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 the one most likely to occur, is that in which the radiant point is at the opposite point of the sphere from the centre of the mirror.

It will occur to every one, that of the two foci $∆=2r$ and $∆′=∆r⁄2∆−r=2⁄3r$, that which lies between $Q$ and $q$ moves much more slowly than the other, when their places are changed; in fact, we have seen that by merely bringing up $E$ from $A$ to $Q$, $E$ was sent from $F$ to an infinite distance, and that when $q$ moved on from $E$ towards $Q$, $F$ came back from an infinite distance on the reverse side of the reflector to meet $A$ at $q$.

13. We have hitherto considered only one species of spherical reflector, the concave; let us now take the convex, (Fig. 11.) where as before, $Q$ is the centre, $A$ the radiant point, $E$, $Q$ an incident and a reflected ray, making equal angles with $QR$ the radius or normal. Let $RS$ cut $ER$ in $SR$.

Then we have, keeping the same notation as before,

which is the same result as before, except the sign of the 2d term; it will however immediately occur that they may be reconciled completely by supposing the radius $AE$ to be positive in the one case, and negative in the other, which is exactly true in algebraical