BRIDGMAN. — THERMODYNAMIC PROPERTIES OF WATER. 325 



At A, i\= r.t + Vu 

 MB, F/= JV+ rV 

 Ate, To = ['.,,+ roH,o+ To, 



AtD, r-/= IV + fVH.o+ F2/ 



where the suffixes K, Hi>0, or S indicate that the vohime is for the 

 kerosene, the water, or the steel respectively. 



Subtracting- the equations above from each other, we obtain 



(r, -(',)- (iv - To') = (Fu - PV) - {V^k - F2/) 



- (V, H,o - V,' H.o) + (Vu - Vu') - (IV - Fo/). 



We now denote by A/ the difference of displacements at the two 

 positions .1 and C, and by A/' the corresponding difference at the 

 positions B and D. We now assume that Fi and Fo differ only by 

 the volume of the cylinder of length A/, and similarly I'/ and F2' 

 differ only by the cylinder of length A/'. This assumption is justified 

 if only the positions of the pistons at A and C are so far removed from 

 the end of the cylinder that the end effects in the distortion of the 

 interior are the same in the two cases. This condition has been shown 

 by the theory to be satisfied when the distance is two or three diameters, 

 as it always was in these experiments. Hence we may write, 



Fi — Fo = Sq {1 -{- a p) A/ 



where Sq is the initial section of the cylinder at atmospheric pressure, 

 and a is the factor of proportionality by which this is changed with 

 pressure. Now if we call the displacement form A to B, Di and from 

 C to D, D2, then. 



D. -t- A/ = Z)i + A/' 



and the above equation may be thrown into the form 



Vi - Fo - (F/ _ IW) = - SoiD, - Dr) (1 + a p') + .0 A/a (p - p') 



We now make use of the fact that the total change of volume of 

 any sul)stance under pressure is proportional to its mass. If A v 

 (positive for a decrease) is taken as the change of volume of 1 gm. 

 between p and p', then, 



Fit — Fit' — (V-ik— V2k) = A Vk (niik — ^hk) 



F2 H2O — F2' H,0 = At! HjO in HjO 



(V^ - F/) - {1% - F^;) = A V, {mu - m^s) 



