202 



REPORT — 1882. 



Hallstkom's Method. 



In the case of Hallstrom's method the relation between the corrections 

 and the thread-lengths are more complex. They may, however, be 

 obtained as follows. In Table LIII. the first column gives the various 

 B's, the other columns the coefficients with which r's and o-'s occur in 

 the expressions for them. 



Thus, for instance, ? (2) = ^ (1) + 0-3 — o-^ — tj + 7-4, and so on. 

 These are obtained from the formulte given above (p. 170), and from them 

 10^' 1 is found. Using the value thus obtained, and remembering that 

 (p (n) = (1) + (2) + . . . . + ^ (i(.),the values of them's are found in 

 Table LIV. These have been checked by comparison with Table XIV. 



Table LTII. 



Probable errors. 



Table LIV. 



Probable Errors. 



Since now each of the <t's and r's is an independent measure, it is 

 evident that the square of the probable error of the correction of a 

 principal point = square of probable error of a measurement X the 

 sum of the squares of the coefiicients in Table LIV., and is therefore 

 proportional to the number given in the last column of that Table. 



