458 TRANSACTIONS OF SECTION A. 
and indicates that there is a distinct connection between the rainfall in the east 
of Englard and that in the Channel Islands. Another example taken was raiufall 
and typhoid cases in Surrey districts, the water-supply of which is obtained from 
river sources. The coefficient of correlation is 0:116, with a probable error of 0:073, 
so that it is impossible to assert definitely that there is any relation hetween 
rainfall and typhoid—nt any rate on the evidence afforded by these statistics. 
Reference was made to a paper on barometric heights by Professor Karl Pearson, 
F.R.S., and Dr. Alice Lee, and to the use of the coefficient of correlation by Dr. 
Gilbert T. Walker, F.R.S., in his interesting memoranda on the meteorology of 
India. 
The author concluded with an appeal for the more scientific treatment of 
statistics by modern methods. 
2. On the Use of Calcite in Spectroscopy. 
By Professor W. M. Hicks, £.2.S. 
The advantages of the large dispersion in the ultra-violet produced by calcite 
are so great that it may be interesting to describe the method which the author 
has used to get rid of the double refraction which shows itself at a short distance 
from the ray experiencing minimum deviation. The method is based on sup- 
pressing one of the rays by using polarised light. With a parallel beam, vibrating 
either horizontally or vertically, the transmitted light belongs respectively to the 
extraordinary or the ordinary ray. The angle of incidence is not far from the 
polarising angle ; consequently the horizontal vibrations (polarised perpendicular 
to plane of incidence) are transmitted in larger proportion than the other. The 
spectrograph in question had one calcite prism of 60° and two half-prisms of 30° 
each. The calculated intensities of the transmitted light in the two polarised 
rays come out to be in the ratios 2°35, 3:05, 4:67 respectively for minimum deyvia- 
tions for the rays 5600, 3000, and 2500—the horizontal vibration being the 
stronger—whilst the corresponding ratios at points where the doubling is pro- 
nounced are 2°44, 3°31, and 5°03. Itis therefore preferable to polarise the light 
in a vertical plane. It is impossible, however, to use polarised light with a 
quartz lens in the collimator, since the rotations produced by the different thick- 
nesses of the lens give a mixed beam when it falls on the prism. To get over this 
difficulty a composite lens was made, of equal plane convex lenses, one of right- 
handed and the other of left-handed quartz. The spectra obtained are then very 
satisfactory. As polariser a Nicol can be used for light down to about 3000, but 
between 3000 and 2950 the thin layer of Canada balsam completely absorbs the 
light. For wave lengths shorter than this a small Foucault, fixed like a com- 
parison prism, was used, and this was quite satisfactory down to 2300, at about 
which the calcite begins to absorb the light. Near this, however, the ordinary 
ray has only about one-fifth the intensity of the extraordinary, and it is scarcely 
necessary to use any polarising arrangement at all. 
The whole spectrum from 6000 to 2300 covers about 30°. Negatives were 
shown illustrating (1) the doubling and its removal by polarisation; (2) the rela- 
tive intensities of each component; and (3) the almost complete effacement of the 
ordinary ray component for wave-lengths below 2500, 
DEPARTMENT OF MATHEMATICS. 
The following Papers and Reports were read :— 
1. The Introduction of the Idea of Infinity. 
By W. H. Youna, Se.D., FBS. 
It was pointed out that there are three methods of treating mathematics, viz., 
the logical, the formal, and the practical methods, and it was urged that the 
formal method had had for many years more than its share of attention in 
