———- 
TRANSACTIONS OF SECTION A. 451 
and it follows that we can compute e* with arbitrarily close approximation by the 
2 ne 
formula 1 +. + = +5490 5 ,- This result is the exponential theorem. 
In this method e is introduced as a limit which presents itself naturally, e* is 
defined as the «th power of e in accordance with the theory of indices ; the differen- 
tiations of e* and of log w are effected very simply. The proof of the existence of 
the limit by which e is defined is not intricate. The exponential theorem is pre- 
sented as a formula for the approximate computation of et, and the proof of it is 
effected by the same process as is used to prove Taylor's theorem (with a remainder 
after m terms) in the case of functions of a more general character. The theory of 
infinite series is avoided entirely. 
DEPARTMENT OF GENERAL Puysics. 
The following Papers and Report were read :— 
1. The Transmission of the Active Deposit from Radiwm Emanation 
to the Anode. By Stoney Russ, B.Sc. 
A comparison has been made between the amount of active deposit obtained 
on a wire charged positively and that obtained on the same wire charged negatively 
at pressures ranging from 0-001 cm. to 10 ems. Diffusion experiments, ¢.e., experi- 
ments made with the wire and containing vessel maintained at the same potential, 
have also been made over this range of pressure. 
Whereas the amount of active deposit obtained on the negative electrode 
diminishes as the pressure is diminished, as has already been found by Makower, 
it is found that the amount obtained on a positive electrode increases as the 
pressure is diminished. 
A comparison has next been made of the quantity of active deposit obtained 
on positive and negative electrodes in different gases at pressures between 0:1 mm. 
andl mm. Up to the time of writing experiments have been completed in air 
and hydrogen, and the work is being continued for sulphur dioxide. 
It is found that whereas in air the amount of active deposit obtained on a 
negative wire is appreciably greater than on a positive wire over this range of 
pressure, in the case of hydrogen just as much active deposit is obtained on a 
positive wire as on the same wire charged negatively. 
Thus the quantity of active deposit which is directed by an electric field at 
these low pressures depends on the nature of the molecules with which the radium 
emanation is mixed. 
2. The Absorption of Gases by Charcoal. By Miss I. Homrray. 
The experiments of which an account is here submitted were devised, at the 
suggestion of Sir W. Ramsay, to throw some light on the question of the absorp- 
tion of gases in charcoal. The gas which appeared most suitable for the purpose, 
on account of its molecular simplicity and chemical inertness, was argon. The 
apparatus used was similar to a constant-volume gas thermometer, the bulb con- 
taining 3 grams of charcoal. This was connected with a gas burette, a gas 
reservoir, anda Sprengel pump, all connections being of glass and sealed, 
Various constant temperature baths were used, ranging from boiling water to 
liquid-air temperatures, and successive quantities of argon were admitted from the 
burette, the pressures being read at each temperature. Isothermal curves were 
then plotted, taking pressures as ordinates and concentrations, corrected for dead 
space and reduced to standard conditions, as abscisse. From these curves points 
of equal concentration were read off and a fresh series of curves were obtained, 
haying pressures as ordinates and absolute temperatures as abscissw. Such curves 
have been termed by Ostwald ‘isosteres.’? Each curve corresponds thus to a 
Ga@2 
