Periodic Law of the Chemical Elements. 97 



are already in possession of mathematical methods, of the 

 artificial kind, fully sufficient for all our present, and at least 

 our immediately prospective, wants. What is required for 

 physics is that we should be enabled at every step to feel 

 intuitively what we are doing. Till we have banished artifice 

 we are not entitled to hope for full success in such an under- 

 taking. That Lagrange and Cauchy missed the import of 

 their formulae, leaving them to be interpreted some half- 

 century later, is merely a case of retributive justice : — 



" . . . neque enim lex aequior ulla 

 Quam necis artifices arte perire sua," 



Lagrange in the preface to that wonderful book, the Mecanique 

 Analytique, says : — 



" Les methodes que j'y expose ne demandent ni construc- 

 tions,, ni raisonnemens geometriques ou mecaniques, mais 

 seulement des operations algebriques, assujeties a une marche 

 reguliere et uniforme." 



But note how different is Poinsot's view : — 



" Gardons-nous de croire qu^une science soit faite quand 

 on l'a reduite a des formules analytiques. Rien ne nous 

 dispense d'etudier les choses en elles-memes, et de nous bien 

 rendre compte des idees qui font l'objet de nos speculations." 



No one can doubt that, in this matter, the opinion of the 

 less famous man is the sound one. But Poinsot's remark 

 must be confined to the analytical formulae known to him. 

 For it is certain that one of the chief values of quaternions is 

 precisely this : — that no figure, nor even model, can be more 

 expressive or intelligible than a quaternion equation. 



VIII. An Approximate Algebraic Expression of the Periodic 

 Law of the Chemical Elements. By Thos. Caenelley, 

 JD.Sc, Prof essor of Chemistry in the University of Aberdeen .* 



[Plate I.] 



SEVERAL attempts have of late years been made to ex- 

 press the atomic weights of the Elements by algebraic 

 formula. Of these that of Dr. E. J. Mills (Phil. Mag. [5] 

 xviii. p. 393 ; xxi. p. 151) expresses the atomic weights by a 

 logarithmic function 



15(^-0-9375'), 



in which p and t are whole numbers. 



Another attempt, referred to by Prof. Mendeljeff in his 



* Communicated by the Author. 

 Phil. Mag. S. 5. Vol. 29. No. 176. Jan. 1890. H 



