Local Attraction on Geodetic Opei'ations, 



259 



Russian, Indian II. (or Great Arc), Indian I., Prussian, Peruvian, Hano- 

 verian, and Danish Arcs. Suppose 



wz, + + /3,v + x^, 7n\ + a> +Jd\v + x^, 



are the corrections of the latitudes of the extremities of the subdivisions of 

 the Anglo-GalUc Arc, x\ being the correction for the standard or reference 

 station in this Arc. Similarly, let 



m.^+a.ji+(3^v-j-cc.^, m + ct' + (i' + 



m^ + oc^u + j3^v + x,, w^'3 + a> + /3> + '^'3, 



be the corrections for the divisions of the other Arcs. 



Then the values of u and v which give the most likely form are those 

 which make the sum of the squares of all these corrections a minimum. 

 The sum of the squares will involve u and and also eight quantities 

 ^1 . . . a?g. The usual course is to regard, not only u and but . . . a?g as 

 independent variables, and to differentiate the sum of the squares with 

 regard to each of them in succession, and so obtain as many equations as 

 quantities to be determined. 



7. This mode of proceeding is, I conceive, erroneous ; as I shall now 

 endeavour to show. The corrections x^ , , . ,Xq are not properly indepen* 



