of Water at High Temperatures. 125 



of drawing the curve through them by means of a flexible straight 

 edge held in one position for the whole length accounts for this. 

 If the law of continuity is maintained, the true line must be one 

 of a similar kind with regular curvature; and if not exactly coin- 

 cident with this, must intersect it with flat loops of very limited 

 divergence, or be nearly parallel to it, because the straight edge 

 is fixed from end to end of the range of points, and is assisted 

 by the observations quoted in the previous paper ; one of which, 

 viz. that at 200° is computed backwards, and marked off on 

 fig. 8. In this figure a faint dotted line has been drawn below 

 the one now discussed. It coincides with certain of the obser- 

 vations, which, from some recurring cause (connected with the 

 increasing of the temperature by steps), appear on a lower level 

 than the others. I have carefully analysed this curve in the 

 same way as the first, and find the projection of the points in 

 fig. 10 is so close to those given that it would only confuse to 

 add them. -i 



§ 17. The question now occurs, what is the value of- given 



by the line A A ? (see § 2 in original paper on Liquid Expansion, 

 Phil. Mag. June 1861.) 



The general equation that expresses the law is v p = -. To 



find y, we produce AA to meet the axis of temperature, which it 

 does at 389°. This therefore is the value of 7 indicated by these 

 observations. The value of k, which is equal to y — t when v=l f 

 must not be taken from the temperature 4° at which the volume 

 of water is unity, because the curve of expansion departs from 

 the theoretical curve at the lower part of its range. We must 

 compute it from a scale-reading of an ordinate of the line A, as 



. n Afmn , . , . ~,~ dt.v , . dt.v 1 , 



nn at 24o , winch is 517= — ; — : and since - 1 — l - = - and 



dv dv(y—t) p 



1 517 

 7—^ = 144, we have - = ^-—7 =3*59. 



/ ' p 144 



What is the value of - required by the theory that connects 

 the expansion of a liquid with the density of its saturated vapour ? 



By referring to § 3 of original paper, the rule is that hx - is a 



P 

 constant quantity F (French measures) for all bodies ; and refer- 

 ring to the value of h derived from M. Regnault's observations 

 given in Appendix I. to paper in Phil. Mag. March 1858, we 



find the theoretical value of - =3*21. 



P 

 § 18. The results hitherto have been with temperatures by the 



