210 Proceedings of the Royal IriaJi Aeademy. 
A=--a (2) 
It appears from this expression that, without impairing the bright- 
ness of the lines, we may increase the dispersion of a spectroscope in 
cither of two ways. Either by adding to the number of the prisms, 
which increases ^, or by enlarging their size, which increases a. 
It becomes then a matter of practical importance to determine in 
which of these two ways very powerful spectroscopes can best be 
made; and the object of this communication is to point out the ad- 
vantages to be expected from increasing the aperture rather than the 
number of the prisms. In the first place, there is less loss of light. The 
loss of light by absorption is the same as when the number of prisms is 
increased, but there are fewer surfaces at which light is wasted by 
reflection and scattering. But the great advantage would appear to be 
in defining power, for in the proposed arrangement much of the opti- 
cal work will be thrown on the telescope lenses instead of on prisms ; 
and as telescope lenses can in practice be made much more perfect as 
optical appliances than prisms, a considerable advantage may be 
expected in this way. Prom this is to be deducted the consequence of 
any increased defect which may arise in the manufacture of large 
rather than small prisms ; but making every probable allowance for 
this, there seems a large outstanding balance of advantage to be rea- 
sonably expected from the employment of large prisms. 
The substance of the foregoing investigation is taken from an 
inquiry into the geometrical optics of the spectroscope, especially in 
its application to astronomy, which I wrote out in February, 1866, 
for the use of a friend. But T had not, until lately, an opportunity of 
testing the conclusion to which it seemed to lead. It will, however, 
be fully tested in using a powerful spectroscope, which Mr. Grubb 
has undertaken to make as part of the apparatus furnished to me by 
the Academy for investigations into the properties of gases. 
In this instrument we propose to employ an object mirror in pre- 
ference to an object lens, to save expense ; and to save expense, bulk, 
and complexity, the light will be reflected back upon its course, so as 
to make one object mirror do duty both as collimator and telescope. 
"With these arrangements the light will sufl'er three reflections from 
silver films, but on the other hand the instrument will be extremely 
simple in its mechanical arrangements, very compact, and of great 
aperture, as compared with its cost. 
The sketch on the following page of a plan of the apparatus will 
give an idea of its construction. 
& is the chink, of which an optical image is formed within the 
minute reflecting prism /3, which is cemented to the back of the 
larger reflecting prism a. The light after reflection from /3 falls in a 
diverging beam upon the mirror i¥", by which it is transmitted as a 
parallel beam into the tank T, from which it enters the semi-prism P. 
It is then reflected by a silvered mirror, which forms the back of the 
Bemi-prism, and returned on its course, so that falling on Jf as a paral- . 
