182 PROCEEDINGS OF THE AMERICAN ACADEMY 



The remarkable agreement of the residuals in columns 1, 2, and 3, shows 

 conclusively that the observations by Pond were most carefully made ; but his 

 pivots have transmitted as a legacy to all subsequent observations, a periodicity 

 wliich renders their value quite doubtful. 



We have here also a partial explanation of the reason Avhy the negative 

 residuals do not follow the irregular motion of Sirius. In the interval between 

 1816 and 1835, the Right Ascension of Sirius increased about .15s ; but tliis in- 

 crease is neutralized by the error depending on the Declination. On the other 

 hand, both causes act together between 1843 and 1868; and it is during this 

 interval that the periodicity of all observations depending on Pond is the most 

 marked. It should also be remarked, that Pond's provisional catalogue, brought 

 forward from Maskelyne, contains shght errors of single period. . 



IV. That the position of the zero point of the errors depending on the Declin- 

 ation is entirely due to the distribution of the fundamental stars ; and that the 

 reason why it remains unchanged, is because these stars retain the same relative 

 positions. The mean Declination of the stars under consideration is about -1-9°. 

 Had the stars having large south Declinations, been all situated in the first quad- 

 rant, the zero points would have been differently located. 



V. That the periodic errors of single period have been transmitted to subse- 

 quent observations in proportion to their dependence on Pond's catalogues of 

 720 and 1112 stars, and that the Nautical Almanac, has been largely instrumental 

 in the perpetuation of these errors. The errors of single period found in the 

 Greenwich observations under Airy, are to be ascribed to similar errors in the 

 provisional catalogue adopted in 1836. It would have been fortunate if the 

 first Cambridge Catalogue had been adopted instead. Airy's Cambridge system 

 was continued at that observatory till 1860 ; and as will be seen by simple in- 

 spection of the various sets of residuals, the errors are very small and are mostly 

 due to the Cambridge pivots. But in 1860 there was a return to the Nautical 

 Almanac positions of the clock stars, and immediately the periodicity becomes 

 apparent. The Edinburgh observations for 1835-36 depend on Bessel's Tabulae 

 Eegiomontanse ; those for 1837-41, on the mean of the Greenwich, Cambridge, 

 and Edinburgh observations for each preceding year ; while those subsequent to 

 1841, depend on the Greenwich clock stars, the places being communicated each 

 year. In the first case, the errors follow those of the Tabulae Regiomontanae 

 quite closely ; in the second, the errors of single period are partially ehminated 

 through the values of a and b, peculiar to each instrument ; while in the last 

 case, the errors of the Greenwicli system are largely reproduced. The errors 

 depending on the Declination are not as apparent previous to 1860, as since 

 that date. 



VI. That the variations in the relative values of m and n are due to two 

 causes : viz, — 



(«). To the confi-guration of the clock stars. 



(h). To the declination errors peculiar to each instrument. 



Under the first head, the most marked case is that of Oxford. The value of n 

 is persistently larger than for other observatories. I apprehend the reason for this 

 is to be found in the fact tliat in the earlier observations and especially in those 

 made in 1841-2 but few of Maskelyne's clock stars between 17'' and 2i^ were 

 used; a Lyrae, a Aquilte, /3 Aquilce, a- Capricorni, a Cygni, and a Piscis 

 Australis being omitted. Thus the weight of the errors of the provisional 



