Mr. Herschel on the parallax of the fixed stars. 267 
must occasion a periodical change in the angle of position, as 
well as in the distance of the two stars composing a double 
star, and that this variation is much more susceptible of ready 
and exact appreciation with our present micrometers than 
that of their distance. To render this sensible, we need only 
remark, that the effect of parallax is to cause each star to 
describe (apparently) a small ellipse in the heavens, the major 
axis of which is parallel to the ecliptic, and the minor in the 
direction of a secondary to that great circle, the true place 
of the stars being in the centre. Were these ellipses of the 
same magnitude, for each of two contiguous stars, the line 
joining their apparent places (which are necessarily homolo- 
gous points in the circumferences of each) would preserve its 
parallelism at all times ; but as the axes of the ellipses are 
reciprocally as the distances of the stars, that parallelism 
cannot obtain when the stars are situated at very unequal 
distances from the earth, and an alternate increase and de- 
crease of the angle of position made by this line with any 
fixed direction must be the necessary consequence. 
To estimate the extent of this variation, let us conceive two 
stars so situated as to have their apparent line of junction 
in the direction of a secondary to the ecliptic, and therefore 
at right angles to the major axes of their parallactic ellipses— 
let their distances from us be such that the nearer one shall 
have a parallax of 1", and the farther no appreciable amount 
of it. Also, let their apparent angular distance from each 
other be 5". It is evident that the variation alluded to will 
equal the angle subtended by a line of 1" in length, at a 
point 5" distant from its middle, that is, to 11 0 25'. 
Now this is a quantity which is quite beyond all conceivable 
limits of error of observation in the measurement of double 
