_o shall_v conclude_v this_o subject_a with_o the_o follow_a account_n of_o it_o a_o thin_a glass_n bubble_n blow_v at_o the_o flame_n of_o a_o lamp_n and_o hermetical_o seal_v when_o the_o contain_v air_n be_v exceed_o rarify_v be_v counterpoise_v in_o a_o nice_a pair_n of_o scale_n and_o then_o the_o seal_a apex_n be_v break_v off_o and_o put_v again_o into_o the_o same_o scale_n the_o weight_n appear_v to_o be_v increase_v by_o the_o readmit_v air_n a_o pretty_a deal_n above_o 11_o 16_o this_o and_o consequent_o very_o near_o if_o not_o full_a ¾_n of_o a_o grain_n last_o have_v by_o some_o slight_n for_o it_o be_v no_o very_a easy_a matter_n fill_v it_o with_o common_a water_n we_o weigh_v the_o glass_n and_o water_n together_o and_o find_v the_o latter_a beside_o the_o former_a to_o amount_v to_o 906_o grain_n so_o that_o suppose_v according_a to_o our_o former_a estimate_n countenance_v by_o some_o trial_n that_o the_o readmit_v air_n which_o amount_v to_o ¾_n of_o a_o grain_n fill_v but_o ¾_n of_o the_o whole_a cavity_n of_o the_o bubble_n the_o air_n that_o be_v in_o it_o when_o seal_v possess_v one_o quarter_n of_o that_o cavity_n the_o whole_a air_n contain_v in_o the_o bubble_n may_v be_v reasonable_o presume_v to_o weigh_v a_o whole_a grain_n in_o which_o case_n we_o may_v conclude_v abstract_v from_o some_o little_a nicety_n not_o fit_a to_o be_v take_v notice_n of_o here_o as_o elsewhere_o that_o the_o water_n in_o our_o experiment_n weigh_v very_o little_o more_o than_o nine_o hundred_o time_n as_o much_o as_o a_o equal_a quantity_n of_o air_n and_o therefore_o though_o we_o allow_v that_o in_o a_o experiment_n so_o diligent_o make_v as_o this_o be_v the_o air_n praexistent_a in_o the_o bubble_n do_v not_o adaequate_o possess_v so_o much_o as_o a_o four_o part_n but_o about_o a_o five_o or_o a_o six_o of_o its_o cavity_n the_o air_n will_v yet_o appear_v so_o heavy_a that_o this_o experiment_n will_v agree_v well_o with_o those_o other_o record_v in_o another_o treatise_n wherein_o we_o assign_v numero_fw-la rotundo_fw-la a_o thousand_o to_o one_o for_o the_o proportion_n wherein_o the_o specific_a gravity_n of_o water_n exceed_v that_o of_o air_n paradox_n i._n that_o in_o water_n and_o other_o fluid_n the_o low_a part_n be_v press_v by_o the_o upper_a provide_v a_o glass_n vessel_n of_o a_o convenient_a height_n and_o breadth_n a._n b._n c._n d._n fill_v with_o water_n almost_o to_o the_o top_n then_o take_v a_o glass_n pipe_n open_v at_o both_o end_n cylindrical_n and_o of_o a_o small_a boar_n as_o about_o the_o eight_o or_o six_o part_n of_o a_o inch_n in_o diameter_n put_v the_o low_a end_n of_o this_o pipe_n into_o clear_a oil_n or_o spirit_n of_o turpentine_n and_o have_v by_o suction_n raise_v the_o liquor_n to_o what_o part_n of_o the_o pipe_n you_o think_v fit_a as_o soon_o as_o it_o be_v there_o you_o must_v very_o nimble_o remove_v your_o lip_n stop_v the_o upper_a orifice_n with_o the_o pulp_n of_o your_o finger_n that_o the_o raise_v liquor_n may_v not_o fall_v back_o again_o then_o take_v the_o pipe_n and_o that_o liquor_n out_o of_o the_o oil_n of_o turpentine_n place_v it_o perpendicular_o in_o the_o glass_n of_o water_n so_o as_o that_o the_o surface_n of_o the_o oil_n in_o the_o pipe_n be_v somewhat_o high_a than_o that_o of_o the_o water_n without_o the_o pipe_n and_o have_v so_o do_v though_o you_o take_v off_o your_o finger_n from_o the_o upper_a orifice_n of_o the_o pipe_n
bring_v in_o a_o year_n or_o two_o since_o to_o this_o learned_a society_n by_o a_o deserve_o famous_a member_n of_o it_o geometry_n for_o though_o his_o supposal_n be_v make_v upon_o occasion_n of_o a_o experiment_n of_o another_o nature_n than_o any_o of_o the_o ensue_a it_o may_v be_v easy_o accommodate_v to_o my_o present_a purpose_n this_o postulatum_fw-la or_o lemma_n consist_v of_o three_o part_n the_o first_o of_o they_o more_o and_o the_o two_o last_o less_o principal_a suppose_v we_o then_o first_o that_o if_o a_o pipe_n open_a at_o both_o end_n and_o hold_v perpendicular_a to_o the_o horizon_n have_v the_o low_a of_o they_o under_o water_n there_o pass_v a_o imaginary_a plain_n or_o surface_n which_o touch_v that_o orifice_n be_v parallel_n to_o the_o horizon_n and_o consequent_o parallel_v as_o to_o sense_n to_o the_o upper_a surface_n of_o the_o water_n and_o this_o be_v but_o a_o help_n to_o the_o imagination_n will_v ready_o be_v grant_v second_o to_o this_o it_o will_v be_v consonant_n that_o each_o part_n of_o this_o designable_a surface_n will_v be_v as_o much_o and_o no_o more_o press_v as_o any_o other_o equal_a part_n of_o it_o by_o the_o water_n that_o be_v perpendicular_o incumbent_a on_o it_o for_o the_o water_n or_o other_o fluid_a be_v suppose_v to_o be_v of_o a_o homogeneous_a substance_n as_o to_o gravity_n and_o be_v of_o a_o equal_a height_n upon_o all_o the_o part_n of_o the_o imaginary_a surface_n there_o be_v no_o reason_n why_o one_o part_n shall_v be_v more_o press_v by_o a_o perpendicular_a pillar_n of_o that_o incumbent_a fluid_n than_o any_o other_o equal_a part_n of_o the_o same_o surface_n by_o another_o perpendicular_o incumbent_a pillar_n of_o the_o same_o or_o equal_a basis_n and_o height_n as_o well_o as_o of_o the_o same_o liquor_n but_o three_o though_o whilst_o our_o imaginary_a surface_n be_v equal_o press_v upon_o in_o all_o part_n of_o it_o the_o liquor_n must_v retain_v its_o former_a position_n yet_o if_o any_o one_o part_n come_v to_o have_v a_o great_a weight_n incumbent_n on_o it_o than_o there_o be_v upon_o the_o rest_n that_o part_n must_v be_v displace_v or_o depress_v as_o it_o happen_v when_o a_o stone_n or_o other_o body_n heavy_a than_o water_n sink_v in_o water_n for_o wherever_o such_o a_o a_o body_n happen_v to_o be_v underneath_o the_o water_n that_o part_n of_o the_o imaginary_a plain_n that_o be_v contiguous_a to_o the_o low_a part_n of_o the_o stone_n have_v on_o it_o a_o great_a weight_n than_o other_o part_n of_o the_o same_o surface_n must_v needs_o give_v way_n and_o this_o will_v be_v do_v successive_o till_o the_o stone_n arrive_v at_o the_o bottom_n and_o if_o on_o the_o other_o side_n any_o part_n of_o the_o imaginary_a surface_n be_v less_o press_v upon_o then_o all_o the_o rest_n it_o will_v by_o the_o great_a pressure_n on_o the_o other_o part_n of_o the_o surface_n be_v impel_v upward_o till_o it_o have_v attain_v a_o height_n at_o which_o the_o pressure_n of_o the_o raise_a water_n and_o the_o light_a or_o float_a body_n if_o any_o there_o be_v that_o lean_v upon_o it_o and_o gravitates_fw-la together_o with_o it_o upon_o the_o subjacent_a part_n of_o the_o imaginary_a surface_n will_v be_v equal_a to_o that_o which_o bear_v upon_o the_o other_o part_n of_o the_o same_o surface_n and_o because_o this_o seem_v to_o be_v the_o likely_a thing_n to_o be_v question_v in_o our_o assumption_n paradox_n though_o he_o that_o consider_v it_o attentive_o will_v easy_o enough_o be_v induce_v to_o grant_v it_o yet_o i_o shall_v here_o endeavour_v to_o evince_v it_o experimental_o and_o that_o by_o no_o other_o way_n of_o proof_n than_o the_o same_o i_o employ_v all_o along_o this_o present_a discourse_n take_v then_o a_o cylindrical_a glass_n pipe_n of_o a_o convenient_a boar_n open_a at_o both_o end_n let_v the_o tube_n be_v steady_o hold_v perpendicular_a to_o the_o horizon_n the_o low_a end_n of_o it_o be_v two_o or_o three_o inch_n beneath_o the_o surface_n of_o a_o convenient_a quantity_n of_o water_n which_o ought_v not_o to_o fill_v the_o glass_n vessel_n that_o contain_v it_o the_o pipe_n be_v hold_v in_o this_o posture_n it_o be_v manifest_a that_o the_o water_n within_o the_o pipe_n will_v be_v almost_o in_o a_o level_n with_o the_o surface_n of_o the_o water_n without_o the_o pipe_n because_o the_o external_a and_o internal_a water_n as_o i_o be_o wont_a for_o brevity_n sake_n to_o call_v they_o have_v free_a intercourse_n with_o one_o another_o by_o the_o open_a orifice_n of_o the_o immersed_a end_n of_o the_o pipe_n yet_o i_o think_v fit_a to_o insert_v the_o word_n almost_o because_o if_o the_o pipe_n be_v any_o thing_n slender_a the_o surface_n of_o the_o water_n in_o it_o will_v always_o be_v somewhat_o high_a than_o that_o of_o the_o water_n without_o it_o for_o reason_n that_o it_o be_v not_o so_o necessary_a we_o shall_v now_o inquire_v after_o as_o it_o be_v that_o we_o shall_v here_o desire_v to_o have_v this_o take_v notice_n of_o once_o for_o all_o that_o mistake_n may_v be_v avoid_v without_o a_o troublesome_a repetition_n of_o the_o difference_n in_o height_n of_o the_o surface_n of_o liquor_n within_o pipe_n and_o without_o they_o in_o case_n they_o be_v any_o thing_n slender_a the_o pipe_n be_v hold_v in_o the_o new_o mention_v posture_n if_o you_o gentle_o pour_v a_o convenient_a quantity_n of_o oil_n upon_o the_o external_a water_n you_o shall_v see_v that_o as_o the_o oil_n grow_v high_a and_o high_o above_o the_o surface_n of_o that_o water_n the_o water_n within_o it_o will_v rise_v high_a and_o high_o and_o continue_v to_o do_v so_o as_o long_o as_o you_o continue_v to_o pour_v on_o oil_n of_o which_o the_o reason_n seem_v manifest_o to_o be_v this_o that_o in_o the_o imaginary_a plain_n that_o pass_v by_o the_o orifice_n of_o the_o immersed_a end_n of_o the_o pipe_n all_o that_o be_v not_o within_o the_o compass_n of_o the_o orifice_n be_v expose_v to_o a_o additional_a pressure_n from_o the_o weight_n of_o the_o oil_n which_o swim_v upon_o the_o water_n and_o that_o pressure_n must_v still_o be_v increase_v as_o there_o be_v more_o and_o more_o oil_n pour_v on_o whereas_o a_o circular_a part_n of_o the_o imaginary_a plain_n equal_a to_o the_o orifice_n of_o the_o glass_n be_v by_o the_o side_n of_o the_o pipe_n fence_v from_o the_o immediate_a pressure_n of_o the_o oil_n so_o that_o all_o those_o other_o part_n of_o the_o water_n be_v far_o more_o press_v than_o that_o part_n which_o be_v comprehend_v within_o the_o cavity_n of_o the_o tube_n and_o consequent_o the_o press_v part_n of_o the_o external_a water_n be_v by_o the_o equal_a gravitation_n of_o the_o oil_n upon_o the_o part_n of_o the_o external_a water_n impel_v up_o into_o the_o cavity_n of_o the_o pipe_n where_o they_o find_v less_o resistance_n than_o any_o where_o else_o till_o they_o arrive_v at_o such_o a_o height_n that_o the_o cylinder_n of_o water_n within_o the_o pipe_n do_v as_o much_o gravitate_fw-la upon_o the_o subjacent_a part_n of_o the_o imaginary_a surface_n as_o the_o water_n and_o oil_n together_o do_v upon_o every_o other_o equal_a part_n of_o the_o same_o surface_n or_o plain_n but_o as_o well_o the_o former_a lemma_n as_o this_o experiment_n will_v be_v sufficient_o both_o clear_v and_o confirm_v by_o the_o follow_a explication_n to_o which_o i_o shall_v for_o that_o reason_n forthwith_o proceed_v be_v it_o not_o that_o since_o divers_a passage_n of_o the_o follow_a treatise_n suppose_v the_o air_n to_o be_v a_o body_n not_o devoid_a of_o weight_n which_o yet_o divers_a learned_a adherent_n to_o the_o peripatetic_a philosophy_n do_v resolute_o deny_v it_o seem_v requisite_a to_o premise_v something_o for_o the_o proof_n of_o this_o truth_n and_o though_o i_o think_v the_o argument_n we_o have_v employ_v to_o that_o purpose_n already_o do_v strong_o evince_v it_o yet_o if_o i_o may_v be_v allow_v to_o anticipate_v one_o of_o my_o own_o experiment_n of_o the_o appendix_n i_o shall_v give_v a_o instance_n of_o the_o weight_n of_o the_o air_n not_o liable_a so_o much_o as_o to_o those_o invalid_a objection_n which_o some_o of_o the_o aristotelian_o have_v make_v against_o those_o proof_n wherewith_o we_o have_v be_v so_o happy_a as_o to_o satisfy_v the_o learned_a even_n of_o our_o profess_a adversary_n we_o cause_v then_o to_o be_v blow_v at_o the_o flame_n of_o a_o lamp_n a_o bubble_n of_o glass_n of_o about_o the_o bigness_n of_o a_o small_a hen-egge_n which_o that_o it_o may_v be_v light_a enough_o to_o be_v weigh_v in_o exact_a scale_n aught_o to_o be_v of_o no_o great_a thickness_n then_o be_v judge_v necessary_a to_o keep_v it_o from_o be_v when_o seal_v up_o with_o none_o but_o very_o much_o expanded_a air_n in_o it_o break_v by_o
of_o the_o imaginary_a superficies_n that_o pass_v by_o the_o low_a orifice_n of_o it_o be_v the_o same_o with_o the_o pressure_n which_o other_o part_n of_o that_o imaginary_a superficies_n sustain_v from_o as_o much_o of_o the_o external_n water_n and_o of_o the_o atmosphaere_n as_o come_v to_o lean_v upon_o it_o that_o there_o may_v be_v case_n wherein_o water_n may_v be_v raise_v by_o suction_n not_o upon_o the_o account_n of_o the_o weight_n of_o the_o air_n but_o of_o its_o spring_n i_o have_v elsewhere_o show_v and_o have_v likewise_o in_o other_o place_n endeavour_v to_o explicate_v more_o particular_o the_o ascension_n of_o water_n in_o pump_n what_o have_v be_v say_v already_o may_v suffice_v to_o be_v say_v in_o this_o place_n where_o it_o be_v sufficient_a for_o i_o to_o have_v show_v that_o whither_o or_o no_o the_o ascension_n of_o water_n may_v have_v other_o cause_n yet_o in_o the_o case_n propose_v it_o need_v no_o more_o than_o the_o competent_a weight_n of_o a_o external_n fluid_n as_o be_v the_o air_n who_o not_o be_v devoid_a of_o gravity_n the_o cogency_n of_o our_o experiment_n have_v bring_v even_o our_o adversary_n to_o grant_v we_o for_o confirmation_n of_o this_o i_o will_v here_o add_v because_o it_o now_o come_v into_o my_o mind_n what_o may_v perhaps_o be_v elsewhere_o somewhat_o more_o proper_o mention_v a_o experiment_n that_o i_o do_v but_o light_o glance_v at_o in_o the_o explication_n of_o the_o first_o and_o the_o scholium_fw-la of_o the_o second_o paradox_n in_o order_n to_o this_o i_o must_v advertise_v that_o whereas_o i_o there_o take_v notice_n that_o some_o ingenious_a man_n have_v complain_v that_o contrary_a to_o the_o experiment_n propose_v by_o monsieur_n paschall_n they_o be_v not_o at_o all_o able_a to_o keep_v mercury_n suspend_v in_o tube_n however_o very_o slender_a though_o the_o low_a end_n be_v deep_o immerse_v in_o water_n if_o both_o their_o end_n be_v open_a the_o reason_n of_o my_o doubt_n whether_o our_o ingenious_a author_n have_v ever_o make_v or_o see_v the_o experiment_n be_v not_o only_o that_o it_o have_v be_v unsuccessful_o try_v and_o seem_v to_o i_o unlikely_a to_o succeed_v in_o tube_n more_o slender_a than_o his_o appear_v but_o because_o the_o impetus_fw-la which_o fall_v quick_a silver_n gain_v by_o the_o acceleration_n of_o motion_n it_o acquire_v in_o its_o descent_n must_v in_o all_o probability_n be_v great_a enough_o to_o make_v it_o all_o run_v out_o at_o the_o bottom_n of_o a_o tube_n open_a at_o both_o end_n and_o fill_v with_o so_o ponderous_a a_o liquor_n though_o the_o tube_n be_v very_o much_o short_a than_o that_o propose_v by_o monsieur_n paschall_n this_o advertisement_n i_o premise_v to_o intimate_v that_o notwithstanding_o the_o hopelessness_n of_o the_o experiment_n as_o it_o have_v be_v propose_v and_o try_v i_o may_v have_v reason_n not_o to_o think_v it_o impossible_a to_o perform_v by_o another_o way_n the_o main_a thing_n desire_v which_o be_v to_o keep_v quicksilver_n suspend_v in_o a_o tube_n open_a at_o both_o end_n by_o the_o resistance_n of_o the_o subjacent_a water_n for_o by_o the_o expedient_a i_o be_o go_v to_o propose_v i_o have_v be_v able_a to_o do_v it_o even_o with_o a_o liquor_n much_o light_a than_o water_n find_v then_o that_o even_o a_o very_a short_a cylinder_n of_o so_o ponderous_a a_o fluid_a as_o mercury_n will_v if_o it_o be_v once_o in_o fall_v descend_v with_o a_o impetus_fw-la not_o easy_a to_o be_v resist_v by_o the_o subjacent_a liquor_n i_o think_v upon_o the_o follow_a expedient_a to_o prevent_v this_o inconvenience_n i_o take_v a_o slender_a pipe_n the_o diameter_n of_o who_o cavity_n be_v little_a above_o the_o six_o part_n of_o a_o inch_n and_o have_v suck_v in_o at_o the_o low_a end_n of_o it_o somewhat_o less_o than_o half_a a_o inch_n of_o quicksilver_n and_o nimble_o stop_v the_o upper_a orifice_n with_o my_o finger_n i_o thrust_v the_o quicksilver_n into_o a_o deep_a glass_n of_o oil_n of_o turpentine_n with_o a_o care_n not_o to_o unstop_v the_o upper_a orifice_n till_o the_o small_a cylinder_n of_o quicksilver_n be_v 18_o or_o 20_o time_n its_o depth_n beneath_o the_o surface_n of_o the_o oil_n for_o by_o this_o mean_n when_o i_o unstop_v the_o pipe_n the_o quicksilver_n need_v not_o as_o otherwise_o it_o will_v begin_v to_o fall_v as_o have_v a_o long_o cylinder_n than_o be_v requisite_a to_o make_v a_o aequilibrium_fw-la with_o the_o other_o fluid_fw-la for_o by_o our_o expedient_a the_o pressure_n of_o the_o oil_n be_v already_o full_a as_o great_a if_o not_o great_a against_o the_o low_a part_n of_o the_o mercurial_a cylinder_n as_o that_o which_o the_o weight_n of_o so_o short_a a_o cylinder_n can_v exercise_v upon_o the_o contiguous_a and_o subjacent_a oil_n and_o according_o upon_o the_o removal_n of_o my_o finger_n the_o quicksilver_n do_v not_o run_v out_o but_o remain_v suspend_v in_o the_o low_a part_n of_o the_o pipe_n and_o as_o if_o i_o raise_v it_o towards_o the_o superficies_n of_o the_o oil_n the_o mercury_n will_v drop_v out_o for_o want_n of_o its_o wont_a counterpoise_n so_o if_o i_o thrust_v the_o pipe_n deep_o into_o the_o oil_n the_o increase_v pressure_n of_o the_o oil_n will_v proportionable_o impel_v up_o the_o mercury_n towards_o the_o high_a part_n of_o the_o pipe_n which_o be_v again_o a_o little_a and_o but_o a_o little_a raise_v the_o quicksilver_n will_v fall_v down_o a_o little_a near_o the_o bottom_n of_o the_o pipe_n and_o so_o with_o a_o not_o unpleasant_a spectacle_n the_o ponderous_a body_n of_o quick_a silver_n be_v make_v sometime_o to_o rise_v and_o sometime_o to_o fall_v but_o still_o to_o float_v up_o on_o the_o surface_n of_o a_o liquor_n light_a there_o common_a spirit_n of_o wine_n itself_o but_o beside_o that_o the_o experiment_n if_o the_o maker_n of_o it_o be_v not_o very_o careful_a may_v easy_o enough_o miscarry_v the_o divertisement_n it_o give_v seldom_o prove_v last_v the_o oil_n of_o turpentine_n after_o a_o while_n insinuate_v itself_o betwixt_o the_o side_n of_o the_o pipe_n and_o those_o of_o so_o short_a a_o cylinder_n of_o mercury_n and_o thereby_o disorder_v all_o and_o therefore_o though_o i_o here_o mention_v this_o experiment_n as_o i_o try_v it_o in_o oil_n of_o turpentine_n because_o that_o be_v the_o liquor_n i_o make_v use_n of_o all_o along_o these_o paradox_n and_o because_o also_o i_o will_v show_v that_o a_o light_a fluid_n than_o water_n and_o therefore_o why_o not_o air_n if_o its_o height_n be_v great_o enough_o increase_v may_v by_o its_o weight_n and_o pressure_n either_o keep_v the_o mercury_n suspend_v in_o pipe_n or_o even_o raise_v it_o in_o they_o yet_o i_o find_v water_n wherewith_o i_o fill_v tall_a glass_n a_o fit_a liquor_n than_o oil_n for_o the_o experiment_n in_o which_o though_o i_o seek_v and_o find_v some_o other_o phaenomena_n yet_o because_o they_o more_o proper_o belong_v to_o another_o place_n i_o shall_v leave_v they_o unmentioned_a in_o this_o and_o since_o experience_n show_v we_o that_o a_o cylinder_n of_o mercury_n of_o about_o 30_o inch_n high_a be_v aequiponderant_a to_o a_o cylinder_n of_o water_n of_o about_o 33_o or_o 34_o foot_n high_a it_o be_v very_o easy_a to_o conclude_v that_o the_o weight_n of_o the_o external_n air_n which_o be_v able_a to_o raise_v and_o keep_v suspend_v 33_o or_o 34_o foot_n of_o water_n in_o a_o pump_n may_v do_v the_o like_a to_o 29_o or_o 30_o inch_n of_o quicksilver_n in_o the_o torricellian_a experiment_n paradox_n v._n that_o the_o pressure_n of_o a_o external_n fluid_n be_v able_a to_o keep_v a_o heterogeneous_a liquor_n suspend_v at_o the_o same_o height_n in_o several_a pipe_n though_o those_o pipe_n be_v of_o very_o different_a diameter_n the_o contrary_n of_o this_o proposition_n be_v so_o confident_o assert_v and_o believe_v by_o those_o mathematician_n and_o other_o that_o favour_n the_o doctrine_n of_o the_o school_n that_o this_o persuasion_n of_o they_o seem_v to_o be_v the_o chief_a thing_n that_o have_v hinder_v man_n from_o acknowledge_v that_o the_o quicksilver_n in_o the_o torricellian_a experiment_n may_v be_v keep_v suspend_v by_o the_o counterpoise_n of_o the_o external_a air_n and_o a_o famous_a writer_n that_o have_v late_o treat_v as_o well_o of_o the_o hydrostaticks_n as_o of_o the_o 〈◊〉_d of_o the_o torricellian_a experiment_n 〈…〉_z the_o falsehood_n of_o our_o paradox_n that_o lay_v aside_o all_o other_o argument_n he_o content_v himself_o to_o confute_v his_o adversary_n with_o one_o demonstration_n as_o he_o call_v it_o ground_v on_o the_o quite_o contrary_a of_o what_o we_o here_o assert_v for_o his_o objection_n run_v to_o this_o sense_n that_o if_o it_o be_v the_o pressure_n of_o the_o external_n aire_n that_o keep_v the_o quicksilver_n suspend_v in_o the_o new_o mention_v experiment_n the_o
other_o part_n of_o the_o same_o superficies_n and_o consequent_o neither_o the_o one_o nor_o the_o other_o of_o those_o liquor_n will_v subside_o but_o they_o will_v both_o rest_n in_o a_o aequilibrium_fw-la but_o here_o it_o will_v not_o he_o amiss_o to_o note_v first_o that_o it_o be_v not_o necessary_a that_o the_o glass_n cylinder_n l_o m_o n_o shall_v be_v all_o of_o the_o same_o length_n since_o the_o low_a orifice_n be_v open_a the_o water_n will_v rise_v to_o the_o same_o height_n within_o they_o whether_o the_o part_n immerse_v under_o the_o water_n be_v exact_o of_o the_o same_o length_n or_o no._n and_o second_o that_o throughout_o all_o this_o discourse_n and_o particular_o in_o the_o explication_n of_o this_o paradox_n we_o suppose_v either_o that_o the_o slender_a pipe_n that_o be_v employ_v about_o these_o experiment_n be_v of_o a_o moderate_a size_n and_o not_o exceed_v small_a or_o that_o in_o case_n they_o be_v very_o small_a allowance_n be_v make_v in_o such_o pipe_n for_o this_o property_n that_o water_n will_v rise_v in_o they_o to_o a_o great_a height_n then_o can_v be_v attribute_v to_o the_o bare_a counterpoise_n of_o either_o the_o water_n or_o the_o oil_n that_o impel_v it_o upward_o and_o keep_v it_o suspend_v but_o this_o difference_n be_v of_o so_o little_a moment_n in_o our_o present_a inquiry_n that_o we_o may_v safe_o neglect_v it_o as_o hereafter_o we_o mean_v to_o do_v now_o we_o have_v take_v this_o notice_n of_o it_o for_o prevention_n of_o mistake_n paradox_n vi._n if_o a_o body_n be_v place_v under_o water_n with_o its_o uppermost_a surface_n parallel_v to_o the_o horizon_n how_o much_o water_n soever_o there_o may_v be_v on_o this_o or_o that_o side_n above_o the_o body_n the_o direct_a pressure_n sustain_v by_o the_o body_n for_o we_o now_o consider_v not_o the_o lateral_a nor_o the_o recoil_n pressure-to_a which_o the_o body_n may_v be_v expose_v if_o quite_o environ_v with_o water_n be_v no_o more_o than_o that_o of_o a_o column_n of_o water_n have_v the_o horizontal_a superficies_n of_o the_o body_n for_o its_o basis_n and_o the_o perpendicular_a depth_n of_o the_o water_n for_o its_o height_n and_o so_o likewise_o if_o the_o water_n that_o lean_v upon_o the_o body_n be_v contain_v in_o pipe_n open_a at_o both_o end_n the_o pressure_n of_o the_o water_n be_v to_o be_v estimate_v by_o the_o weight_n of_o a_o pillar_n of_o water_n who_o basis_n be_v equal_a to_o the_o low_a orifice_n of_o the_o pipe_n which_o we_o suppose_v to_o be_v parallel_n to_o the_o horizon_n and_o its_o height_n equal_a to_o a_o perpendicular_a reach_v thence_o to_o the_o top_n of_o the_o water_n though_o the_o pipe_n be_v much_o incline_v towards_o the_o horizon_n or_o though_o it_o be_v irregular_o shape_v and_o much_o broad_a in_o some_o part_n than_o the_o say_a orifice_n stevinus_n in_o the_o ten_o proposition_n of_o his_o hydrostatical_a element_n have_v propose_v in_o more_o general_a term_n the_o former_a part_n of_o our_o paradox_n annex_v to_o see_v a_o demonstration_n to_o this_o purpose_n if_o the_o bottom_n e_o f_o be_v charge_v with_o a_o great_a weight_n then_o that_o of_o the_o water_n g_o h_o f_o e_o that_o surplusage_n must_v come_v from_o the_o adjoin_a water_n therefore_o if_o it_o be_v possible_a let_v it_o be_v from_o the_o water_n a_o g_o e_o d_o &_o h_n b_o c_o f_o which_o grant_v the_o bottom_n d_o e_o will_n likewise_o have_v a_o great_a weight_n incumbent_n on_o it_o upon_o the_o score_n of_o the_o neighbour_a water_n g_z h_o f_o e_o then_z that_o of_o the_o water_n a_o g_o e_o d._n and_o the_o reason_n be_v the_o same_o in_o all_o the_o three_o case_n the_o basis_n f_o c_o must_v sustain_v a_o great_a weight_n then_o that_o of_o the_o water_n h_o b_o c_o f._n and_o therefore_o the_o whole_a bottom_n d_o c_o will_n have_v a_o great_a weight_n incumbent_n on_o it_o then_o that_o of_o the_o whole_a water_n a_o b_o c_o d_o which_o yet_o a_o b_o c_o d_o be_v a_o rectangular_a body_n will_v be_v absurd_a and_o by_o the_o same_o way_n of_o reason_v you_o may_v evince_v that_o the_o bottom_n e_o f_o sustain_v no_o less_o a_o weight_n then_o that_o of_o the_o water_n g_o h_o f_o e._n and_o so_o since_o it_o sustain_v neither_o a_o great_a weight_n nor_o a_o less_o it_o must_v sustain_v just_a as_o much_o weight_n as_o the_o column_n of_o water_n g_o h_o f_o e._n this_o demonstration_n of_o the_o learned_a stevinus_n may_v well_o enough_o be_v admit_v by_o a_o naturalist_n though_o according_a to_o some_o hypothesis_n touch_v the_o cause_n and_o nature_n of_o gravity_n it_o may_v fail_v of_o mathematical_a exactness_n and_o by_o it_o may_v be_v confirm_v the_o first_o part_n of_o our_o propose_a paradox_n and_o some_o thing_n annex_v by_o stevinus_n to_o this_o demonstration_n may_v be_v also_o apply_v to_o countenance_v the_o second_o but_o because_o this_o be_v one_o of_o the_o noble_a and_o useful_a subject_n of_o the_o hydrostaticks_n we_o think_v it_o worth_a while_n to_o illustrate_v after_o our_o manner_n each_o of_o the_o two_o part_n of_o our_o paradox_n by_o a_o sensible_a experiment_n first_o then_o take_v a_o slender_a glass_n pipe_n of_o a_o even_a boar_n turn_v up_o at_o one_o end_n like_o the_o annex_v syphon_n 8._o into_o this_o syphon_n suck_v oil_n of_o turpentine_n till_o the_o liquor_n have_v fill_v the_o short_a leg_n and_o be_v raise_v 2_o or_o 3_o inch_n in_o the_o long_o then_o nimble_o stop_v the_o upper_a orifice_n with_o your_o finger_n thrust_v the_o low_a part_n of_o the_o syphon_n so_o far_o into_o a_o deep_a glass_n full_a of_o water_n that_o the_o surface_n of_o the_o oil_n in_o the_o long_a leg_n of_o the_o pipe_n may_v be_v but_o a_o little_a high_o than_o that_o of_o the_o external_n water_n and_o upon_o the_o removal_n of_o your_o finger_n you_o will_v find_v the_o surface_n of_o the_o oil_n to_o vary_v but_o little_a or_o not_o at_o all_o its_o former_a station_n and_o as_o if_o you_o then_o thrust_v the_o pipe_n a_o little_a deep_o you_o will_v so_o the_o oil_n in_o the_o short_a leg_n to_o begin_v to_o be_v depress_v so_o if_o afterward_o you_o gentle_o raise_v the_o pipe_n towards_o the_o top_n of_o the_o water_n you_o shall_v see_v the_o oil_n not_o only_o regain_v its_o former_a station_n but_o flow_v out_o by_o degree_n in_o drop_n that_o will_v emerge_n to_o the_o top_n of_o the_o water_n now_o since_o the_o water_n be_v able_a at_o first_o to_o keep_v the_o oil_n in_o the_o long_a leg_n of_o the_o pipe_n suspend_v no_o high_a than_o it_o will_v have_v be_v keep_v by_o a_o cylinder_n of_o water_n equal_a to_o the_o orifice_n of_o the_o short_a leg_n of_o the_o pipe_n and_o reach_v direct_o thence_o to_o the_o top_n of_o the_o water_n as_o may_v be_v easy_o cry_v by_o make_v a_o syphon_n where_o the_o short_a leg_n may_v be_v long_o enough_o to_o contain_v such_o a_o cylinder_n of_o water_n to_o conterpoize_v the_o oil_n in_o the_o long_o &_o since_o when_o once_o by_o the_o raise_n of_o the_o pipe_n the_o height_n of_o the_o incumbent_a water_n be_v lessen_v the_o oil_n do_v more_o than_o counterbalance_n it_o as_o appear_v by_o its_o flow_v out_o of_o the_o syphon_n we_o may_v well_o conclude_v that_o though_o thence_o be_v in_o the_o vessel_n a_o great_a deal_n of_o water_n high_a than_o the_o immersed_a orifice_n of_o the_o syphon_n and_o it_o will_v be_v all_o one_o though_o the_o syphon_n be_v placid_a at_o the_o same_o depth_n in_o a_o pond_n or_o lake_n yet_o of_o all_o that_o water_n no_o more_o do_v gravitate_fw-la upon_o the_o orifice_n then_o that_o which_o be_v place_v direct_o over_o it_o which_o be_v such_o a_o pillat_n of_o water_n as_o the_o paradox_n describe_v and_o by_o the_o way_n we_o may_v hence_o learn_v that_o though_o water_n be_v not_o include_v in_o pipe_n yet_o it_o may_v press_v as_o regular_o upon_o a_o subjacent_a body_n as_o if_o it_o be_v and_o therefore_o we_o may_v well_o enough_o conceive_v a_o pillar_n of_o water_n in_o the_o free_a water_n itself_o where_o there_o be_v nothing_o on_o any_o side_n but_o the_o contiguous_a water_n to_o bound_v the_o imaginary_a pillar_n but_o i_o have_v forget_v to_o add_v that_o the_o first_o part_n of_o our_o paradox_n will_v hold_v not_o only_a when_o the_o water_n superior_a to_o the_o body_n it_o press_v upon_o be_v free_a but_o also_o when_o it_o be_v include_v in_o vessel_n of_o never_o so_o seem_o disadvantageous_a a_o shape_n for_o if_o you_o so_o frame_v the_o short_a leg_n of_o a_o syphon_n that_o it_o may_v expand_v its_o self_n into_o a_o funnel_n like_o that_o of_o fig._n 6._o employ_v about_o the_o proof_n of_o the_o forego_n