306 TRANSACTIONS OF SECTION A. 
According to J. J. Thomson,* the direction of maximum polarisation for 
perfectly conducting particles should make 120° with the incident light. From 
the above table it appears that for very small particles this angle is 90°, as it 
would be for dielectric particles (a fact which we find was previously observed 
by Professor R. Threlfall*), but that it increases as the diameter of the particle 
increases to a value above the theoretical limit. 
Measurements were also made of the electrical conductivity of the sus- 
pensions. Since the average distance between the particles was about 100 times 
their diameter, Maxwell’s theory of the conductivity of compound media is 
applicable. The conductivity was measured in every case for concentrations 
containing the same amount of silver and other bodies per unit volume, but 
differing only in the size of the particles. In these circumstances the con- 
ductances should be the same unless there is a difference in the conductivity of 
the silver particles. It will be seen that the conductivity of the mixture in- 
creases as the particles increase in size. It would seem, therefore, that the 
anomalous behaviour of the silver is due to a real change in resistance with size, 
and is not simply a consequence of the fact that Thomson’s theory is limited to 
the cases for which the conductivity is sufficiently large. ; 
No numerical Calculation has previously been made for large particles. By 
transferring Thomson’s equations so as to express the result in terms of the same 
functions which have been calculated by Lord Rayleigh for fairly large values 
of the argument, his work becomes available for the present problem; and one 
of us (EH. T. P.) has calculated the degree of polarisation of the light scattered 
in different directions for perfectly conducting particles for which gies 
=unity, when A=wave-length of the light. The maximum polarisation corre- 
sponds to an angle for about 108°. The value indicated by our experiments 
lies between 110° and 120°, but further experiments are necessary to fix it more 
exactly. 
It is not difficult to suggest a reason for the diminution of the conductivity 
with size. Separated molecules, as in a vapour, are perfectly non-conducting ; 
we conclude that there are then no free electrons. Aggregation of molecules 
of silver as in a solid gives rise to free electrons (and consequent conductivity) 
owing to the mutual action of the molecules upon one another. In small particles 
the number of free electrons may be proportionately less than for silver in mass. 
It must not be forgotten, however, that a colloid particle in its medium is 
surrounded by a double layer consisting of polarised molecules of the medium, 
and it is quite possible that it is this polarised layer of a dielectric medium 
which modifies the optical properties of the silver. 
4. On the Viscosities of the Halogens in the Gaseous Slate. 
By A. O. Ranxrng, D.Sc. 
In this paper various methods which have been used for measuring the 
viscosities of the vapours of Chlorine, Bromine, and Iodine at a number of 
different temperatures were described. 
The relations between the viscosities of these three gases were discussed. The 
laws are similar to those which the author has previously shown to apply to 
the group of inert gases. 
DEPARTMENT OF MATHEMATICS. 
1. Symbolic Solution of Linear Partial Differential Equations of the 
Second Order. By T. W. Cuaunpy, M.A. 
STATEMENT OF RESULTS. 
2 . 
Take equation in form goes + Be +B Be + yz=0, where a, B, y denote functions 
dady da by 
: 5 da 5B as) 
of x,y. The invariants h, k are — + aB—y=h, — +oB-y=k. 
ox by 
4 Recent Researches in Electricity and Magnetism, p. 449.  ° Phil. Mag., 1894. 
