360 Proceedings of Royal Society of Edinburgh. [sess. 
in reality this effect is inappreciable, the cement layer being so 
extremely thin ; and we are leaving out of account the effect of 
the reflection by such a junction, which is not inappreciable, as 
will be shown later. Now, were it the case that all the light of 
the upper beam fell on the silvered part OC of the interface DC, 
and none of it on the unsilvered part OD, then each of the two 
beams would lose the same fraction of its light as it passed 
through the cemented joint in its path, Ae., as the upper beam 
passed through the junction GB and the lower beam passed 
through the junction DO. It is necessary, however, that the 
lower edge of the upper beam should fall at least some distance 
below the point 0 in the figure, because only in this way can 
the full intensity of light be ensured right up to the edge of the 
silvered part OC of the interface CD. Assuming then that we 
have the lower part of the upper beam of light falling on the 
unsilvered part of the interface DO, there must exist the following 
state of affairs : — A certain fraction of the light of the upper beam 
is reflected by the junction GB and passes out through the face 
AG, leaving the beam that passes on towards the interface CD so 
much the less intense. The light lost in a similar manner by 
the lower beam, however, by being reflected at the junction DO 
and sent out through the face CD is more or less made up for by 
the light of the lower part of the upper beam which is reflected 
vertically upwards from the same junction DO. 
If, however, the junction BG (fig. 2/3) were to be omitted, and 
the upper beam of light arranged to cover the whole face AB (fig. 
3), then the gain and the loss to the light of the lower beam, 
caused by the interface at OD, would exactly balance each other. 
Provided always that is, that the juxtapositor is placed in the 
optical train after that piece of apparatus, whatever its particular 
form, whose function it is to equalise the intensity of the two 
beams of light, for then we have two beams of equal intensity 
falling on the same surface (OD) at the same angle, and 
accordingly the reflections will be of exactly the same magnitude. 
In those cases where the juxtapositor is not so placed we have 
the loss or gain of intensity of the lower beam given by a quantity 
which is the reflection at the cement of the difference of the in- 
tensities of the two beams, and even here the error introduced 
