254 M. Fraunhofer on the Laxvs 



is constantly obtained for r. * Therefore, as the equation 

 shows ah-eady clearly enough, the value of s^ — (s sin. ^ (± "») * 

 disappears against 4 z/*, it may therefore be neglected ; and 

 thence we obtain corrected : 



tang . *+'> _ VO^-0-sin..±.^) n ^,. 



£ . sin. 6 -^jCfi. 



r\T \ (+0 £ . sin. 6 + m 

 (V.) cos r - = =- 



These equations represent the experiments with non-symme- 

 tric spectra stated in page 112 of last Number as accurately 

 as the equation III. does. In both cases the sign -f gives the 

 position of the coloured rays on one side of the axis, and the 

 sign — that of the opposite side in the various spectra. In the 

 comparisons it must not be forgotten, that in the experiments 

 the distances were measured from the axis ; but r expresses the 

 distance from the plane of the system of hnes. It is hardly ne- 

 cessary to remark that in those special cases, when, for in- 

 stance, the above equation is employed for the ray C, instead 

 of w, (C w) is to be put : thus also, when it is employed for 

 the ray D, (D w) &c. 



In these cases I denote the magnitude r for the ray C with 

 (C t), for the ray D with (D r), &c. The equation (V.) ac- 

 cordingly in these cases is this : 



cos (C r) ^- ' z= = — ^^ — ' 



cos (D r) - -^ =: = — i ^ &C. 



^ 6 



When the rays fall vertically on the system of lines, sine 6 

 •=. 0, and the equation (V.) becomes : 



(+ »N + VCiJ 



COS. r - ^— 



£ 



• I had also measured these angles with a telescope of four inches ibcus ; 

 but, as was to be expected, conformably with the equation, I found no 

 other differences but those which may be attributed to an inferior telesco- 

 pic power, and which are sometimes positive, and sometimes negative. 

 If a curvature of the modified ray were to be observed where the distance 

 of the luminous point is not large, then these experiments are subject 

 to many difficulties, and demand a different and extremely perfect appa- 

 ratus. 



