396 
PHYSICS: A. A. MICHELSON 
are rifts or openings in a luminous background which look out into the 
blackness of space beyond. From investigations elsewhere in the sky, 
I lean towards the idea that these are relatively non-luminous, opaque 
bodies, seen against a luminous background. 
THE RULING AND PERFORMANCE OF A TEN-INCH 
DIFFRACTION GRATING 
By A. A. Michelson 
RYERSON PHYSICAL LABORATORY. UNIVERSITY OF CHICAGO 
Presented to the Academy, May 13, 1915 
The principal element in the efficiency of any spectroscopic appHance 
is its resolving power — that is, the power to separate spectral lines. 
The limit of resolution is the ratio of the smallest difference of wave- 
length just discernable to the mean wave-length of the pair or group. 
If a prism can just separate or resolve the double yellow line of sodium 
its limit of resolution will be (5896-5890) /5 893 or approximately one 
one-thousandth, and the resolving power is called one thousand. 
Until Fraunhofer (1821) showed that' light could be analysed into 
its constituent colors by diffraction gratings these analyses were effected 
by prisms the resolving power of which has been gradually increased 
to about thirty thousand. This limit was equaled if not surpassed by 
the excellent gratings of Rutherford of New York, ruled by a diamond 
point on speculum metal, with something like 20,000 lines, with spacing 
of 500 to 1000 hues to the mihimeter. These were superseded by the 
superb gratings of Rowland with something over one hundred thousand 
lines, and with a resolving power of 150,000. 
The theoretical resolving power of a grating is given as was first shown 
by Lord Rayleigh by the formula R=mn, in which n is the total number 
of lines, and m the order of the spectrum. An equivalent expression is 
furnished by = ^ (sin i -f sin o), where / is the total length of the 
X 
ruled surface, X the wave-length of the light, i the angle of incidence, 
and 6 the angle of diffraction; and the maximum resolving power which 
a grating can have is that corresponding to i and d each equal to 90° 
which gives R = 2 //X, that is twice the number of light waves in the 
entire length of the ruled surface. 
This shows that neither the closeness of the rulings nor their total 
number determine this theoretical limit, and emphasizes the importance 
of a large ruled space. 
