73 
The solution is expressed in a series, the sum of which is 
found to he as below : — 
O 
n 
„ r _ 2) -+l 2"(n — l)’ 1-1 
cos i — 0 cos 0 cos 
n — 1 
n 
j«— 2- 
n — 1 ) 
2 " + 1 ( rc — 1)" _1 
n 
cos ” 0 cos (« — 2) 0x n ~' l -{- 
, 2 2, ‘(m I) 2 ' 
t»-o 
2/1 
cos 2 " Ox 2 "- 3 
In a brief note the Author indicates the method by which 
the series employed were derived from the differential 
equations. 
Mr. Crookes F.C.S., exhibited a specimen, weighing 
450 grains, of the new metal, thallium, which he discovered, 
by spectrum analysis. He stated that he had been fortunate 
enough to find this element in comparatively large quantities 
in the deposit from the flues of Mr. Spence’s pyrites burners. 
Dr. Joule made the following communication respecting 
a new and extremely sensitive thermometer : — “ Some years 
ago I remarked the disturbing influence of currents of air 
on finely suspended magnetic needles, and suggested that it 
might be made use of as a delicate test of temperature. I 
have lately carried out the idea into practice, and have 
obtained results beyond my expectation. A glass vessel in 
the shape of a tube, two feet long and four inches in diameter, 
was divided longitudinally by a blackened pasteboard dia- 
phragm, leaving spaces at the top and bottom, each a little 
over one inch. In the top space a bit of magnetised sewing 
needle, furnished with a glass index, is suspended by a single 
filament of silk. It is evident that the arrangement is 
similar to that of a ‘ bratticed’ coal pit shaft, and that the 
slightest excess of temperature on one side over that on the 
other must occasion a circulation of air, which will ascend 
