180 PEOCEEDINGS CF THE AMERICAN ACADEMY 



It is obvious that we have here an explanation of the positive residuals which 

 appear in all subsequent catalogues in the region of IS*", this point being nearly 

 the mean of the Right Ascensions of stars having large south Declinations. As 

 will be seen, these jjositive residuals appear in all catalogues depending directly 

 on Pond's observations, and notably in those found in the earlier volumes of the 

 Nautical Almanac. Wherever these catalogues were made the basis of obser- 

 vations Avith other instruments, these errors were transferred ; a little differently 

 distributed but not eliminated. 



Pond seems to have assumed that his first pivots became worn unequally. 

 This proves not to have been the case. On the otlier hand, the steel pivots seem 

 to have undergone a decided change of form, giving nearly opposite results in 

 1825 and 1832. Tlie change probably took place after 1828, and it is just here 

 that the confusion becomes inextricable, without a re-reduction of Pond's obser- 

 vations. 



We must not assum j, however, that the values of a and b for tlie new pivots 

 are entirely due to the pivots themselves, for by thte method of observation, the 

 errors of the old pivots were largely transferred to the new. Hence, the later 

 values of a and b are to be considered as only approximately correct ; i. e., they 

 are not the values wliich would liave been found if tiie observations e.g. between 

 1832 and 1835 had been absolute determinations. It is to be noted also, that 

 the change in the values of a and b, indicates that the irregularity is due to an 

 actual change of form in the pivots ratlier tlian to flexure or to weakness of the 

 axis. 



This tendency to positive residuals for low southern stars by no means escaped 

 the attention of so illustrious an astronomer and so careful an observer as Pond ; 

 but after a thorougii investigation of tlie differences between his observations 

 and tliose of Bessel and Brinkley, he does not seem to have reached any definite 

 conclusion. Nevertheless, a Piscis Australis was finally dropped from his list of 

 time stars, probably on tliis account. The following remarks on this subject I 

 quote from the Greenwich observations for 1833. 



" With all these precautions, we do not find, by comparing the present obser- 

 vations with these of Bradley, made eighty years ago under the same roof, and 

 computed by the same table of refractions, that we can obtain by interpolation, 

 any intermediate Catalogue that shall agree with the observations witliin the 

 probable hmits of error. This inclines me to my former opinion, that the proper motions 

 of the stars are not uniform, and that at present our knowledge of them is in a very 

 imperfect state. It has always appeared to me extremely improbable that the 

 proper motions of the stars should be uniform." "And, again, we can hardly 

 obtain a better test of our power of predicting the future positions of the stars, 

 than by trying by the same formula how accurately we can interpolate for the 

 paSt. In a variety of papers which I have submitted to tiie Royal Society, I 

 have endeavoured to shew that with us the latter experiment entirely fails." 



If it is admitted that periodic errors of single period have their origin liere, 

 we might expect that when the corrections depending on the Declination are 

 applied, the periodicity should disappear from Pond's observations. But just 

 here is introduced an opposite error through e ; that is, the value of e is, on 

 account of these positive residuals, less than it would have been with perfect 

 pivots, the equinox remaining constant. Excluding 8 stars having large south 

 Declinations, the value of e is, in general, about .01s numerically greater than the 



