254- The Rev. J. H, Pratt's Beply to Disjota. 



more general than ^ x z= a^^: But assign a relation between 

 X and y, say x ■=. y, and the solution ot'(<f) xf = 45 (2 .r) is 



..= {.(c„s.,iM|)}^ 



where 3 is any function which does not invert the cosine. 

 And this is only a very limited solution. 



LI. Reply to Disjota's Remarks. By the Rev. J. H. Pratt, B.A. 



To the Editors of the Philosophical Magazine aiidjouiiial. 



Gentlemen, 

 T AM sorry that three of your valuable pages should have 

 ■*- served no better purpose than to convince me that your 

 correspondent Disjota, has entirely mistaken the object of my 

 communication printed in your June Number. 



It will be seen upon referring to that communication, that 

 the words "only one" are emphatic: and by this I expected 

 my readers to understand, that my object was not to revive 

 the controversy respecting the proposition, that a function of 

 9 and ^ can be developed in a series of Laplace's coefficients; 

 but to show, u]ion the supposition of Poisson's demonstration 

 of this proposition being rigorous, that there is only one such 

 series. In short, I conceive that the whole question involves 

 two propositions, thejirst to show that the development is pos- 

 sible, the second to show that only 07ie such development ex- 

 ists; and it is clear that your correspondent fancies that I in- 

 tended to prove the^f/s/, when, in fact, it was the second that 

 I wished to demonstrate. 



If Disjota will turn to page 387 of vol. ii. Camb. Phil. 

 Trans., he will see that the object of the Astronomer Royal 

 in that place is to show thaty (fl, \J/) admits of only one de- 

 velopment and it is to Laplace's demonstration oi this that he 

 objects; and he will observe that the possibility of the deve- 

 lopment is not called in question. 



But I fear that without a few more words my communica- 

 tion will still be misunderstood by Disjota. 



I agree entirely with what he says at page 85, in the [)ara- 

 graph, "It is obvious .,."; and wonder much why Poisson sets 

 about to 2}rove in the way that he does in art. 112. page 225. 

 of the Theorie Math e mat i que de la Chaleur, that his method 

 of development will lead to only one series of Laplace's coeffi- 

 cients, since it appears to me (as it does to your correspon- 

 dent) self-evident, because P, admits of only one form. 



