TRANSACTIONS OF SECTION A, 4.63 
strips to radiation during the night, the black band is cooled more than the 
bright one, and in order to restore the equilibrium of the temperature it is necessary 
to conduct an electric current of certain intensity through the other. 
The two strips being identical, excepting the difference in radiating power of 
the upper surfaces, we may easily find the value of the radiation w in question. 
The value of the electric current being 7, the resistance of the strips per cm. m, the 
width 4, the ratio between the radiating power C,/e, we have : 
m % * 
NM ce 4186" 
1-C,/e 
C,/e can be determined very accurately in the laboratory once for all, and the not 
quite strict supposition that this quantity is a constant can be of no great 
consequence to the result, C,/e being such a little quantity that a variation in it 
of 10 per cent. will only introduce an error of 1 per cent, in the results. 
This instrument has, as will be easily understood, the same advantages as the 
pyrheliometer—that it is independent of the loss of heat through air-currents. 
Among the questions which may be studied by means of this instrument I 
will mention the following:—(1) The variations of the radiation from the earth 
during the night and during the year; (2) the connection between this radiation 
and the quantity of humidity, ozone, and carbonic acid contained in the air; (8) 
ue connection between the absorption of solar radiation and the radiation from 
the earth. 
DEPARTMENT OF MATHEMATICS. 
The following Papers and Reports were read :— 
1. The Law of Error. By Professor F. Y. Epgrwortn, D.C.L. 
The approximate expression for the frequency with which different values are 
assumed by a quantity that depends on a great number of independently varying 
elements is investigated by a new method: corroborating the first and second 
approximations, which had already been obtained, and obtaining the third, fourth, 
‘and, generally, the ¢‘* approximations. The results are extended to the case in 
which the elements fluctuate in several dimensions, and to the case in which the 
compound isa function other than linear of the elements, a function capable of 
expansion in powers of the elements, which are not neglected. 
2. Report on the Theory of Point-groups.—Part IV. By FRANcEs 
HaArpbcastLE.—See Reports, p. 20. 
3. Motes on Plane Curves. By Harouip Hinton, WA. 
The effect of an ordinary multiple point of the X-th order with superlinear 
branches of orders 7, s, t,... on the class, deficiency, and number of inflexions 
of a curve is the same as the effect of {4k(A—1)—S(r—1)} nodes and 3(7-1) 
cusps. 
The number of conics through four fixed points touching a curve is 22+): 
the harmonic envelopes of any fixed conic 7 and (3+ ) conics passing through 
two fixed points on 7 and osculating the curve (or $[4n? + 4nm + m* —4n—10m— 3x] 
conics passing through two fixed points on 7 and having double contact with the 
curve) are degenerate. The number of conics through two fixed points having 
