126 Prof. F. L. 0. Wadsworth or the 



curve [as oiven by (6)]*, and i)lace it with its centre on the 

 o])tioal axis, the aberration at any other point of the fiehl 

 near the axis, i. e. for small values of ^, will be 



Zb = + - sin^/3 tang 6 cos /( 1 + cos i) 



+ 1 sin*jS(l + cos i) [cos^i - (1 + 2 cos i) '-^tang"!?] sec'^^. ( 14) 

 For the Rowland mounting it will be similarly 



Zio=-^ sm^l .+ ^ . . . . (15) 



8 Lcos I cos 6 J ^ 



This expression (14) may be put in the form 



„ — P . ,^tano;^ .^ c 



Zb = + ^ sm^yg ^ ( 1 + cos i) cos^ 



2 cosi 



+ I sin^/Sa + cos cos^z [l -( "^^,7'' ) ^'^^^S'^l ^^^'^^ ( ^ C) 



in which the same functions of i appear as in (10). The only 

 new function is 



The values of /i(i)-i- cos i = ai and oi f..(i)^b have been 

 computed for the same values of i assumed before, and are 

 given in columns 4 and 5 of Table 1. 



(C) Let the grating be mounted so that the angles of in- 

 cidence and diffraction are equal but opposite in sign, i. e. 

 so that 6= — i. This is the form of mounting discussed and 

 illustrated on pp. 58, 59, and on Plate VII. fig. 1) of my 

 former paper. As there shown, the central spectral image 

 in the field always lies on a circle whose centre is on the axis 



of the grating, and whose radius is j-. The mechanical 



mounting which fulfils this condition is very simple, but it 



* For small values of the equation of the curve may be written 



which is the equation of a circle with its centre on the axis of the grating 

 and a radius equal to one-half u. The statement made by Poor and 

 Mitchell in their paper (Astrophysical Journal, vol. vii. p. 159) that 

 '* The spectra . . are brought to a focus on a circle whose radius is z^," is 

 an error probably due to an oversight in considering cos-0 to be of the 

 same order as cos 0. 



