1818.] On Mr. Daniell's Theory of Crystallization. 280 



and .' . the other pyramid = — '- — ' n* 



whence the sum of the particles in the octohedron 



_ 9 f n.n + l.2n + l ) __ , 

 ' I 1.2.3 J 



.• . sum of spheres in tetrahedron : sum in octohedron 



».n+l.n + 8n f "•"-+* .2«+ h t 



\ i . 2T3 J "" n 



1.2.3 



:: n . n + 1 . n + 2 : 2 n . n + 1 . 2 /* + 1 — 6 »* 



which is general for every tetrahedron and octohedron whose 

 linear side consists of (n) finite particles, and is 



:: n 3 + 3 n a + 2 « : 4 « $ + 6 n» + 2 w - 6 ?i e 

 :: ra s + 3 a/ 8 + 2 « : 4 « 3 + 2 n 

 which when n = oo , or the body becomes solid :: 1 : 4. 



Tliis must, I tmst, convince Mr. Daniell that the summation 

 of a finite number of spherical particles is never a correct esti- 

 mate of the solid content of a body, and may, perhaps, induce 

 him to repeat his experiments on this subject. 



With the utmost respect allow me to subscribe myself, 



Philo-chemicus Cantab rigiensis. 



Article X. 

 On welding Cast Steel and Cast Iron. By T. Gill, Esq. 

 (To the Editors of the Annals of Philosophy.) 



Covent Garden Chambers, 

 GENTLEMEN, London, March 14, 1818. 



I presume that I need not make any apology for introducing 

 the following remarks, on the above subjects, to the notice of 

 your readers. 



It has always been considered a difficult task to weld the 

 higher converted cast steel to iron ; and indeed the public are 

 indebted to Sir Thomas Frankland for the first accurate inform- 

 ation on the means of performing it ; namely, by heating the 

 iron to a welding heat, and the steel as hot as it would safely 

 bear; when, by dexterous management, the union may be 

 effected, and without much injury to the steel. 



I was, however, lately very much surprised, by being informed 

 by Mr. Samuel Varley, a scientific mechanic, who was many 

 years employed in assisting the late Earl Stanhope in his 

 philosophical pursuits, that a smith in the neighbourhood of his 



Vol. XI. N° IV. T 



