448 M. H.Dcville on the Decomposition of Bodies by Heat, 



my fifth term on the square root of 2. Making a or r=l, p or 

 N=2, his tenth term gives 



..'* = 1-41 421 36249; 



my fifth term gives 



ggg = l-41421 35623 7469; 



while the real value of */2 is 1-41421 35623 73096. My 

 method thus appears to give twelve figures correct, while the other 

 gives seven. I have tried several cases with a similar result. 



A remarkable expression for Mr. Sylvester's successive approxi- 

 mations is afforded by Dr. Booth's Trigonometry of the Parabola. 

 Divested of any peculiarities of symbol it is as follows : — let 6 m 

 be determined by the equation 



C'm M m '_ C* d6 x 



J cos0 w -m J o COS 0,' 



then if we make \/N . sin #!=r, the with approximation will be 



expressed by ** ■ . 

 , sin0 m 



Kensington, Nov. 6, 1860. 



LXII. On the Decomposition of Bodies by Heat, and on Disso- 

 ciation. By M. H. Sainte-Claiue Deville*. 



FROM what has long been known on the subject, and from 

 facts which I myself have published, it appears well esta- 

 blished that the action of heat finally decomposes all bodies. As 

 this decomposition does not take place suddenly, I have assumed 

 that the elementary or constituent molecules of a compound 

 body, before reaching the point at which affinity ceases to act, 

 gradually remove from each other, or dilate under the influence 

 of heat, as do the compound or integrant molecules themselves. 

 1. Simple decomposition. — When the divergence of the elements 

 has become so great as to overstep the sphere of activity of the 

 force which keeps them united under the ordinary circumstances 

 of affinity, and when, further, the molecules have not the power 

 of combining again by the simple fact of their contact, the de- 

 composition is definite, and shows itself by its products. We 

 see such a case of simple decomposition when we subject to the 

 action of heat ammonia, nitric acid, all nitrogen compounds in 



* Communicated to the Societe de Physique et d'Histoirc Naturelle de 

 Geneve, September 8, 1860; translated by Dr. E. Atkinson. 



