DETERMINATION OF ATOMIC WEIGHTS 519 



and choosing as the unit of volume the volume occupied by the 

 gas at N. T. P., van der Waals' equation becomes 



(p + £)(v-b)-(i +a)(i -b)(i + at) (13) 



where a = 1/273 and t = temperature in degrees Centigrade. 

 This is the equation used by Guye. Assuming the validity of 

 the fundamental assumption of the method of limiting densities 

 and also assuming that equation (13) represents the behaviour of 

 a gas between o and 1 atmos., Guye's fundamental formula 

 follows readily from equation (4) on p. 507, viz. : 



M = RL(i - Ao) (4) 



For, since 



AS-i-E^-i--!- 



P0V0 P0V0 



at o° C. with the preceding choice of units, the equation (4) may 

 be written 



ro o 



Also, at o°C. equation (13) may be written 



a ab 

 pv = (i +a)(i-b) + pb - — + ^r 



and since, when p = o, v = 00, we have 



Po v o = (1 + a) (1 - b). 



Hence equation (14) becomes 



M = r-r^h- c* ('5) 



(1 + a)(i-b) 



which is Guye's formula. 



Guye arrived at his formula in the following manner. It has 

 been shown by van der Waals (4) and independently by Guye 

 and Friderich (5) that the acceptance of van der Waals' equation 

 leads to the following result: 



At normal temperature and pressure, the relative volumes 

 of different gases that contain equal numbers of molecules are 

 proportional to 



(1 + a)(i - b)' (1 + a')(i - b')' (1 + a")(i - b") 



the accents referring to different gases, the units being chosen 

 as previously described. 



As the molecular weights (M, M', M" . , ,) are proportional 



