434 



HYDRODYNAMICS. 



Fahrenheit, by subtracting from each of them the cor- 



vapour at the temperatures I T = 0.0185 metres, responding dilatation of mercury. Hence we shall 

 /, i', t", calculatedjrom a for- f- T' = 0.0190 have 



0.7547 . 20.9 



Spttific Elastic forces of the aqueous") 



Gravities- 



Specific 

 Gravities. 



mula given by Biot, vol. i. j T" = 0.0182. Conse 

 p. 27. 



quently f T = 0.0069. J T" = 0.0068. Hence 

 p 4. T = 0.7547 metres ; 

 p' |T' =0.74W; 

 p" I T" = 0.7554. 



But as the pressures p, p', p", or the altitude of the 

 mercury in the barometer, were observed at different 



n 



P' 



51.12 

 0.7440 . 214. 



= 0.0029 metres. 



0.7554 . 20.6 

 ~5412~~ 



= 0.0029. 



= 0.0029; so that the 



temperatures, they must be reduced to that of 32 of barometrical columns thus reduced will be 

 p fT = 0.7518 ; p' f T' = 0.7411 ; /' fT" = 0.7525. 



. 1 + K i sr 1.000549; 1 + t -0,00375 = 1.078375 

 1 + Kt' = 1.000562; 1 + t' .0,00375 = 1.080250 

 1 + K t" = 1.000541 ; 1 + /". 0,00375 = 1.077250. 



With these elements, and with X, which has been found, we have 



We have also 



X(l+KQ(p-|T) 

 1 + t 0.00375 

 Difference . . 



Hence we have the difference of these two terms, or 



= 5.078947 

 . 0.009988 



By adding to this (P" P) .0.76 metres ........ =0.43016 



we have 0.440148 



which is the sum of all the positive terms of the numerator. 



By subtracting the negative term, or 8(1^0.00375) ' ' ' = - 797783 



The difference is ;.,... 0.360370 



which is the value of the numerator of the formula. 



. =0.6891163 



we have Y = 



0.36037 

 0.6891163 



sr 0.522945 grammes, 



which is the weight of the volume of hydrogen gas contained in the glass vessel at 32 of Fahrenheit, and 0.76 

 metres, or 29.99* inches of the barometer. Hence we have the specific gravity of hydrogen gas, or 



0.522945 



PROP. XII. FHOB. 



To determine accurately the specific gravity of li- 

 quids. 



The accurate determination of the specific gravity of 

 liquids is like that of gaseous bodies, attended with con- 

 siderable difficulty. As the specific gravities of the gases 

 are referred to that of atmospheric air, so in liquid and 

 solid bodies the specific gravities are referred to that 

 of water, when at the temperature of + S.42 of the 

 centigrade scale, or 38. 15 of Fahrenheit, which cor- 

 responds to the maximum density of that fluid. 



In measuring the specific gravities of liquids, a glass 

 vessel with a narrow neck, after having been accurately 

 weighed when empty, is successively weighed when 

 Slled with distilled water, and with the liquid whose 



1 



specific gravity is required, and the temperature and 

 atmospherical pressure are carefully marked. The 

 volume of water and of fluid may then be obtained by 

 the following formulae which have been given by M. 

 Biot. In these formula, 



V == the interior capacity or volume of the glass vessel 

 in cubic centimetres, at the temperature of 32 

 of Fahrenheit, or that of melting ice. 



L =: the apparent weight of the liquid when it is 

 weighed. 



X =. dilatation of the liquid at 32 of Fahrenheit, taking 

 its volume at this temperature for unity. 



3' = the dilatation of water from its maximum density 

 to the temperature t'. 



F = the apparent weight of the water at the tempera, 

 ture t'. 



