178 Dr. F. A. Lindemann on the 



probably the temperature at which, according to the quantum 

 theory, the gas begins to deviate from the equation j>t> = RT. 

 This temperature may of: course depend upon the atomic 

 dimensions, but so long as it is equal in both isotopes it does 

 not affect the present problem. One may therefore write 



i = log Pq — oo log m + y log k + z log h + u log 6 + const. 



The dimensional equations are therefore given by 



LT 2 \T 2 eJ V T J ' 



whence .i i = 3/2, y=5/2, z—— 3, and u = 5/2, 



iz= log j^- h const. = const, -f log m 6 '*. 



If A x and A 2 are the atomic weights of the two isotopes, 

 therefore 



H-i^d/Hog^-. 



Inserting this value in the equation found above, and 



v /A V' /2 

 remembering that !-± = — =[ — ) , it is immediately seen 



-that the first order terms cancel out and the vapour pressures 



Qy J± J± 



only differ in the higher orders of ^ . — l -^ — -. 



Putting A! = A 2 (1 + S), where 8 is small as it probably 

 .always is in isotopes, 



In lead S is about 1 per cent, and /u, = 0*16 at the melting- 

 point, so that the vapour pressures cannot be expected to 

 differ by more than 1/50 of 1 per cent. This estimate of 

 course only represents the order of magnitude since a number 

 of second order terms were neglected in the course of the 

 argument. A much larger difference, about 1 per cent., 

 would occur if the chemical constants were identical. 



A very similar consideration shows that the affinities, 

 which may be measured by the constant of the law of mass 

 action or by the electromotive force, differ very little. In 

 the first case 



log K P = - H +£j!p [^(tW^T + Si, 

 from which it is obvious that, the heat of combination at the 



