H. A. Rowland—Concawe Gratings for Optical Purposes. 87 
Art. XI.—On Concave Gratings for Optical Purposes ;* by 
Henry A. Row ann, Professor of Physics, Johns Hopkins 
University, Baltimore. 
GENERAL T'HEORY. 
HAVING recently completed a very successful machine for 
ruling gratings, my attention was naturally called to the effect 
of irregularity in the form and position of the lines and the 
form of the surface on the definition of the grating. Mr. C. S. 
Peirce has recently shown, in the American Journal of Mathe- 
matics, that a periodic error in the ruling produces what have 
been called ghosts in the spectrum. At first I attempted to 
calculate the effect of other irregularities by the ordinary 
method of integration, but the results obtained were not com- 
mensurate with thelabor. I then sought for a simpler method. 
around the radiant point satisfies the condition for waves of all 
Society of London in November last, the paper being in my in its presen 
shape at that tim s I wished to make some additions, for which I have not 
yet had time, I did not then publish it. I w i r to 
See an article on this subject, which had been presented to the hysical Society 
and was n the Philosophical Magazine. The article contains no 
ore than an extension of my remarks at the Physical ty and formula simi- 
lar to those in pa s I have not before this published anything except 
