506 G. Barns — Fluid Volume and its 



surface v dp will be generated by moving the initial section, 



when 6 is constant, parallel to itself, in such a way that each 

 point describes an oblique horizontal. It is not to be inferred 

 that these horizontals are parallel, though within the limits of 

 the above investigation such a result is nearly given. 



Compressibility increasing inversely as the square of 

 the pressure binomial. 



34. Properties of the equations. — Equation (2) as used in 

 § 27, furnished a family of curves which in their ultimate con- 

 tour necessarily fall below the corresponding isothermals of 

 the substance under discussion. It is the object of this section 

 to investigate a similar family, the ultimate contours of which 

 are above the actual isothermals. This may be done by assuming 



v 

 d—/dp=jui/(l+ip)% whence 



v/V=Mp/(l + vp) . . . (6) 



In this case, when p = oo, v/ F=///v=2/9, as will be seen in 

 the following tables. In the actual case,* v/ T 7 ", though it can 

 not be greater than 1, will in all probability eventually ex- 

 ceed 2/9. 



The method of discussion to be adopted is similar to that in 

 the foregoing section. Let 



2/o=/A)i?o/( 1 + v i ? o) and y f =fio(p +p)/(l + u{p +p)). . 



Then y^y'-y^frp/^ ■»oPoYQ-+»ol>)/0-+»ol>o)) 5 or if 



M=M /{ 1 + V oPoY and * = V o/( l + v oPo) • ( 7 ) 



equation (6) again results. Hence if p and p are consecutive 

 pressure intervals between and p+p , then the constants 

 obtained from observations within the interval p, may be 

 reduced to those applying to the whole interval po+p, by 

 equations (7), or their equivalents 



/*o=M/{l- y Po)*9 v o= v /( l - v Po) • • ( 8 ) 



According to Mendeleef, Thorpe and Riicker, (1. c), the 

 volume of liquids in case of thermal expansion may be repre- 

 sented by V e —l/(i—lc0\ where pressure is constant, V Q the 



actual volume at temperature 6, and k a constant. Introduc- 

 ing equation (6) and denoting by V, the volume for pressure p 

 and temperature 0, V=(l+(v—fi)p)/(l — lc6)(l-\-vp), which for 

 pressures and temperatures not too great may be put V= 

 l+(v— fji)p/(l— k6 + vp). If, therefore, V= V c is constant, 



* Cf. Riicker (Nature, xli, p. 362, 1890). Converging lines of evidence obtained 

 from optical, electrical and thermal researches show that liquids can not be com- 

 pressed more than 2 to *3 of their normal bulk. 



