70 CELESTIAL SPECTROSCOPY. 
we do not know, of a few only of its more important problems, giving a 
prominent place, in accordance with the traditions of this chair, to the 
work of the last year or two. 
In the spectroscope itself advances have been made by Lord Ray- 
leigh by his discussion of the theory of the instrument and by Prof. 
Rowland in the construction of concave gratings. 
Lord Rayleigh has shown that there is not the necessary connection, 
sometimes supposed, between dispersion and resolving power, as be- 
sides the prism or grating other details of construction and of adjust- 
ment of a spectroscope must be taken into account. 
The resolving power of the prismatic spectroscope is proportional to 
the length of path in the dispersive medium. For the heavy flint glass 
used in Lord Rayleigh’s experiments, the thickness necessary to resolve 
the sodium lines came out 1-02 centimeters. If this be taken as a unit, 
the resolving power of a prism of similar glass will be (in the neighbor- 
hood of the sodium lines) equal to the number of centimeters of its 
thickness. In other parts of the spectrum the resolving power will 
vary inversely as the third power of the wave length, so that it will be 
eight times as great in the violet as in the red. The resolving power 
of a spectroscope is therefore proportional to the total thickness of the 
dispersive material in use, irrespective of the number, the angles, or 
the setting of the separate prisms into which, for the sake of conven- 
ience, it may be distributed. 
The resolving power of a grating depends upon the total number of 
lines on its surface and the order of spectrum in use, about 1,000 lines 
being necessary to resolve the sodium lines in the first spectrum. 
As it is often of importance in the record of observations to state 
the efficiency of the spectroscope with which they were made, Prof. 
Schuster has proposed the use of a unit of purity as well as of resolv- 
ing power, for the full resolving power of a spectroscope is realized 
in practice only when a sufficiently narrow slit is used. The unit of 
purity also is to stand for the separation of two lines differing by one- 
thousandth of their own wave length, about the separation of the 
sodium pair at D. 
A further limitation may come in from the physiological fact that, 
as Lord Rayleigh has pointed out, the eye, when its full aperture is 
used, is not a perfect instrument. If we wish to realize the full resolv- 
ing power of a spectroscope, therefore, the emergent beam must not be 
larger than about one-third of the opening of the pupil. 
Up to the present time the standard of reference for nearly all spec- 
troscopic work continues to be Angstrém’s map of the solar spectrum 
and his scale based upon his original determinations of absolute wave 
length. It is well known, as was pointed out by Thalén in his work 
on the spectrum of iron, in 1884, that Angstrém’s figures are slightly 
too small, in consequence of an error existing in a standard meter used 
by him. The corrections for this have been introduced into the tables 
of the wave lengths of terrestrial spectra collected and revised by a 
