15 



The final adopted values of P in the last column are the means of the 

 numbers in the three prcceding columns, giving double weight to those obtained 

 in the direct comparison column. ïhe two columns headed „Scale B Direct" 

 can only differ from each other on account of errors of observation in the 

 direct comparison of the two scales, and on account of uncertainty in Gill's 

 previously determined division errors. They do not involve the projection er- 

 rors at ail. An examination of Table 3 shows thorefore that neither the 

 projection error investigation nor even Gill's division errors, can be regarded 

 as altogether satisfactory; but the final values of P hâve been applied in the 

 further réductions. 



3. Investigation of Formulae of Réduction. 



Passing over processes 3 to 7 for the present, we shall proceed at once 

 to dérive the formulae used in the computation of the final division errors of 

 the reseau. We shall use the figure and the notation already given. We shall 

 first adjust the observations for the m-lines by themselves, and those for the 

 w-lines by themselves. Finally we shall détermine the angle between the m- 

 lines and w-lines, and apply a correction so as to make the mean micron of 

 the six principal lines the unit of length, and the angle between the m- and 

 n-lines exactly 90°. 



Let us now suppose a star situated at the intersection of the lines m and 

 M, and put: 



[^„] _ = the total correction which must be added to its coordinate measured 

 along the line m, so far as this correction can be derived from a con- 

 sidération of the n-lines only. 



We shall proceed to find the value of [-SC,],,,- 



Using our former notation, let us put: 



a = 43[2]„-«[14]„ (3) 



so that (7„ is the excess of the 2-line over the 14-line, between the 43-line 

 and the «-line. Also put: 



A = 43[26]„-43[14]„ (4) 



