OF ARTS AND SCIENCES. 95 



have been measured with the micrometer. Then, the first line of the 

 group being assigned the value of zero, and the distance from this 

 line to the one numbered 12 being called unity, the relative distances 

 of the intermediate lines are expressed in decimal fractions, which 

 are multiplied by the difference in wave-length of the limiting lines, 

 and the products added to the wave-length of the more refrangible 

 one, which is distinguished in each case by a subscript zero attached 

 to its cognominal letter. It is evident that for these small angles, 

 the largest of which does not exceed 30', the sine differs so inappreci- 

 ably from the arc, that the readings of the micrometer may be con- 

 verted directly into angular measure. The difference between the 

 wave-lengths of the limiting lines of the group has been taken from 

 Angstrom's measurements in the case of the large B group. The 

 line called A 12 in this paper was not measured by Angstrom. Its 

 wave-length has been approximately determined by the following 

 method : — 



The centre of the comb being midway between two known lines of 

 the spectrum, the difference of micrometer readings for these lines 

 was observed. Let the angular distance between them be 2x. Then 

 from the general formula nSX = sin i -\- sin r, where S= 681 lines 

 to the millimeter, and n is 1, we have — 



1 X 681 X *i = — sin i -f- sin (V — x) ) 



1 X 681XI = - sin i + sin (r + x) J als0 r + * = 61 ° 16 ' 



Measures taken without disturbance of the micrometer focus 

 gave — 



rev. 



Angstrom (6561.8) C to Angstrom (6716.4) = 14.942 



(6716.4) „ „ (6866.8) B = 14.490 



„ (6866.8) B „ „ (6927.8) B 12 = 6.087 



A „ „ A 12 = 7.727 



Substituting these numbers in the appropriate equations, and solving, 

 we have — 



m.m. 



C 681 X 0.000 6561.8 = .44686 = — sin i x -f- sin (r, — x x ). 

 (6716.4) 681 X 0.000 6716.4 = .45739 =— sin i x -f sin fo + arj. 

 i x = 15° 24' 02" r x = 46° 51' 58" 



rev. rev. 



whence 2x a = 51' 57" = 14.942 .% 1. = 3' 28".6. 



