388 TRANSACTIONS OF SECTION Ag 
DrpaRTMENT OF MATHEMATICS. 
The following Papers were read :— 
1. The Dynamics of a Globular Stellar System. 
By Professor A. 8. Eppineton. 
In considering the gravitational attraction of the whole stellar system on a 
star, it seems probable that we may neglect the part due to the chance distri- 
bution of stars in the immediate neighbourhood, and consider only the smoothed 
central force. We have thus to study a new kind of dynamics, which 
resembles molecular dynamics in being a statistical subject, but differs from it 
in that there is nothing corresponding to the ‘encounters’ of molecules. The 
first problem to attack is the determination of the different possible distribu- 
tions of velocity which correspond to a steady state. A number of the simpler 
cases are worked out in the paper. It is of particular interest to find a system 
in which there is strong preferential motion to and from the centre, compared 
with the transverse velocities (following Professor Turner’s suggested explana- 
tion of the two star-streams). It is a little difficult to reconcile preferential 
radial motions with a finite density at the centre of the system; but systems 
satisfying both these conditions seem to be possible. 
2. The Expression for the Electrical Conductivity of Metals as deduced 
from the Electron Theory. By W.F. G. Swany, A.R.C.S., D.Sc. 
nerrAv 
a 
on the assumptions that all the electrons move with the same velocity v, and that 
there is no persistence of velocity after coliision. Though more elaborate for- 
mul have since been deduced by different methods, the above formula is not without 
interest, in that it corresponds to a better ratio for the electrical to the thermal 
conductivities than is given by some of the more elaborate formule. The 
object of the present paper is, however, to show that the assumptions on which 
it is based do not lead to it, but to the formula o= eR which is much less in 
Drude’s formula «= for the electrical conductivity « was developed 
agreement with the facts. 
In the deduction of Drude’s formula it is assumed 
(1) that since the velocity given by the field X to an electron while travel- 
ling over its mean free path A is a, the average velocity given by the field 
to the electrons is Xen 
2mv 
’ 
(2) that the average velocity of the electrons parallel to the field is the 
average velocity which the field has created in the electrons. 
The first assumption is equivalent to the assumption that the electrons to 
be found in any element at any instant are on the average in the middle of 
their free journey, and that they have consequently at that instant travelled on 
the average a distance ; Although this is apparently obvious, it is not true. 
The true average distance turns out to be A. Correcting for this we should 
: 1e?hv 
obtain o = oe 
The objections with regard to assumption (2) will perhaps be clear when it is 
remarked that if all the electrons to be found per cc. at any point O were 
suddenly robbed of the velocity which the field had given them, while their 
positions were left unchanged, we should still have a resultant current, for if 
the field, for example, urges the electrons from left to right, and if we draw 
a plane through O perpendicular to the field, and if, further, we consider the 
action of the field in bending the paths of the electrons, we see that the 
electrons which have come to O from any element to the right of the plane 
started out more nearly parallel to X than the electrons which have come 
from the element symmetrically situated to the left of the plane. When due 
ee 
