872 Royal Society. 



At 12^ 30"^ the streams were frequent; the arch now ex- 

 tended from the N. by W. to tiie E. by N., and at every part 

 of this arch an occasional streamer, with its taper-like form, 

 sprung up; and this appearance continued till after \'S^. 



I did not observe any halo around the moon at any time, 

 and the Aurora, with the exception of the beautiful white 

 clouds, was confined to the northern hemisphere. 



On Friday the 22nd, and on Saturday the 23rd, the mag- 

 netic instruments at the Royal Observatory were greatly 

 disturbed, as they were during the auroral appearances on 

 the 24th ultimo*. 



Many of the preceding observations were made by an 

 assistant at my residence, as my own attention was almost 

 completely occupied by observations of the magnetical instru- 

 ments; so much so, that I was oblijied to neijlect some of its 

 finest appearances, but which I believe were pretty vvell ob- 

 served as above described. The watch by which the times 

 were taken was compared at about midnight, so that the se- 

 veral times are true Greenwich mean solar times. 



James Glaisher. 

 Blackheath, Oct. 26, 1847. 



P.S. An Engraving of its appearance, as seen at about 10^, 

 will appear in the Illustrated London News of Oct. 31. 



LXII. Proceedings of Learned Societies. 



ROYAL SOCIETY. 

 [Continued from p. 227.] 

 June 17, "/^N the Solution of Linear Differential Equations." By 

 1847. ^^ Charles James Hargreave, Esq., B.L., F.R.S., Pro- 

 fessor of Jurisprudence in University College, London. 



1. By the aid of two simple theorems expressing the laws under 

 which the operations of differentiation combine with operations de- 

 noted by factors, functions of the independent variable, the author 

 arrives at a principle extensively applicable to the solution of equa- 

 tions, which may be stated as follows : — " if any linear equation 

 <p{x,'D).u=X have for its solution M=\|/(a?,D).X, this solution being 

 so written that the operations included under the function ^ are not 

 performed or suppressed, then (p(D,— a?).M=X has for its solution 

 M=i//(D,— a?).X." The solution thus obtained may not be, and often 

 is not, interpretable, at least in finite terms ; but if by any trans- 

 formation a meaning can be attached to this form, it will be found 

 to represent a true result. 



An important solution immediately deducible from this principle 

 is given by Mr. Boole in the Philosophical Magazine for February 



• See the weekly reports of the weather supplied by the Astronomer 

 Royal to the Registrar-General. 



