for Optical Purposes. 209 
liar to every spectroscopist. Hence we are free to suppose 
that all lines have some physical width ; and we are limited 
by that width in the resolving power of our spectroscopes. 
Indeed, from a theoretical standpoint we should suppose this 
to be true ; for the molecules only vibrate freely while swing- 
ing through their free path ; and in order to have the physical 
width n * „' of the wave-length, the molecule must make 
100000 s> ? 
somewhat nearly one hundred thousand vibrations in its free 
path ; but this would require a free path of about two inches ! 
Hence it would be only the outermost solar atmosphere that 
could produce such fine lines ; and we can hardly expect to 
see much finer ones in the solar spectrum. Again*, it is 
found impossible to obtain interference between two rays 
whose paths differ by much more than 50,000 wave-lengths. 
All the methods of determining the limit seem to point to 
about — 1 — — of the wave-length as the smallest distance at 
150000 & 
which two fines can be separated in the solar spectrum by 
even a spectroscope of infinite power. As we can now nearly 
approach this limit, I am strongly of the opinion that we have 
nearly reached the limit of resolving-power, and that we can 
never hope to see very many more lines in the spectrum than 
can be seen at present, either by means of prisms or gratings; 
for the same limit holds in either case. It is not to be 
supposed, however, that the average wave-length of the line is 
not more definite than this; for we can easily point the cross- 
hairs to the centre of the line to perhaps 1 in 1,000,000 of the 
wave-length. The most exact method of detecting the coin- 
cidences of a line of a metal with one in the solar spectrum 
would thus be to take micrometric measurements first on one 
and then on the other ; but I suppose it would take several 
readings to make the determination to 1 in 1,000,000. 
Since writing the above I have greatly improved my 
apparatus, and can now photograph 150 lines between the H 
and K lines, including many whose wave-length does differ 
more than 1 in about 80,000. I have also photographed the 
1474 and b 3 and 5 4 widely double, and also one of the E lines 
just perceptibly double. With the eye much more can be 
seen ; but I must say that I have not yet seen many signs of 
reaching a limit. The lines yet appear as fine and sharp as 
with a lower power. If my grating is assumed to be perfect, 
in the third spectrum I should be able to divide lines whose 
wave-length differed 1 in about 150,000, though not to photo- 
graph them. 
* This method of determining - the limit has been suggested to me by 
Prof. 0. S. Hastings, of this University. 
PHI. Mag. S. 5. Vol. 16. No. 99. Sept 1883. K 
