172 PROCEEDINGS OF THE AMERICAN ACADEMY 



increase the value of 7n relatively to that of n, inasmuch as sin a is at this point 

 nearly maximum, while cos a is nearly minimum. Including these stars, the 

 coefficients become as follows : — 



Nautical Almanac . . . . m = — 50 n = +20 



American Ephemeris . . . m=- — 28 n = +26 



Of course the same fundamental catalogue may, through erroneous or irregular 

 proper motions, give different coefficients at different epochs. Thus, for Lever- 

 rier, 1870, m = — 23, and n = +2, excluding Sirius and Procyon. 



As this tendency to negative residuals in the case of Sirius and Procyon 

 appears in nearly all modern catalogues, it occurred to me that we might find 

 here, an explanation of the way in which periodic errors came to be introduced. 

 I accordingly began the inquiry, whether the errors in question may not be due 

 to the irregular proper motions of the stars employed for determining clock 

 errors, and especially of Sirius and Procyon. An examination of Maskelyne's 

 observations indicates an apparent periodicity in a few cases. This subject, 

 however, is in its detail, reserved for a future communication. It is sufficient 

 for our present purpose to limit the inquiry to Sirius and Procyon. In case these 

 stars were persistently used as clock stars, with places largely in excess of their 

 true positions, all resulting Right Ascensions in their vicinity would be in- 

 creased in proportion to the number and range of the stars employed. There 

 seems, however, to be several objections to this supposition as a complete 

 explanation. 



(1.) The residuals given by various catalogues, at different epochs, do not 

 wholly follow the irregular motions of these stars. Taking Sirius alone and 

 assuming its Right Ascension to be known for 1816 (which I assume to be the 

 time when the present system of differential observations was first introduced), 

 the predicted Right Ascension for each successive year would be too small, and 

 between this date and 1843, the change would amount to .30^ Hence, we should 

 expect a tendency to positive instead of negative residuals between these dates ; 

 if Sirius was the sole cause of the disturbances. On the other hand, between 

 1843 and 1868, the Right Ascension was continually decreasing, hence, if the 

 place given by the first Greenwich Catalogue was carried forward through this 

 interval, the resulting clock errors given by this star were too large. This would 

 of course produce a tendency to the negative residuals which actually exist. 



(2.) In the Greenwich system of observations adopted in 1836, and generally 

 followed by all Enghsh Observatories, the places of the clock stars have been 

 derived from the observations of the previous year. Hence the periodicity of 

 Sirius and Procyon has since that date been completely allowed for. 



(3.) If the irregular motions of these stars were the sole cause of the observed 

 periodic errors of single period, the formula, r = in sin a + n cos a, would no 



