498 C. Bar us — Fluid Volume and its 



not predict a maximum. It is therefore more in keeping with 

 the isothermals of the above pages. In view of its simplicity, 

 and of the additional fact that for p=oo , y=oo generally, it 

 may be taken as one limit of the isothermal band described in 

 § 25. 



(A+p), where A is constant, is conveniently termed the 

 pressure binomial. Approximate values of the constants in 

 (2) might be derived from table 20, since a=b(m—a)/m, and 

 d-/a=m 2 /b(m—a), nearly. I was inclined to infer that at the 

 melting poiDt, for the above class of substances, compressibility 

 is constant and independent of pressure. In such a case #=$ 

 would be the criterion of fusion. Subsequent results did not 

 substantiate this surmise. Another similar inference that the 

 resistance to compression is equal to the incipient resistance to 

 extension even in liquids, and that therefore l/# must have a 

 constant value at the boiling point independent of substance 

 is not warranted by the experiments made. 



28. Properties of the exponential. — Certain salient properties 

 of equation (2) may be grouped together here. The occur- 

 rence of y=10 3 v/ V=oc for p—oo is not a fatal objection 

 against the equation. For its application necessarily ceases at a 

 finite value of p, i. e. at the point of solidification of the sub- 

 stance, by pressure. As far as this point equation (2) may 

 faithfully represent the volume decrements observed. Sup- 

 pose for a given substance y / =ln(l+a (p+p ) and simulta- 

 neously y =ln(l+a p ) , where p and p are any two con- 

 secutive intervals of pressure. Then 



1+ t^F) ■ ■ : ■ (3) 



Hence, if a=a /(l+a p ) and #=# /(l + a ^> ), equation (3) at 

 once reverts to the form (2). Thus from the observations y 

 made along any arc of the whole curve, between p=0 and 

 p—Pt it is at once possible to obtain the constants for the 

 whole curve referred to an origin at zero atmospheres, by the 

 equations 



a *= a /( l ~ a P,) andS =3/(l-ap ) .... (4) 

 so that the reductions are simple. Equations (4) suggest an 

 important consequence : when ap ^>l, both a and # become 

 imaginary. It is a matter for curious remark, that this takes 

 place in case of ether and of alcohol, near or above the critical 

 temperature. I inferred that the compressibility of liquids 



v 

 d^/dp= — $/(l-\-ap) changes form and passes into the com- 



dv 

 pressibility of gasses — fdp= — 1/p, through an imaginary form. 



