208 Prof. H. A. Rowland on Concave Gratings 
r o 
— = cos v , 
c,db sw . , . .f-, , sin/LA tan/ti + sinv tanvo s3 - "I 
2 -r cos 6 (sin /i + sin v Q ) < 1 — i — — ~ — = o 6 + &c. 
ds v 7 t sm^ +sinv J 
But in the automatic arrangement we also have v =0; and so 
the formula becomes 
2 -?■ = cos 8 (sin fi + sin v ) j 1 — j tan //, 8 3 + &c. j- . 
To find the greatest departure from theoretical perfection, 
8 must refer to the edge of the grating. In the gratings 
which I am now making, p is about 260 in., and the width of 
the grating about 5 # 4 in. Hence S = t £q approximately, and 
the series becomes 
*~ 2000000 tan ^- 
Hence the greatest departure from the theoretical ruling, 
even when tan fi = 2, is 1 in 1,000,000. Now the distance 
apart of the components of the 1474 line is somewhat nearly- 
one forty-thousandth of the wave-length ; and I scarcely 
suppose that any line has been divided by the best spectro- 
scope in the world whose components are less than one third 
of this distance apart. Hence we see that the departure of 
the ruling from theoretical perfection is of little consequence 
until we are able to divide lines twenty times as fine as the 
1474 line. Even in that case, since the error of ruling 
varies as 8 s , the greater portion of the grating would be ruled 
correctly. 
The question now comes up as to whether there is any limit 
to the resolving power of a spectroscope. This evidently 
depends upon the magnifying power and the apparent width 
of the lines. The magnifying power can be varied at pleasure ; 
and so we have only to consider the width of the lines of the 
spectrum. The width of the line evidently depends in a perfect 
grating upon three circumstances — the width of the slit, the 
number of lines in the grating, and the true physical width 
of the line. The width of the slit can be varied at pleasure; 
the number of lines on the grating can be made very great 
(160,000 in one of mine); and hence we are only limited by 
the true physical width of the lines. We have numerous cases 
of wide lines, such as the C line, the components of the D* 
and H lines, and numerous others which are perfectly fami- 
* I have recently discovered that each component of the D line is 
double, probably from the partial reversal of the line as we nearly always 
see it in the name-spectrum. 
