128 Prof. C. Bams on Elliptic and other 



results may be corroborated by observing the number 

 of fringes between two Fraunhofer lines, like the C, D and 

 other lines used. Differentiating equations (8) and (10) for 

 variable n, X, 0, and N (since dN/dd is equal to dN /dd, 

 equation 12'), and inserting — D cos .dft/dn = d\/dn, it 

 follows, after arranging, that 



dO X 2 1+dNldn X i—6 /10 , 



-r =-ts t~ 7- — ?u = rtan— ^— . . (13) 



dn eu 1 -f cos {i + 6) e cos % 2 



Combining this with (11), 



d6 X sin i — sin 6 



dn eD cos i e cos i 



(14) 



Since in equation (13), e is not determinable it is necessary 

 to compare increments Adn/d0 in terms of the corresponding 

 increments Ae, whence 



A(dnjd6)=( cos i/Xtan^- \Ae. . . , (15) 



My observations contain data of this kind, computed 

 separately for the Fraunhofer lines D, C, &c, employed and 

 their mean values. To find the mean width of fringes 

 between these lines, their angular deviations were divided by 

 the number of fringes counted between them at different 

 values of e. The results agree as closely as the difficulty of 

 the observations warrants. One may note that without 

 removing N, the corresponding coefficients would be 



Ad(n + N)/dQ, 



and these are found to be much more in error, here and in 

 the preceding cases. If from ddjdn^ e is eliminated in terms 

 of (w + N) the equation is 



dO X 1 



^~D(n + N )cosi' "'*■■.' (16j 



so that for a given value of i, 6, N , they decrease in size 

 with n. If n = they reach the limiting size 



dO _ X 



dn ~~ DN n cos i ' 



If the crack N D should be made infinitely small, they 

 would be infinitely large. To pass through infinity, N must 

 be negative, which has no meaning for i > 6 or would place 

 one effective edge of the crack S behind the other. These 

 inferences agree with the observations as above detailed. If, 

 however, i<6, a negative value of N restores equation (16) 



