Stoney — On a Neiv Form of Sjjectroscope. 209 
at the blue end of the spectrum, that it has at the red end. The law 
of variation will depend partly on the material of the prisms, and 
partly on their angle. 
Hence, to give definiteness to a comparison between different 
instruments, some region of the spectrum must be selected, at which 
the comparison shall be made. Accordingly, we shall regard as the 
dispersion of a prism the value of ^ at that point near the middle of 
the spectrum, where i = 2000, and W (the wave-length in tenth- 
metres) = 5000.'^' Defined in this way the dispersion of the battery of 
three prisms in the great Grubb Spectroscope of the Eoyal Dublin 
Society is 12. 
Eut the dispersion of a spectroscope must be carefully distin- 
guished from 8 the dispersion of its prisms. For the dispersion of a 
spectroscope is equal to the dispersion of its prisms multiplied by the 
power applied to its telescope. The actual dispersion accordingly 
depends upon the eye-piece used, and is variable ; but there is in each 
spectroscope a certain standard dispersion, which is perfectly definite, 
and to the credit of which the instrument is entitled. This is the dis- 
persion which is obtained when the telescope is armed with the highest 
power that may, without loss of light, be applied to it. 
When a spectroscope is directed towards an object producing bright 
lines, such as a sodium flame, or nebula, there is a certain intrinsic 
brightness of each line, which no disposition of our apparatus can 
enable us to pass, so long as we confine ourselves to vision with one 
eye. The most the instrument can do is to show us the lines of this 
maximum brightness, diminished only by the inevitable losses from 
absorption in passing through the glass, and from reflection and scat- 
tering at the polished surfaces. 
This maximum brightness will be attained whenever the power of 
the eye-piece, with which the telescope is armed, is sufficiently low 
to emit pencils of light, which fill the whole diameter of the pupil 
of the eye. The highest power which will do this is — 
a 
a 
Where a is the aperture of the spectroscope {i.e. the diameter of the 
pencil of light passing through the prisms, and the two object lenses), 
and a the diameter of the pupil of the eye (which may be taken to be 
five millimetres, or 0*2 of an inch). If a higher power than this 
standard be applied to the instrument, the lines become fainter ; if a 
lower power be applied, a part of the aperture of the spectroscope is 
left out of use, and an instrument with smaller prisms would act as well. 
When armed with this po^er, the dispersion of the spectroscope 
becomes 
* At this point of the spectrum one unit on the scale of inverse wave-lengths is 
equal to 2*5 units on Angstrom's scale of direct wave-lengths. 
K. I. A. rROC. — VOL. 1., SER. II., SCIENCE. 2E 
