of 500 new Nebula, and Clusters of Stars. 481 
distance behind another, and but very little deviating from the 
line in which we see the first, we should then have the ap- 
pearance of a double star. But these stars, being totally uncon- 
nected, would not form a binary system. If, on the contrary, 
two stars should really be situated very near each other, and at 
the same time so far insulated as not to be materially affected 
by the attractions of neighbouring stars, they will then compose 
a separate system, and remain united by the bond of their own 
mutual gravitation towards each other. This should be called a 
real double star ; and any two stars that are thus mutually 
connected, form the binary sidereal system which we are now 
to consider. 
It is easy to prove, from the doctrine of gravitation, that two 
stars may be so connected together as to perform circles, or 
similar ellipses, round their common centre of gravity. In this 
case, they will always move in directions opposite and parallel 
to each other ; and their system, if not destroyed by some foreign 
cause, will remain permanent. 
Figure 1 (Plate XVI.) represents two equal stars a and b , 
moving in one common circular orbit round the centre 0, but 
in the opposite directions of at and bt. In Fig. 2 we have a 
similar connection of the two stars a b; but, as they are of dif- 
ferent magnitudes, or contain unequal quantities of matter, they 
will move in circular orbits of different dimensions round their 
common centre of gravity 0. Fig. 3 represents equal, and Fig. 4 
unequal stars, moving in similar elliptical orbits round a com- 
mon centre ; and, in all these cases, the directions of the tangents 
t t, in the places a b , where the stars are, will be opposite and 
parallel, as will be more fully explained hereafter. 
These four orbits, simple as they are, open an extensive field 
