ON THE RATE OF INCREASE OF UNDERGROUND TEMPERATURE. 97 
at 501 feet. The difference between them agrees well with the generally 
accepted rate of 1° for 300 feet, and indicates about 48° as the surface 
temperature at small elevations, such as 30 feet. The pits in the East 
Manchester coal-field from which we have observations, namely, Astley 
Pit (Dukinfield), Ashton Moss, Bredbury, Denton, and Nook Pit, are all 
sunk in ground at elevations of between 300 and 350 feet. It would 
‘therefore appear that the assumption of a surface temperature of 49°, 
which we made in reducing these observations, is about 2° in excess of 
the truth. 
A very elaborate paper on Underground Temperature has recently 
been communicated to the Royal Society by one of the members of the 
Committee—Professor Prestwich. It contains probably the fullest col- 
ection that has ever been made of observations of underground tempera- 
ture, accompanied in most cases by critical remarks; and adduces 
arguments to show that most of the temperatures observed are too low, 
owing to the influence of the air in mines, and of convection currents in 
wells. Professor Prestwich is disposed to adopt 1° F. in 45 feet as the 
most probable value of the normal gradient. 
Report on Electrical Theories. 
By Professor J. J. THomson, M.A., F.R.S. 
‘In this report I have confined myself exclusively to the consideration of 
‘those theories of electrical action which only profess to give mathematical 
‘expressions for the forces exerted by a system of currents, and which 
make no attempt to give any physical explanation of these forces ; for it 
is evident that before we can test any theory of electrical action we must 
know what the actions are which it has to explain, and we cannot do this 
‘until we have a satisfactory mathematical theory. I have further limited 
myself to the consideration of the fundamental assumptions of each 
theory, and have not attempted to give any account of its mathematical 
‘developments, except in so far as they lead to results capable of distin- 
guishing between the various theories. 
I have divided the theories into the following classes :— 
1. Theories in which the action between elements of current is deduced 
by geometrical considerations combined with assumptions which are 
>. explicitly, at any rate, founded on the principle of the Conservation 
-of Energy. 
This class includes the theories of Ampére, Grassmann, Stefan, and 
Korteweg. 
2. Theories which explain the action of currents by assuming that 
the forces between electrified bodies depend upon the velocities and accele- 
rations of the bodies. 
This class includes the theories of Gauss, Weber, Riemann, and 
—Clausius. 
3. Theories which are based upon dynamical considerations, but which 
neglect the action of the dielectric. 
__ This class contains F. E. Neumann’s potential theory and v. 
-Helmholtz’s extension of it. 
4. C. Neumann’s theory. 
1885, H 
