92 
MR. GALLOWAY ON THE PROPER 
the precession due to the middle epoch, 1790 ; and on examining the proper motions 
of the stars so compared, I have found fifty-six which appear to have changed their 
positions 8"*0 or upwards in the are of a great circle, or to have an annual proper 
motion of not less than 0"*1. To these have been added five others whose annual 
proper motions appear to be somewhat less than 0"*1, according to Mr. Johnson’s 
observations, but to amount to that quantity according to Henderson’s determina- 
tion compared with that of Lacaille. The whole number of stars, therefore, included 
in the present inquiry, whose proper motions are deduced from the comparison of 
the observations of Mr. Johnson with those of Lacaille, is sixty-one. 
Henderson’s catalogue contains the mean right ascensions and declinations of 
172 of the principal southern stars, being part of a very much larger number ob- 
served by him during his short residence at the Cape in 1830 and 1831, while in 
charge of the Government Observatory established in that colony, the reduction of 
which unfortunately he did not live to complete. The declinations were published 
in 1838, in vol. x. of the Memoirs of the Royal Astronomical Society, and the right 
ascensions in vol. xv. of the same series, which appeared only last year (1846). In 
the latter volume he gives a list of fifty-two stars which appear to have a proper 
motion of not less than 0"T annually, deduced in thirty-six cases from a comparison 
of his own observations with those of Lacaille, and in the remaining sixteen cases 
with those of Bradley. Henderson’s mean places are for the beginning of 1833 ; 
so that the interval is eighty-three years in the case of comparison with Lacaille, 
and seventy-eight years in the case of comparison with Bradley. The whole of the 
thirty-six stars compared with Lacaille, are contained in Mr. Johnson’s catalogue, 
but there are four of them in respect of which the comparison is not given by Mr. 
Johnson, and which, therefore, are not included among the sixty-one above referred 
to. Henderson’s catalogue, therefore, gives twenty additional stars, so that on the 
whole the number taken into account is eighty-one ; namely, sixty-five whose proper 
motions depend on Lacaille’s observations, and sixteen on the observations of 
Bradley. 
For the purpose of deducing the direction of the apparent proper motion from the 
observed variations of right ascension and declination, as well as for determining the 
hypothetical direction, every star has been referred to its mean position for 1790. In 
the case of Mr. Johnson’s stars, this reduction has been made by taking the mean 
right ascension and the mean declination of the two compared catalogues. In respect 
of the stars in Henderson’s catalogue, those which are compared with Lacaille’s 
places were first reduced to 1830 by applying the precession given in the catalogue, 
and the mean then taken between these reduced places and the places of Lacaille ; 
and in the case of those compared with Bradley’s catalogue, the mean of the two 
catalogues gave the positions for 1794, from which they were reduced to 1790, by 
applying the precession for that epoch. With respect to the stars common to the 
catalogues of Mr. Johnson and Henderson, the annual variation both in right ascen- 
