16 



SO that D„ is the corresponding excess of the 26-line o ver the 14-linc. The 

 quantities C„ and D„ are derived from the observations of operation 6 mentioned 

 above. As the several réseau lines were compared with the scale on dif- 

 férent days, when the total lengths of the scale and réseau may have been 

 différent, it is necessary to correct C'„ and D„ by means of the observations 

 of operation 4. If we let: 



A =3i[2]55-ai[l'i]K, obtained in operation 6, 



-t''l=3l[2]K-3l[14joô, „ „ „ 4, 



then we must use in the further computations instead of C„, the quantity G'„, 

 given by the équation: 



And if we put, similarly: 



Lo = ai[26]55 — yi[14].r,r,, obtained in operation 6, 

 J/. = 3i[26].%-,,,[14]k, „ „ „ 4, 



we must Substitute for />„, the quantity i)'„, coniputed by the équation: 



(6) D', = D„ + {L'.,-L,)'^^ 



Now let: 



so that F,, and G„ are the values of C'„ and D'„ corrected for sinuosity. 

 Since these corrections are supposed to turn the actual lines into ideal straight 

 lines, and since the distance between two straight lines ought to vary unifornily 

 as we move along the lines, we should have: 



