206 Dr. G. J. Stoney on Proofs of 



great (in the case of mineral powders) the powder became a 

 soft paste ; but that with a great increase of temperature (in the 

 case of charcoal, sawdust, &c.) the powder was transformed 

 into a consistent mass resembling stone. 



This curious phenomenon would tend to confirm the opinion 

 that the production of heat is due to the molecular energy 

 being transformed into thermal energy. 



In another communication I will give further notice in 

 regard to this interesting question. 



Venice, June 1897. 



XXX. On Proofs of a Theorem in Wave-motion. 



To the Editors of the Philosophical Magazine. 

 Gentlemen, 



I CRAVE permission to correct an error on p. 101 of ni}' 

 letter in the July number of the Philosophical Magazine, 

 where 1 described the waves in each of the equations 



Z=F^(x,y,z,t), 



£=F 3 (.^y,M) 



(when extended to all space and expanded by Mr. Preston's 

 valuable corollary to Fourier's theorem) as waves that are 

 non-natural in two respects. In fact, they are non-natural 

 in only one of these respects. The wave-lengths, in the case 

 there dealt with, do not range in these equations from infinity 

 down to cypher as I supposed when writing the letter, but 

 are of one wave-length, as may be proved by a slight modifi- 

 cation of the well-known theorem given on p. 435 of my 

 second paper on Microscopic Vision in the Phil. Mag. for 

 November, 1896. The waves of each of the above equations 

 are non-natural, i. e., merely kinematical, in consequence of 

 their transversals standing in impossible posit ions. ^ 



Nevertheless, as is the case with every kinematical resolu- 

 tion when applied to a real motion, the resultant of combining 

 the three kinematical components in any one direction, must 

 of necessity give the real undulation in that direction if there 

 be any such. That there is a real undulation I had previously 

 shown by MacOullagh's method of proof, and further that it 

 consists of uniform plane waves of the kind which the medium 

 can propagate unchanged. 



