230 Mr. G. Owen on the Discharge of 
given by the equation 
V= Be ¢—@tipe 
or by V=He~™ {cos (pt—Ba) +) sin (pt—Bx)}. (17) 
If, therefore, the numerical value of the potential at the 
origin at any instant. is represented by the real part of 
Ke? ot viz. by Ecos pt, then the numerical or algebraic value 
of the potential at the same instant but at the distance a 
along the cable will be given by the real part of (17’), viz. 
by 
v= He “ cos (pt—Ba). 
The above equation is the ordinary algebraic expression 
for the potential in a semi-infinite cable ‘at any time ¢ and 
any distance w from the origin. Under the above conditions 
the time ¢ would be reckoned from the instant when the 
potential at the origin has its maximum value. 
The last equation is the usual expression for a wave of 
decreasing amplitude and wave-length 27/8 moving with 
velocity p/P. 
Similar expressions can be obtained for the numerical or 
algebraic value of the current in the cable at any place and 
time. 
XXVI. On the Discharge of Electricity from a Nernst Filament. 
Gwitym Owen, B.A. (Cantab.), M.Sc. (Viet. and 
Liverpool) ; Christ’s College, Cambridge; 1851 Exhibition 
Research Scholar of the University of Liverpool *. 
T is well known that from incandescent metals and carbon 
filaments there is a discharge of electricity both positive 
and negative. The experiments of Prof. J. J. Thomsont on 
the discharge from a carbon filament have shown that the 
carriers of the negative electricity at very low pressures are 
corpuscles. The carriers of the positive electricity, on the 
contrary, are of atomic dimensions, their masses being usually 
many times that of the atom of hydrogen, 
The present paper contains an accomnt of some experiments 
made to see if such a discharge of electricity takes place in 
the case of the glowing filament of a Nernst lamp. While 
the experiments were in progress, | found that E. Bose t 
* Communicated by Prof. J. J. Thomson, F.R.S. 
+ Phil. Mag. vol. xviii. p- 047 (1899). 
t Annalen der Physik, Ba. ix. p. 177 (1902). 
