On the Laws of Chemical Change. 121 



Hence 



^sin- 1 ^ v'l — t 2 1 f 1 sin-^-f i/1— t 



, 1 f V sin^-f i/l-*n {1 } 



and integrating 



sin- 1 ; 2 ^ 3 2_^4 * 5 2 . 4 . 6 I 7 



s/\~C~ + 1"3 1.3*5 1.3.5 7 + 

 Thus we have the remarkable identity 



1 1.3 ,,.1.3.5 



/-. , 1 , 1.3 , , 1.3.0 3 \ 



( 1+ 2- T+ 2Tl T+ 2T4^ T ---) 



V 23^2.4 5 ^2.4.6 7 V 



■)• 



= 1 2t 2.4t 2 2.4.6t 3 



13 ' 1.3 5 ' 1.3.5 7 



I do not recollect ever having met with these remarkable 

 series before I discovered them by the preceding method ; but 

 on showing them to Dr. Story of this University, he ascer- 

 tained that they had been stated not long ago by Mr. Glaisher 

 in a paper in the ' Mathematical Messenger/ and made the 

 foundation there of various summations for calculating it ; 

 but where Mr. Glaisher found these series, which are not 

 given in the ordinary books on the Calculus, or (if new) how 

 he lighted upon them, he has not stated, and it is desirable 

 that he should do so. 



Johns Hopkins University. 

 26th May, 1879. 



XV. On the Laws of Chemical Change — Part II. By John 

 J. Hood, Royal Exhibitioner in the Government School of 

 Mines, London*, 



WHEN ferrous sulphate in an acid solution is oxidized by 

 potassic chlorate, the two salts being in the proportion 

 required by the equation 



6FeO + KC10 3 = 3Fe 2 3 + KCl, . . . (1) 

 I have shown f that the reaction which takes place may be 

 very accurately represented by the algebraical equation y(a + i) 

 =6, y being the residue of unoxidized iron after the action 

 has continued for t minutes, and ab two constants. 



* Communicated by the Author. 

 f Phil. Mag. Nov. 1878, p. 371. 



