LIQUIDS AND ALLIED EXPERIMENTS. 1 5 



Then if the position of the swimmer remains unaltered and temperature is 

 constant 



P+h"p w g-Tr = P a + Pn = rt (13) 



while above, equation (8) 



B+h" PlB g-T=p a +p h =1I 

 II' is variable in time, whereas IT is constant. Moreover 



B-P=(p a -p'a)MpH-pn)™dP=Pa + Pk (14) 



Pa + fa = ° (15) 



The ratio (pa+p^/ipa+pl) is not the same as B/P but equal to U/Tl'. 



The imprisoned volume v' at constant temperature on flotation will be 

 rigorously 



v , = M(i/ Pw -i/ Po ) 



1 ~Pa/ ' R aP r -Ph/ 'R h pr-T/ 'R v p v r 



if R is the gas constant for air, hydrogen, and water vapor, as indicated 

 by subscripts. The second, third, and fourth terms of the denominator are 

 not larger than 0.00098 at ordinary temperatures and variable to less than 

 0.0000 1 per degree. Hence they are negligible as compared with the large 

 variations of m found in experiment, which amount to several per cent. 

 Thus 



v' = M(i/ Pw -i/p e ) (17) 



nearly enough for all purposes, and hence 



„-„.+ „,_ Mi^lM (| + |) {I8) 



in terms of mercury heads if 



A=v'p m S> (19) 



the condition of flotation is 



A (K ,H' h \ , , 



We may, on the other hand, express the pressures without coefficients, 

 v' being given by equation (17), 



v'n'={R a m a +R n m h )T (21) 



Again, since v' is constant, 



v'P = (R a m a +R h m h )T (22) 



at constant temperature; or from equation (18) 



m = ~ — ( — + — ) (23) 



gPnJ \ R a R h' 



