On the Numerics of the Elements. 543 



These must await a more fitting opportunity ; meanwhile let 

 me conclude as I began, by thanking you very heartily for 

 placing me in this position, and assuring you of my desire to 

 forward your best interests. 



LYII. On the Numerics of the Elements. — Part III. 

 By Edmund J. Mills, D.Sc, F.R.S.* 



IT has been shown in previous parts f that the numerics of 

 the elements are of the form 



y 



^-Ks^iT 5 



where p represents the number of the periodic group, n + 1 

 the number of periods in the system, and x the integral 

 ordinal within a given group. So far as is known, all the 

 numerics of the existing elementary bodies, excepting that of 

 hydrogen, are included in the above equation when n = 15 ; 

 and the range in value is from y=Q to ?/ = 240. 



It has been objected J to this method of representation that 

 it includes an infinite number of elements within the range 

 indicated. Ample precedent, however, for this is found in 

 the phenomena of Cumulative Resolution §. In the de- 

 nitration of bismuthic nitrate by water, for instance, there 

 are three distinct continuous stages : — 



I. n Bi 2 3 . 3N 2 ? - (n - 1)N 2 5 =Bi 2w 3 » . N 4tt+2 O 10)l+5 , 

 and at infinity Bi 2 3 . N 4 O 10 . 



II. n Bi 2 3 . 2N 2 O5 - (n - 1) N s 5 = BUn 3n . N 2n+2 5n+5 , 

 and at infinity Bi 2 3 . N 2 5 . 



III. n Bi 2 3 . K 2 5 - (n - 1) N 2 5 = Bi 2)l 3n . N 2 5 , 

 and at infinity Bi 2 3 . 



In the first stage ratios are known for w= , l and 1 ; in the 

 second, for n = 2 ; in the third, for n — f, | 3 f, 1, and 00 . 



Another objection has been raised to the method that it is 

 too easily applicable to any numeric. This objection, however, 

 is not so much a criticism of the mathematical method, as a 

 censure on the weakness of experimental processes. These, 

 in the most favourable cases, cannot be depended upon more 

 nearly than '02 ; and the mathematical method can only 

 follow them. So far, increasing experimental accuracy has 

 been attended by a closer coincidence with the theory, The 



* Communicated by the Author. 



t Phil. Ma-. 1884, vol. xviii. p. 393 ; 1886, vol xxi. p. 151. 

 t Ibid. 1902, vol. iv. p. 103. § Ibid. 1877, vol. lii. p. 492, 



2 2 



