MOTION OF THE SOLAR SYSTEM. 
99 
the star), or 0"-51 xsec & in arc. Taking, as a mean value, §=45°, this gives the 
probable error in right ascension =0" - 72. He also states the probable error in de- 
clination, from five observations, to be 0"‘35, exclusive of the error occasioned by 
uncertainty of refraction. Assuming the average error in declination from all causes 
to be the double of this, or 0" - 70, we shall have the probable error in the place of the 
star, in the arc of a great circle, =\/ {0 ,, *72 2 + 0" , 70 2 } = l ,, '0. In the case of Hen- 
derson’s catalogue, the probable errors may be regarded as still smaller, owing to 
the superiority of the instruments of the Cape Observatory. But with respect to 
Lacaille’s observations, there is considerable uncertainty. His right ascensions 
were not determined, as in modern practice, by means of a transit instrument, but by 
the method of equal altitudes, with a 3-foot quadrant ; and it is not certain whether 
the clock, on the accurate performance of which during the interval of the two ob- 
servations of altitude the result mainly depends, was compensated for temperature. 
The declinations were observed with a 6-foot sector and a 6-foot sextant ; and it is 
to be remembered that some of the most important elements of reduction — the aber- 
ration, nutation, refraction — were then imperfectly known. On the other hand, 
Lacaille’s well-known skill as an observer, the care he bestowed on the catalogue 
in the Fundamenta Astronomise, and the repeated examinations it has undergone by 
Delambre and others, may be considered as rendering his positions trustworthy 
within limits which warrant their application to the purpose in hand. Delambre, 
who had made extensive comparisons of Lacaille’s observations, estimated the pro- 
bable error of one of his positions as double the probable error of one of Bradley’s. 
But the probable error in declination of a star observed by Bradley is estimated by 
Bessel at 0 "‘7 ; and the probable error in right ascension of an equatorial star, or, 
generally, the probable error of aXcosd, is nearly the same as the probable error in 
declination ; whence the probable error in the position of a star on the arc of a great 
circle may be taken at \/2 x 0'7 2 =0"'94, or less than one second. Assuming, then, 
the probable error of one of Lacaille’s positions to be 2", and that of one of Johnson’s 
(as above shown) to be 1", the probable error of the difference of the catalogues 
becomes \/4-f-l=2" , 236 ; which divided by 80, the interval between the epochs, 
gives 0"‘028 as the probable error of the annual proper motion deduced from 
the comparison of the two catalogues, so far as it depends on errors of ob- 
servation. Hence it appears that a proper motion amounting to 0"T annually 
(the smallest which has been admitted in the present inquiry) considerably ex- 
ceeds the probable errors of the catalogues, and consequently that the proper 
motions which have been under consideration not only have a real existence, but 
are determined with sufficient precision to give a result worthy of considerable 
confidence. 
On the whole it may be said, that although the present result, if it stood by itself, 
would scarcely be considered as of sufficient weight to establish the fact and direc- 
tion of the solar motion in space, yet coinciding as it does with those of Argelander 
