398 Dr. E. J. Mills on Statical and 



latter equation, in case the above condition can be fulfilled, is 

 really of the third order. 



I have now reached the conclusion of my researches in the 

 Calculus of Variations, having succeeded at length in removing 

 from its analysis the reproach of failing to solve a class of pro- 

 blems which unquestionably should thereby be capable of solu- 

 tion. For instance, it is obvious that there must be a conti- 

 nuous surface of revolution which for a given amount of surface 

 and a given length of the axis encloses a maximum volume. 

 But so far was this problem from being solved, that, on account 

 of its peculiar difficulties, those who from their reputation as 

 analysts might be expected to furnish a solution, have only 

 endeavoured to show that it is insolvable. Probably, there- 

 fore, it will be ljeld to be excusable that in my first attempts 

 to solve it I adopted views and processes of reasoning which I 

 had afterwards to abandon as untenable. I persevered, how- 

 ever, in my efforts to arrive at the solution, not being able 

 to admit the possibility of the failure of analysis ; and the re- 

 sults now comnvmiicated I consider to be a justification of this 

 course. 

 Cambridge, October 8, 1873. 



L. On Statical and Dynamical Ideas in Chemistry. — Part IV. 

 (conclusion). On the Idea of Motion. By Edmund J. Mills, 

 D.Sc* 



Contents. 



A criterion of scientific progress is needed. This criterion is an idea 

 common to all the sciences — namely, the idea of pure motion. It was first 

 announced by Herakleitos of Ephesus ; we afterwards trace it through the 

 Platonic Sokrates, the Sophists, Aristotle, the Epicureans, and the Skep- 

 tics. It reappears in Hobbes and Hegel. Ferrier and Spencer compared 

 with reference to this idea. All conscious knowledge is but knowledge of 

 motion. The science of the naturalist, mathematics, and geology are illus- 

 trations of the directive force of the idea. In chemistry — which has not, 

 like those sciences, assumed a " new " phase — a theory of absolute limits 

 prevails ; but its great epochs are intelligible only by the light of this cri- 

 terion : its imaginary pursuits ; study of the chemical process neglected. 

 The extinction of ethics. Questions. Summary. Practical tendency of 

 the discussion. 



IloTafxov pofj anziKafav ra ovra. 



IF a chemist, in the course of his researches, were to suspend 

 for a moment his more immediate investigation and ask 

 himself Is this Progress*? he would have a difficult question to 

 answer. I do not think it advisable that this question should 

 often be asked, or that every chemist should ask it. But it does 

 arise in the most legitimate manner; and, as it has a tran- 

 * Communicated by the Author. 



