15 
and if m=n=. - l , we have 
d(3 a da _ Q dy d/3 _ da dy 
a dx ~ J dx ~ clx y dx y dx a dx > 
relations which must be satisfied by the roots of (v) or of any 
cubic whereof the coefficient of the second term vanishes. 
(Compare art. 73 of my “Notes,” &c.,' in the Messenger of 
Mathematics for November, 1864 ) We have, indeed, gene- 
rally 
G"° + + q f ) - ( m % + n t)f + s/5 ) = ( m? - np ) 
f d(3 n da\ 
VTx-Pdx) 
a relation which of course holds when we replace a and (3 
respectively by a and b, two independent particular integrals 
of the differential resolvent. 
“ Oakwal,” near Brisbane, Queensland, Australia, 
August 1, 1865. 
Mr. Baxendell drew attention to the auroral phenomena 
which occurred on the 19th and 26th instant, and showed 
sketches of the arches, &c., taken by Mr. R. P. Greg, F.G.S., 
at Frestwich. 
Dr. Joule, F.R.S., said he had observed the effect of the 
aurora on the former date, on his sensitive magnetic needle. 
The needle was violently agitated, as many as 36 changes of 
deflection, varying from 10" to V 40 // occurring per minute. 
The cause of the movements seemed to he instantaneous in 
its action. It was remarked that when the beams prepon- 
derated on the west of the magnetic north the needle took an 
easterly direction. 
A paper was read entitled “ Questions regarding the Life 
History of the Foraminifera, suggested by Examinations of 
their Dead Shells,” by Thomas Alcock, M.D. 
