18 



Now returning again to the figure, we see that if G'„ is the excess of a 

 distance measured along line 26 över the corresponding distance along line 

 14, and if we corapute J„ by the formula: 



/WÎ — 14 



(11) J„ = (?'„(^y- 



J„ will be the excess of the corresponding distance along line m över the 

 distance along line 14. Now let: 



-E„ = the excess of the distance in question along line 14, över the scale 

 of the machinC; as obtained in operation 6. And it must not be forgotten that 

 all the observations of operation 6 were reduced with corrections of the form : 



a + hx 



for reasons already explained. Also let: 



T„ — the excess of the actual distance on the scale över its nominal value, 

 as computed with Gill's division errors of scale A. 



Then remembering that we have shown distances along the middle line 

 to be really longer than their comparison with the scale shows by the quantity: 



h{F„ + G,) 



we get the final correction \K,^^^^, Mhich is to be added to the coordinate mea- 

 sured along the m-linc, of a star situated at the intersection of the w-line 

 and the «-line, by the équation: 



(1 2) [JC,],„ = E,, + T„ + /„ - [./„],„ - (P„ - P«) + \ {F„ + G,) 



The observations of operation 5 will have furnished us with the excess 

 of the total length of line 43 över line 14. The adopted value of this quan- 

 tity we will call M, fuUy corrected of course for sinuosity. If we adopt as 

 our standard of length the mean micron of the lines 14 and 43^ which is of 

 course identical with the mean micron of the six lines 2, 14, 26, 31, 43, 55, 

 then for the above value of [Ä'„]__ we must Substitute the corrected quantity 

 [Ä^'„]^^^, computed by the équation: 



/n - 43\ 



(13) LX.L = [^.,]„. - Uf (^^j 



