292 



Dr. J. Hopkinson on the 



[June 14, 



is the most refrangible of the group of magnesium lines, (G-) is the 

 hydrogen line near G. 



The method of smoothing the results by the aid of each other has been, 

 first, to calculate a, b, and c from the mean values of fx for the lines 

 B, F, H x ; second, to calculate values of fi from the formula obtained; third, 

 to plot on paper the differences between ~jx observed and fx calculated, and 

 to draw a free-hand curve among the points, and then inversely to take 

 ji for each line from the curve. 



It appeared desirable to express the standard values of jU, which are 

 the means of those for Hard Crown, Soft Crown, Light Flint, and Dense 



Mint, in terms of ~. In the following Table column 



I. gives X, the wave-length in 10 -4 centims. ; 



II. the values of -i ; 



X 2 



III. the standard values of • 



IV. the values of jj, calculated from 



p = a+ b^+c~, where 



« = 1-539718, 

 6=0-0056349, 

 c = 0-0001186; 

 V. the differences of III. and IV. ; 

 VI. the values of Ji from the extended formula 



^ = a -f b A -f c i + d i , where 



1*538414, 

 6 = 0-0067669, 

 c= -0-0001734, 

 c?=0-000023; 

 VII. The differences of III. and VI. 





I. 



II. 



III. 



IV. 



Y. 



VI. 



VII. 





X. 



1 



X 2 " 



IK. 











B. 



•68668 



2-12076 



1-552201 



1-552201 



0000000 



1-552203 



- 2 



C. 



•65618 



232249 



1-553491 



1-553444 



+0000047 



1-553481 



+ 10 



D. 



•58890 



2-88348 



1-557030 



1-556951 



+0-000079 



1-557033 



- 3 



E. 



•52690 



3-60200 



1-561612 



1-561553 



+0-000059 



1-561613 



- 1 



b. 



•51667 



3-74605 



1-562530 



1-562490 



+0-000040 



1-562538 



- 8 



F. 



•48606 



4-23272 



1-565692 



1-565692 



0-000000 



1-565693 



- 1 



a. 



•43072 



5-39026 



1-573459 



1-573536 



-0-000077 



1-573457 



+ 2 



h. 



•41012 



5-94536 



1-577356 



1-577409 



-0-000053 



1-577349 



+ 7 



H r 



•39680 



6-35121 



1-580287 



1-580287 



o-oooooo 



1-580289 



- 2 



