912 rEPORT—-1885. 
and the equation of motion 
ddT\ , dF 
dae) * ae ° 
gives as the solution 6 « e~”', whence 
(TIA +[2]Ae+ 
It is evident that the value of p (and therefore of r) is stationary when all but. 
one of the coefficients A,, A,, &c., vanish, that is when the type coincides with one 
of those natural to the system. 
From this theorem corollaries may be drawn as from the corresponding theorem 
for times of vibration. The greatest time-modulus can only be reduced by the 
application of constraint, and where the normal mode is difficult of calculation a 
good approximation to the greatest time-modulus may be had from a hypothetical 
type chosen so as not to deviate too widely from the real one. Any increase in T or 
diminution in F asa function of the co-ordinates entails in general an augmentation 
in all the time-moduli. In the case of free electric currents, already referred to 
as an example, this augmentation of time-moduli would result from the approxi- 
mation of iron (treated as a non-conductor), or from an improvement (however 
local) in conductivity. 
5. On a new Polariser devised by Mr. Ahrens. 
By Professor Sirvanus P. Tuompson, D.Sc. 
This prism consists of a tetragonal block of cale-spar, the square ends of which 
are principal planes of section of the crystal; the axis of symmetry of the prism 
being at right angles to the crystallographic axis. It is divided by two planes 
making an angle of about 36° with one another; their intersecting line lying across 
the middle of one of the end faces. These two planes divide the prism into three 
wedges which are united together by Canada balsam. The polarised field of vision 
has about 28° of angular aperture. The line of junction which traverses the end 
face is quite imperceptible when the prism is used as a polariser, though it inter- 
feres slightly with the field when the prism is used as an analyser. In the writer’s 
opinion it is the best polariser hitherto designed. 
6. On a simple Modification of the Nicol Prism giving Wider Angle of 
Field. By Professor Sirvanus P, Taompson, D.Sc. 
This modification consists in reversing the obliquity of slope of the end-faces 
making them incline about 5° instead of 45° with the crystallographic axis, and in 
cutting the crystal across in such a plane that the balsam film makes 89° with the 
new end faces, or about 94° with the crystallographic axis, This ‘ reversed’ prism 
may have, externally, exactly the same form as the ordinary Nicol prism if cut 
from a longer piece of spar. If cut from a piece of the same proportions as an 
ordinary Nicol prism, the new prism will be somewhat shorter; but will have a 
slightly wider field. The 2 ‘reversed’ prisms presented to the section have angu- 
lar fields of 32° and 37° respectively. That of the ordinary Nicol is about 25° 30’. 
This method of construction may be looked upon as a compromise between the 
methods of Hartnack and of Nicol. It combines most of the advantages of the 
former with the cheapness of the latter. 
7. On some of the Laws which regulate the Sequence of Mean Temperature 
and Rainfall in the Climate of London, By H. Courtenay Fox, M.B.C.8. 
_ The materials used in preparing this paper are the monthly temperature and 
rainfall for the Royal Observatory, Greenwich, from 1815 to the present time. 
They form a series of carefully recorded facts extending over the long period of 
