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CAPTAIN L. DARWIN, DR. A. SCHUSTER, AND MR. E. W. MAUNDER 
the width of the slit,the focal length of the collimator, the geometrical image of the 
slit will subtend an angle Hajfr at the centre of the lens of the telescope or camera, 
and to this we must add the width (X/r) of the diffraction band of an indefinitely 
small slit in order to obtain the actual angular width of the image. The angle 
between two rays having a refractive index differing by Sp., is on leaving the prisms, 
as shown hy Lord Ka.yleigh, tSfijr, where t is the aggregate effective thickness of 
the prisms. This angle must be equal to the angular width of the slit in order that a 
double line may just be resolved. We then obtain tS/x = ai// -}- X, when ij/ stands for 
Pt// and means the angle subtended by the useful horizontal aperture of the collimator 
at the slit. If 8X is the difference in wave-length of the two lines, we find 
SX/X = g (X + oixp)lXt. 
In order to define the actual and possible power of a spectroscope, it is convenient 
to distinguish between the resolving power of a spectroscope and the purity of a 
spectrum, and to introduce the following definitions (see ‘ Encycl. Britann.,’ 
“Spectroscopy”):— 
llie unit of resolving 2 ^oiver of a spectroscope in any part of the spectrum is that 
resolving power which allows the separation of two lines differing hy the thousandth 
part of their own wave-length. 
The unit of purity of a sp)cctrum is that p)urity which cdloivs the separation of two 
lines differing hy the thousctndth part of their own wave-length. 
We speak, therefore, of the resolving power of a spectroscope, which is a constant 
for each instrument, and of the purity of a spectrum, which differs according to the 
width of the slit. Both resolving power and purity vary inversely as^8X/X, and are 
equal to unity if that fraction is equal to 10~^. Hence, as from Ijord Rayleigh’s 
investigation for narrow slits, 
8p, = X/b 
or 
A, _ 0yU. 
lOOOR = 
dX. 
Also, from the above equations, 
1000 P= axfj), 
or 
P RX/(X -|- ai|;). 
Here P stands for the purity, and R for the resolving power. They are both 
numei ically equal if the slit a is indefinitely reduced. If the light is weak, narrowing 
