" Law " in Physical Optics. 323 



2. It is true in the case of liquids whose density is changed 

 by varying pressure *. 



3. It is true (or a very close approximation) in the case of 

 dissolved salts, especially in dilute solution. 



4. It is a less close approximation in the case of simple 

 liquids undergoing thermal expansion. 



5. It altogether fails when a liquid is changed into vapour. 

 On studying the results included in 4, it appeared that they 



had one point in common. If the variation be expressed in 

 symbols, it may be put in the form 



V=« (l±««), 



where e and e t are the values of , at 0° and t° respectively. 



Examination showed that all good experiments gave a nega- 

 tive sign for the coefficient a. In other words, the value of 

 e always diminishes as the density diminishes. If we put 

 (fi — l)/d=(fi — l)v, where v is the volume of unit mass, we 

 may say that (ft— l)v always diminishes as v increases. This 

 statement is still more emphatically true when the liquid 

 becomes a vapour. 



Therefore, in classes 4 and 5, whenever v increases the 

 product {jjl — l)v diminishes. In liquids, where the change in 

 v is not very great, the diminution of the product is small ; 

 but in passing to vapour, where the change in v is enormous, 

 the product (ji— 1)^ undergoes a large diminution. To put 

 the same thing in the inverse sense, the results show that 

 when v becomes comparatively small, there is a marked 

 increase in the product. So stated, they afford criteria by 

 which we may possibly find the cause of the deficiency. 

 The conditions are almost a reproduction of those which led 

 to the second approximation in the case of Boyle's law. 

 Experiment showed that the product pv was only constant 

 when v was comparatively large. As v diminished, there was 

 a tendency for the product to increase, and it became 

 necessary to suppose that the expression pv referred not to the 

 whole space symbolized by v, but to v minus the space occupied 

 by the particles. Hence p(y — b), where b is the actual 

 volume of the matter, has taken the place of pv. 



It appeared to me, that the similar experimental results 

 would warrant the introduction of a similar symbol in the 

 Gladstone expression, thus transforming it into 



(fi — 1) (v—/3)= constant. 



* Quincke, Phil. Mag. 1884, xvii. r. 65. 

 Z2 



