ARE THERE ANY FIXED STARS? 
361 
For let E be the earth, Sj the position of a star at the begin- 
ning of a century, its position at the end of a century, the 
star being one of those which is moving at right angles to the 
line of sight. And let us suppose that the star is also one of 
those which is moving most rapidly in appearance, so that the 
angle 5 ^e which measures the proper motion in a century is as 
large as possible. Then we cannot assume with any probability 
that any star in the heavens has a greater proportional motion of 
recess or of approach than the motion indicated by or S 1 S 4 
(each equal to s^s^). That is, the ratio of ESg or to es indi- 
cates the greatest relative change of distance we may look for 
among the stars during the course of a century. 
But we can calculate the value of this ratio at once, and so 
see at once what chance there is that a change in a starts bril- 
liancy caused by such a change of distance could be estimated 
by means of our photometers. 
There is no star in the heavens which has so large a proper 
motion as ten seconds of arc per annum. Therefore in taking 
the angle s^ESg at 1,000 seconds or 16' 40", we are taking a very 
favourable view of our prospect of estimating change of distance 
by change of brilliancy. If SjES 2 be an angle of 16' 40", then 
SjSg is "equal to *004848 where ES^ is called 1 . Put for con- 
venience Sj §3 or S 1 S 4 as equal to *005. Then the brilliancy of 
the star at the beginning of the century would bear to its 
brilliancy at the end (supposing there has been in the mean- 
time no change in the actual amount of light emitted by the 
star) the ratio 
fhoooy .. /i,^oy 
k 995 J U,005V 
according as the star had approached or receded from the earth 
with the assumed (and altogether over-estimated) velocity re- 
ferred to. These ratios reduce severally to 
101 
100 
and 
99 
100 
In other words, the star’s brilliancy would only be increased 
or diminished by about one hundredth part in one hundred years 
even in this altogether exceptional case. 
No instrument ever yet devised by man could give any indi- 
cations of so slight a change of brilliancy as this, even if it 
occurred in a single instant, so that one and the same observer 
could measure the star’s light under unchanged atmospherical 
conditions. 
We see, then, that the problem of attempting to measure the 
motions of recess or approach which the stars may have is one 
