198 



REPORT ON 



In the following table the columns headed r s , r 5 , r B , r e , contain respectively the 

 probable errors of a single observed value of 53, (J, ), and (v, for each compass, 

 computed from the residuals just given. But as these residuals were got by sub- 

 tracting the computed from the observed values of the coefficients, and as each 

 observed value was found from a set of deviations observed on all the thirty-two 

 points, it follows that the probable errors here given belong to the coefficients 

 when they have been computed from a set of deviations observed on all the thirty- 

 two points. For convenience of reference we will designate these as the probable 

 errors derived from all the observations of the cruise. 



But we have before found the probable errors of B } , Oi, Z)j, and E^ when com- 

 puted from observations made at a single station on each of the thirty-two points, 

 by a totally different process, namely, from the thirty-two observed deviations the 

 values of .A,, B C t , Z>,, and E^ were computed; next, with the values of A^ B lt 

 (\, Z)j, and EI, thus found, the deviations were computed for each point; then, 

 comparing these computed values of the deviation with the observed values, a 

 series of residuals were obtained from which the probable errors in question (which 

 are given in the table on page 185) were easily got. These we will designate as 

 tlic probable errors obtained from observations at a single station; and it will be 

 remembered that it was shown that, no matter what their numerical values might 

 be, the probable errors of B Ci, D and E t must all be equal to each other. 

 Although the difference between the probable errors of B,, C^ D^ E n and those 

 of 33, (J, S5, (, can never be great, yet, in general, it would not be rigorously cor- 

 rect to assume that they are equal to each other. However, in the case of the 

 compasses under discussion we will make this assumption, for by so doing no error 

 greater than the uncertainty of the probable errors themselves will be introduced. 

 In order to facilitate the comparison of the two sets of probable errors, those of B it 



C t , Z),, EI are given in the table above, in the column headed 



I/ !<>' 



This column 



is identical with the column headed in the same manner in the table on page 185, 

 except that the quantities are here expressed in parts of radius instead of minutes 

 of arc. 



Now, comparing the probable errors derived from all the observations of the 

 cruise with those derived from observations at any single station, we see that, taking 

 the mean of the results for all the compasses, TV and r s are almost identical, as they 



should be, but they are each more than twice as great as ! . On the other hand, 



