OF ARTS AND SCIENCES. 171 



The following are the values of m and n, computed from the residuals of 

 Table III. For the purpose of easy comparison, the values derived from the 

 observations are repeated : — 



Greenwich . . . 

 "Washington, I. 

 Oxford .... 

 Paris .... 

 Melbourne . . . 

 Edinburgh . . . 

 Brussels .... 

 Washington, II. . 

 Harvard College . 



—38 +18 —42 +19 



—10 — 2 — 3 +2 



Means . . . —25 +17 —21 +16 



It therefore appears : — 



(a) That the periodic errors of the provisional places are largely transferred 

 to the observations. 



(b) That in general, the coefficients derived from the observations are smaller 

 than those derived from the provisional catalogues, the diminution being quite 

 nearly the amount indicated by theory. But it will be observed that, with the 

 Washington corrections from 1862 to 1865, the periodicity is slightly increased, 

 while in the case of Paris the increase is very decided. 



(c) That observations made at diiferent observatories, but depending on the 

 same star places, give substantially the same coefficients, the difference being 

 the effect of errors depending on the declination. Thus in the case of Greenwich 

 and Edinburgh, the declination errors tend to neutralize the errors of single 

 period ; while in the case of Oxford, the two causes act together, giving larger 

 coefficients. 



{d) That whether the clock errors depend on the places of the Nautical 

 Almanac directly, as in the case of Washington II., or on the same places cor- 

 rected by observations, as in the case of Brussels and Melbourne, the periodicity 

 is transferred to the observations with about equal diminution. 



It will be observed that the residuals for a f ' 'nis Majoris and a Canis Minoris 

 (in parenthesis) have been excluded in the derivation of m and n. Where the 

 erroneous places of these stars enter into the clock errors, as in the case of 

 Wasliington II., they should be included. In this case two errors are intro- 

 duced. First, an error through e, extending over the whole 24 hours. Tlius, 

 when f is negative, all the negative residuals will be too small, and all the 

 positive ones too large. Second, if these residuals are excluded in the forma- 

 tion of £, but are still included in the derivation of m and n, the effect will be to 



