32 
THE ASTRONOMER ROYAL, WAVE-LENGTHS 
Classe der Kaiserlichen Akademie der Wissenschaften,’ LII. Band, II. Abtheilung, 
page 289, &c. This paper gives the details of a new measure of the grating with which 
Fraunhofer's original measures of wave-lengths were made (as I understand M. Dit- 
scheiner’s words) ; and by means of this correction of measure, and the corresponding 
correction of wave-length for the line D common to Fraunhofer’s and Ditscheiner’s 
measures, Ditscheiner computed new values of wave-lengths for the entire series of 
lines, primary and secondary, which he had himself observed. On careful consideration 
of all the circumstances of formation of these new values, it appeared to me that it was 
indispensable for me to base my reduction of Kirchhoff’s measures upon Ditscheiner’s 
new values. I should thus have the opportunity of introducing a value for B, which 
would enable me to adopt a function of the 5th order instead of the 4th order (upon 
which all my preceding calculations were founded) ; and I could use the same oppor- 
tunity for making correction for a petty error which I had committed in the line E (I 
had inadvertently used 1527‘7 instead of 1523 - 2 for Kirchhoff’s measure). 
My immediate object, in calculation, now was, to make such an addition to the 
function embodied in my former calculations as would produce definite alterations in 
the wave-lengths computed for B, C, D, E, F, G. This, it was evident, could be done by 
a function or a sum of functions of the 5th order ; and I had only to adopt the most 
convenient form. Kemarking that Kirchhoff’s measures for B, C, D, E, F (with the 
decimal point thrown back three places) differ very little from 0’6, 0-7, 1*0, F5, 2T, and 
that the measure for G is not very different from 2 - 9, I adopted the following form for 
general correction; whereby [0*6], [0 - 7], [TO], [1‘5], [2T], [2 - 9], are meant certain 
constants whose values will shortly be seen. 
General correction for all values of k. 
X (k— 0-7) X (^ — 1*0) x (£—F5) X (k— 2T) x (£-2-9) 
, correction for k = O' 7 /7 n r*\ n -i n\ / 7 -i r\ m m\ n O 
+ X(k— 0-6) X(&— T0)x(£— F5)x(&— 2 m l)x(k— 2*9) 
+ [To] x °' 6 ) X (k— 0-7) x (k-l-b) x (k- 2T) x (£-2-9) 
+ ^ X (£—0-6) X (k— 0-7) x (£-1*0) X (k-2-1) X (k- 2-9) 
+ X (#—0-6) x (k- 0-7) X (£-1-0) x (k— 1-5) x (k— 2-9) 
+ ^ 9 ] X(k— 0*6) x(&— 0-7) X (A— H))x(&— 1*5) x(^— 2T). . 
The numerical values of the products following the fraction in each line are given, 
for every 0T of k from 0-0 to 3 - 0, in the last six columns of the following Table. 
