714 REPORT—1896. 
The temperature coefficient is only one ten-thousandth of a volt for 1° Centi- 
rade. 
The cell has many other advantages. Its resistance remains constant, and is 
lower than in most other cells used as standards. Notwithstanding this, the cell 
protects itself against a charging current from other sources, as well as from dis- 
turbing tendency due to short circuit. 
The reason for this immunity from permanent disturbance is not yet clear, and 
the authors are engaged in investigating it. 
8. On Reostene, a new Resistance Alloy. 
By J. A. Harxer, D.Sc., and A. Davipson. 
This communication is a descripiion of the physical properties of a new alloy 
for electric resistance coils, which has the extremely high specific resistance of forty- 
five as compared with copper. Its temperature coeflicient is comparatively small, 
0-0011 per ohm per degree Centigrade, and from a large number of tests with heavy 
currents, under varying conditions, it was found to alter only very slightly with 
time. The paper was illustrated with a model and several samples, and the appa- 
ratus by which the specimens were maintained{at a known temperature during the 
measurements of resistance was also shown. 
DEPARTMENT II.—MATHEMATICS. : 
1, Report on the G (r, v) Integrals,—See Reports, p. 70. 
2. Report on Bessel Functions and ozher Mathematicai Tables. 
See Reports, p. 98. 
3. Results connected with the Theory of Differential Resolvents. 
By the Rev. Ropert Hartey, J/.A., F.R.S. 
The linear differential equations whose forms are recorded in this paper stand 
in a very close and important relation to the trinomial forms of algebraic equations. 
For, on the one hand, the complete integration of the differential equations deter- 
mines the form of the roots of the algebraic equations, and, on the other, the general 
solution of the algebraic equations determines the complete integrals of the several 
differential equations; so that the relation is reciprocal. In fact, the algebraic 
equations and their corresponding differential equations are eo-resolvents. 
In a paper printed in the British Association Report for 1878, at pp. 466-8, it 
is shown that if y be a function of x, and a, b, ¢ arbitraries independent of a: and y, 
any root y of the algebraic equation 
ay™ + by" +ex=0... (@) 
will satisfy the linear differential equation 
Ld . ; ” We ro En ni 
poy | 2 "y= ee 1 ay GA) 
m=—-7 b"c" Lm—r m—r 
or, when 7 is greater than m, 
poy | |" (—) ee | Yam. (AD 
r—m = 27 
and any rcot of 
ay” + bry"+e=0..... (0) 
tate meee 
