§ 6 OF ARTS AND SCIENCES. 375 



the coefficients of elasticity and of expansion; we shall 

 find no reason to regard it as an exception to our funda- 

 mental laws. 



In conclusion I would say that too much weight must 

 not be attached to the accidental agreement of the three 

 liquids tabulated, it being not very improbable that a 

 fourth liquid should differ by a hundred per cent, from the 

 value calculated in the same way. The case of alcohol is 

 a good example, which has been explained. In dealing, 

 however, with such large numbers as the elasticity and 

 mechanical equivalent, and such small ones as the coeffi- 

 cient of expansion, the slightest mistake in the formulae 

 would be apt to increase or diminish the result by hun- 

 dreds or perhaps millions of times; and even an approxi- 

 mate agreement between theory and observation must, 

 in such cases, be considered in the light of a confirmation. 



In the case, therefore, of the element bromine, the sym- 

 bol being B}\_^ I will venture to predict that the principal 

 ratio will be found to be equal, very nearly, to 0.95. 

 Since the total latent heat at 63° is given as 45.6 (An- 

 drews), and the density 3.187 (Cooke), the coefficient of 

 expansion at zero is .001038 (Pierre), and since the in- 

 ternal latent heat at 0° is 46.0,* we have 



E, 42,000,000 X 46.0 X ^-187 o 



E = ^i-^ ^ ^ ^ ^ ^ ^ '- = 22,870,000,000, 



0.95 X .001038 X 273 



the same, nearly, as for water at 41° ( Jamin), which value 

 is therefore predicted for the coefficient of resilience of 

 bromine to hold within the ordinary limits of errors of 

 observation. 



§ 6. If in the equation of equilibrium, 



* Calculated by the usual formulae, assuming the absolute vapor density to be .007168 (re- 

 duced to o^ centigrade and 1,014,200 dynes pressure) ; also using the specific heats of 

 the liquid and vapor as determined by Regnault. 



