398 Dr. Edmund J. Mills on the 



these methods might well lead to too high a result. A 

 numeric founded on analyses of cuprous chloride or bromide 

 would be much more satisfactory, and might not improbably 

 correspond to w = 3. 



Zinc. — Marignac (1884), using a method of obviously 

 approximate character, gives Zn = 65*31. 



Yttrium. — Cleve s numeric (1882) has been taken. 



Tellurium. — Wills's best result [Chem. Soc. Journ. (trans.) 

 1879, p. 704] agrees, as will be noticed, closely with calcu- 

 lation. 



Lanthanum, Cerium, and Didymium. — Here I have followed 

 Brauner (1883), who determined the relation between oxide 

 and sulphate. Robinson (1884), who determined the chlorine 

 in cerous chloride, makes Ce = 139*90. If, in this group, 

 57 = 6, y = 139*82. Further experiment is necessary to decide 

 this numeric. 



Samarium. — Brauner (1883). 



Ytterbium. — Nilson (1880). 



Nonvegium. — Dahll (1879). 



Thorium. — Nilson (1883). 



Uranium. — Peligot (1846). 



Remarks and Inferences. 



A comparison of the theoretical with the experimental 

 numerics shows an extremely close agreement between them. 

 Such a comparison is most rigorous when it is made for the 

 best known numerics, and for low values of x ; here the error 

 (if it be indeed all error) does not exceed a moderate amount 

 in the second decimal place. 



The numerics of the elements have not all been determined 

 in the same way — as, for example, by estimation of chlorine 

 in the chlorides ; and, though different methods of obtaining 

 the same numeric lead generally to nearly the same result, 

 they seldom involve exactly the same result. Thus our existing 

 records do not enable us to say that the weight of Na that 

 combines with the weight of CI is precisely identical with the 

 weight that combines with Br ; nor does it necessarily follow 

 that any single method of determination is in effect the same 

 thing for all numerics. It is, in short, open to any theorist 

 to express a given " definite proportion " in the form a+md; 

 a being the invariable definite proportion as at present con- 

 ceived, d the vapour-density of a varied element combining with 

 a constant element, and m a small factor to be calculated from 

 the experimental data. Hence the ''error" of the geometrical 

 theory, small though it is, is not necessarily all error ; and it 



