116 Mr. Lubbock on some Elementary 



lute solution of muriate of ammonia. This precipitate is 

 almost black in the mass, but when spread over the surface 

 of white porcelain or paper, it appears of a fine sap-green ; by 

 exposure to the air it becomes nearly white on the surface, 

 ■which discoloration speedily extends to some depth, (if all 

 the hydrosulphuret has not been washed away, this change 

 does not take place until after some time) ; it is then to be dried 

 on a sand-bath and digested in weak hydrochloric acid, by 

 which almost all the sulphuret of iron is removed ; the inso- 

 luble portion is then to be again dried and ignited, in a pla- 

 tinum capsule over the circular-wick spirit-lamp (or if in con- 

 siderable quantity, on a platinum tray in a small muffle) ; a 

 cream-coloured powder is thus obtained, still containing a 

 minute portion of iron, which may be got rid of by mixing 

 it with muriate of ammonia, and exposing it for some time to 

 a temperature below ignition. The titanic acid thus procured 

 is tolerably pure. 



In conclusion we would wish to remark that titanium ap- 

 pears to be more generally diffused through the mineral 

 kingdom than is generally stated (in chemical works), as ap- 

 pears particularly from the following passage in Thenard's 

 Traite de Chimie : " Le deutoxide de fer se rencontre sous 

 forme de sables. Ces sables contiennent ordinairement de 

 I'oxide de titane ou de Poxide de chrome en combinaison avec 

 Toxide de fer. M. Descotils a retire jusqu'a 30 parties de ti- 

 tane de 100 parties de sables ferrugineux de Saint-Quay, de- 

 partement des Cotes du Nord. M. Robiquet I'a rencontre 

 dans le deutoxide de fer des roches steatiteuses de la Corse." 



Guy's Hospital, Dec. 26th, 1834. 



XlX. On some Elementary Applications of Khei^s Theorem. 

 By J. W. Lubbock, Esq,, KP, ^ Treas. R.S* 



ABEL, in the third volume of Crelle's Journal, gave a 

 theorem, which constitutes one of the most remarkable 

 discoveries ever made in analysis, by which the methods of 

 finding the sum of certain definite integrals were greatly ex- 

 tended. Cut off in the prime of lifef, it was not given to the 

 mathematician of Christiania to pursue the career which is 

 opened to analysts by the theorem in question, or to illustrate 

 its application by examples. This has been done to a certain 

 extent by Legendre in the third Supplement of his work en- 

 titled Theorie des Fonctions Elliptiques %, As, however, no no- 

 tice of this theorem has yet appeared in any work in the En- 



* Communicated by the Author. 



f (.See Phil. Mag. and Annals, N.S. vol. vii. p. 77- — Edit.] 



X [See Lend, and Edinb. Phil. Mag., vol. iv. p. 143.— Edit.] 



