and the Absolute Size of the Fixed Stars. 303 
parently bad figure among the rest, but is by no means to be left 
out on that account merely, seeing the care and the superior means 
for that day with which the measures were made. 
‘¢ Mr Fallowes’ determinations,’ continues Sir John, “ in this 
series, are open to objection, from the decidedly inadequate instru- 
mental means by which they were furnished (a small altitude and 
azimuth circle). Mr Taylor’s results also rest on so few observa- 
tions, as to entitle them to little weight. 
** Though it is obviously impracticable to deduce any elliptic ele- 
ments from such a series, there are some features which it is impos- 
sible not to recognise. There can be no doubt that the distance has 
gone on decreasing since 1822 at least ; and the comparison of the 
measures least open to objection, leads us to conclude, that, for the ten 
years previous to 1838, the rate of decrease was 7%, or a little more 
than half a second per annum, which, if continued, will bring on an 
occultation, or exceedingly close appulse, about the year 1867. The 
small amount of variation in the angle of position shews that the 
plane of orbitual motion passes nearly, but not quite through our 
system, while its actual tendency to increase exemplifies the general 
law of increase of angular velocity, with diminution of distance. 
Mr Fallowes’ distance is probably too great by 3” or 4”; but in the 
long interval between 1750 and 1822 (at the former of which epochs 
the distance must have been on the increase), there is room for a 
very much greater excursion of the small star towards its apparent 
aphelion, so that, although we are sure that the major axis of the 
real orbit must materially exceed 24”, it is impossible to say how 
much it may exceed that limit. Taking, therefore, the co-efficient 
of parallax for a@ Centauri, as determined by Professor Henderson, 
at 1”, it will follow from what has been said, that the real orbit of 
one star about the other cannot be so small as that of the orbit of 
Saturn about the sun, and exceeds, in all probability, that of the 
orbit of Uranus. 
‘The plane of the orbit in the case of @ Centauri, passing 
nearly through our system, my method of approximating to the 
elliptic elements becomes inapplicable, and for their determination, 
measures of the distance of the stars from each other can alone be 
relied on. No subject more worthy of continued and diligent in- 
quiry can possibly be urged on the attention of southern astrono- 
mers.”’ 
Thus the result arrived at, both by Professor Henderson and by 
Sir J. Herschel, and which, though proved since to be erroneous, 
would have been probably concluded by any one else from the same 
data, seems to be, that the smaller star had been employed during 
the last century in gaining its aphelion, without any sensible change 
of angle of position. What the aphelion distance, the diameter of the 
orbit, and the period of revolution, might be, no guess could be at- 
tempted: but in his address, on the occasion of giving the gold 
