6 Mr. G. Boole 07i a Method/or DiffercJitial Equations. 



received, and in it are accounts of two other meteors observed 

 at Dijon on the 17th of October and on the 9th of Novem- 

 ber. M. Meline describes the latter in words which would 

 almost exactly represent the phajnomenon which I have at- 

 tempted, so imperfectly however, to place on record. 



" Je sortais des serres du jardin, quand j'ai ete frappe tout a 

 coup d'une lumiere aussi intense que celle du jour; j'apergus 

 distinctement toutes les parties du jardin, les arbustes comma 

 les arbres, les plantes, etc. Je vis tout avec une teinte jaune 

 serin. D'abord je crus a un incendie; mais, en jetant les 

 yeux au ciel, j'ai vu un globe de feu se mouvant plus lente- 

 ment qu'une fusee, de I'ouest a Test, horizontalement, a 60 ou 

 70 degres de hauteur. Le meteore a laisse, sur toute la lon- 

 gueur de la route qu'il a suivie, une immense trainee d'un blanc 

 couleur de cendre." 



III. Remarks on the Rev. B. Bronwin's Method for Differ- 

 ential Equations. By George Boole, Esq. 



To the Editors of the Philosophical Magazine and Journal. 

 Gentlemen, 



1 DESIRE very briefly to notice an error into which the 

 Rev. B. Bronwin has fallen, in a paper on the Integration 

 and Transformation of certain Differential Equations, pub- 

 lished in the last Number of the Philosophical Magazine. 



In doing this I shall adopt a notation which I have before 

 employed in a similar description of analysis, and which has 

 the advantages of brevity and simplicity. Changing for con- 

 venience p into m and y into u, we may observe that Mr. 

 Bronwin's transformations depend in all cases on the proper- 

 ties of two compound factors, which we shall designate by 7r„, 

 and f, and which, upon whatever subject they may operate, 

 combine in subjection to the relation 



7r,„ p = p7r,„_i, (1.) 



the equation to be solved being 



T^« = (2.) 



Thus, in Mr. Bronwin's first equation, D standing for - — , 



7r„=ar(D2 + F) + 2niD, p = W + lc^', . . . (3.) 

 in the second, 



■rt„, = \y + kx'D—mk, p = T> + kx; .... (-t.) 

 in the third, 



,r,„=,r(D3 + /^) + 3 7«D, p = D^ + k^; . . . (5.) 

 and so on for the rest. 



