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AC — AS, == Ai BS, ER 
ie. A and B lie on different branches of the hyperbola having C 
and S, for foci. This hyperbola is therefore a light path, but not 
one from A to B; neither is this the case with the two hyperbolas 
that have a focus in one of the points of intersection of the circles 
AA’ and BB". 
The two circles AA" and BB" can bave imaginary points of 
intersection; but it is also possible that these points of intersection 
are real. If on the latter supposition S, is such a point, we have 
AC— AS, = 4u = BC — BS,, 
i.e. A and B lie on that branch of the hyperbola having C and S, 
for foci, that is not curved ‘towards the sun, hence just on that 
branch that is not a light path. 
If however S, and S, are the points of intersection of the circles 
AA’ and BB’, C and S, as well as C and S, are the foci of a 
hyperbola of which the same branch, the branch curved towards C, 
passes through A and B. 
Of the 8 hyperbolas through A and B which have C for a focus 
and of which the semi major axis is equal to Zu, there are only two 
that gwe a possible light path; indeed, both are light paths, if only 
the branch on which A and B le, does not intersect the sun. 
Here the question arises: 
Let B be a point of the path of the earth and C the centre of 
the sun; can we place 4 in such a way that B is reached by 2 
rays of light from A? 
We call S, that point of intersection of the circles AA’ and BB’ 
that lies on the same side of AB as C; we put » A’SB =d. It 
is clear that now CS, is less than CP, if P is the point of inter- 
section of the tangents at A’ and B’ to y; hence 
CS, << 4u cotg 4 d. 
The point S, lies therefore inside the sun (as 2u— +3) and the 
hyperbola with C and S, for foci will not be a light path con- 
necting A and B, unless perhaps if d is very small. 
We shall therefore assume, in order to give CS, as great a value 
as possible, that A lies on the production of BC at infinite distance. 
We find 
| CS, < B'S, = V 8u x 2BB' — + 6 x 10* km, 
so that even now SS, lies inside the sun. Ee in It is wm- 
possible to see a point imm 2 different directions out of a point of the 
path of the earth. 
