270 Proceedings of the Royal Society of Edinburgh. [Sess. 
The values tabulated under the heading “ Relative Intensities ” are 
the results obtained by photometric measurements with the apparatus 
described above. (Nos. 14 and 15 are exceptions, being wholly the result 
of a theoretical calculation, as will be explained later on.) For greater 
convenience, in all cases the intensity at the angle zero has been arbitrarily 
taken as 100, and the other values reduced accordingly; except in the case 
of nos. 9 and 10, where the values at the angle zero could not be ascertained, 
and where the intensities at 5° have been arbitrarily taken as 20. These 
results are plotted in figs. 2, 3, 4, and 5. In every case distances along 
the horizontal axis represent the angle to the normal at which the light 
emerges from the plate, and distances along the vertical axis the corre- 
sponding intensity. In all cases it will be seen that the curves are of the 
same general nature, the intensity at first falling off very rapidly with 
increasing angle, but subsequently showing a tendency to become asymptotic 
to the angular axis. The appearance of some of the curves rather suggests 
that they might be fitted by the formula for the error curve y = ae~P x \ 
and I made trial of one of them, but without success. In any case this 
could never prove to be a general formula, as a glance at curve no. 6 
will show. 
The reason for including a column in the table headed “ Relative Total 
Emission ” is as follows. It must be borne in mind that at each point of 
the ground-glass surface light is emitted in all directions, and hence, if an 
imaginary hemisphere be described with its centre at any point of the glass 
surface, the entire hemisphere would be illuminated by light from that 
point. Furthermore, all the rays emerging from that point between, say, 
5° and 6° to the normal will light up a certain zone on the hemisphere, 
those emerging between 6° and 7° an adjacent zone, and so on. Hence, to 
find the total emission of light at any angle, we must multiply the intensity 
at that angle by the area of the corresponding zone. In other words, the 
total emission at any given angle is proportional to the relative intensity 
at that angle, multiplied by the sine of the angle. And the values so found 
(each multiplied by a factor which makes the maximum total emission 
equal to 100), are the values tabulated under the heading “ Relative 
Total Emission.” They have been plotted in the figures, and each of the 
resulting curves appears in the same figure as the curve of relative 
intensity from which it has been derived, and from which it is distinguished 
by being in broken line. 
It is evident that the angle of maximum total emission affords a very 
fair criterion of the effectiveness of the scattering action : the greater the 
numerical value of the angle , the greater the scattering. 
