Variations of the Proper Motions of Procyon and Sirius. 259 



relative declination of Procyon for 1755 to appear to be 7" in error, 

 and the relative right ascension of Sirius for 1 755 more than a se- 

 cond of time. That so great errors cannot exist is proved by the 

 different checks in the Fundamenta Astronomice : but Lacaille's and 

 Tobias Mayer's contemporary results leave no doubt on this point, 

 although they cannot determine it within 2'' in declination and l-4th 

 of a second in right ascension. I regard also as a result rendered 

 certain by the observations, that the supposition of an unchanged 

 proper motion in the case of the relative declination of Procyon, and 

 in the case of the relative proper motion of Sirius in right ascension, 

 is shown to be false. 



The law of the change of each of the two motions is not yet 

 known with sufficient exactness by the observations given. If 

 Piazzi's determination of the relative declination of Procyon is cor- 

 rect (as I believe it to be)*, then has the difference, between 1755 

 and 1820, reached a positive maximum. In the case of the right 

 ascension of Sirius, I have sought to obtain a more approximate 

 knowledge of its change, through the following up of the results 

 of the observations with the transit instrument which Pond (vol. for 

 1811-12) published, and by a new reduction of Maskelyne's ob- 

 servations. This has given a positive maximum of the difference 

 from the TabulcB Regiomontanee of about O^'S, between 1790 and 

 1800 ; but since the ])ivots of the axis were unluckily proved to have 

 been injured, and were corrected in 1803, which correction produced 

 a significant effect on the subsequent observations of right ascension 

 of Sirius, it cannot be certainly maintained that the maximum was 

 produced in reality by the motion of Sirius, and not, at least in part, 

 through the defect of the instrument. In the meanwhile it follows, 

 from what has been advanced at present, and from the tables, that 

 a period, not very different from tliat of a half-century, would serve 

 in both cases for a sufficient explanation of the observations. I 

 think it, however, expedient in the present state of the subject to 

 wait for a further development of the nature of the change, from 

 the observations of the next half-century, before pronouncing a judge- 

 ment thereupon. This has, besides, no real value for the objects of 

 astronomy before the nature of the motion of all the stars of the 

 fundamental list are known. 



I have investigated the conditions which must be fulfilled, that a 

 sensible change of the proper motion, like that observed, may be ca- 

 pable of explanation by means of a force of gravitation. If the star 

 that exhibits it be represented by S ; an attracting mass by Wn, and 

 the corresponding star by Sw ; the sun by O ; the distance SS„ by 

 rn', O S» by Tn' ; O S by f ; the angle at the star S by Sn ; the an- 

 gle made by the plane O S S„ with the plane of motion of the star 

 S by Un, we easily find the expression of the second differential co- 

 efficient of the apparent motion of the star, with respect to the time, 



= — "- . — (1 ^ )sin Sn cos Un, 



rnrn § V r«'V 



* That of Maskelyne for 1770 has little weight. 



