FIRST ORDINARY MEETING. UT 
tion, and that the figure also gives the relation /\ /\’= /? sec? a, 
where /\’ = P’G. 
In the case of a convex mirror X and Y will lie in the opposite 
quadrant and the longitudinal aberration will be found to be 
2 ( bee il 
Baa) 
TEE. 
28. Since writing the above it has occurred to me that the relation 
dd’ = ff’ leads to two other simple geometrical methods for exhibit- 
ing the relations between the conjugate points. 
Thus if we separate the two axes FF’, FF’ so that F in the z axis 
coincides with F” in the y axis, as in Fig. 14, then evidently the feet 
of the ordinates drawn from any point on the hyperbola ry —/f/' 
will be conjugate to one another. This construction gives us a 
readier means of finding many of the points whose positions have 
already been discussed. 
Thus self-conjugate points are at once given by 
xe (2h —2)=—ff"; 
and the points K, K’ (§ 15) by 
Again, H being the middle point of FF’, if H is the image of G, 
and J of H, we have 
RS =f —= JFK — EG, 
29. From the construction of the preceding section it appears that 
the lines joining pairs of conjugate points on the two axes touch the 
hyperbola 
day = ff’. 
Fig. 14 shows that the conjugate points V, V’ are equidistant 
from H, the middle point of FF’, and that 
ye Ve pe 
Prof. Galbraith, Mr. Wm. Houston, and Mr. A. Baker took 
part in the discussion which followed, 
2 
