256 The Rev. B. Bronwin on a 



With the view of ascertaining if any diamagnetic conditions 

 could be induced which would in any way influence chemical 

 change, wires of copper and of zinc were substituted for those 

 of iron ; but in no case was any deflection produced upon the 

 needle of the galvanometer which could be at all attributable 

 to magnetic influence. 



From these experiments, which of course have no bearing 

 upon the disposition of crystali-, or the direction of bodies free 

 to move near the poles of magnets, I am compelled, notwith- 

 standing my former impressions, to conclude that magnetism 

 Jias 710 direct injiucnce upon this form o/" chemical action 

 either as an accelerating or a retarding agent. 

 I am, dear Sir, 



Yours truly, 



6 Craig's Court, RoBEUT HuNT. 



March 12, 18-18. 



XXXVIII. On the Solution of a 'particrdar Differential Equa- 

 tion. By the Rev. Brice Bronwin*. 



IN the seventh Number, new series, of the Cambridge Ma- 

 thematical Journal, Mr. Boole gave a solution of a par- 

 ticular differential etjuation, having for its coefficients certain 

 integral functions of .r. The object of this paper is to show 

 that it admits of an infinite number of solutions; or rather, 

 that an infinite number of equations ma}' be solved by it, and 

 those equations not necessarily having integer coefficients. 

 The symbols tt,,, and tt,, containing symbols both of operation 

 and quantity, the equation in question is 



T,„7r„?i+jOX2^=X, (1.) 



where ^ is constant, X a function of x, as is also X, which I 

 have added to make the equation more general. There are 

 also the two equations of condition, 



7r,„7r„ =7r„7r„j +/(w)a, 7r,„ A. = A7r,„+i. . . [2., 



These are here separated from their subject u, on which tliey 

 operate. To solve (1.), make u = ■lt„^+lU■^^•, it becomes 



i",„ T,, TT^ + , «, +])KTr,„ + 1 ?/ J = X ; 



or by the second of (2.), 



Tm'Trt 7r„,4. 1 ?<, +/)7r„, X?<i = X, 



and 



Tills by the first of (2.) becomes 



* Communicated by the Author. 



