40 HEAT. 



dense. Hence, assuming that the density curve (Fig. 30) is symmetrical 

 about the point of maximum density, t' is further below it than t is 



above it, and is below the maximum density. If the flow is in 



Z 



t + t' 



the opposite direction, is above the point of maximum density. In 

 2 



this manner Joule and Playfair obtained a number of values of - 



a 



respectively above and below the point, and were able to fix the tem- 

 perature at 3-95 C. with very slight error. The alteration of density 

 from this to 4 is so slight as to be for practical purposes negligible, and 

 we may take 4 as the point of maximum density. For tables of the 

 density and volume of 1 gramme of water we refer the reader to 

 Landolt-Bornstein, Physikalisch-Chemische Tdbellen, 1905, p. 37. These 

 contain results beginning at 10, as it is not difficult to keep water 

 liquid even at that temperature in a dilatometer. 



Results. The following table gives the expansion of a mass having 

 volume 10,000 at 4 0. for every 10 degrees up to 100, and the results 

 are represented in Fig. 31 : 



Temperatures. Expansion of Mass 



Degrees. having vol. 10,000 



lit ~t . 



- 10 18-6 



1-32 



4 0-0 



10 2-73 



20 17-73 



30 43-46 



40 78-2 



50 120-7 



60 170-5 



70 227-0 



80 289-9 



90 359-0 



100 434-3 



It will be seen that the curve is nearly a parabola, the expansions being, 

 however, rather greater than in the ratios of the square of the excess of 

 temperatures above 4. 



The expansions of a great number of other liquids have been de- 

 termined. The results may be expressed by the formula 



V, = V (l + at + W + ct 3 + &c.). 



Usually at is the most important term, but in the case of water, as we 

 have seen, bt 2 is very important. The terms after ct 3 may probably be 

 neglected. 



