282 Scientific Proceedinys, Royal Dublin Society. 
the secondary axis drawn from that point. Thus, if A is the 
point in the object, the image of that point will be found some- 
where or other along the line AA (fig. 1). If a is the point, 
its image will be found somewhere along aa (fig. 1). 
& 
Jee, Ie 
Keeping these two principles in view we may proceed. 
Since we always see an object where the rays proceeding from 
that object meet, or seem to meet, and since they always meet 
(approximately), or seem to meet, at some point on the secondary 
axis, evidently the all-important point is to find where they meet 
the secondary axis. 
Now this is found very simply, for if we can show where any 
one ray cuts the secondary axis, all others must cut itat the same 
place. Nowit so happens that it is a matter of extreme simplicity 
to show where a ray drawn from the object parallel to the 
principal axis must cut the secondary axis from that point. And 
this is the great fundamental principle to be attended to in the 
construction of the instrument. 
The secondary axis from any point passes as a straight line 
through the centre of the lens. Consequently we have one point 
(viz. the centre of the lens) in this line always fixed, and so this 
point acts like the centre ofa circle round which the line revolves. 
It may therefore be aptly represented by a pivot and a line 
revolving round it. This may indicate all the positions that the 
secondary axis can occupy, no matter where the object may be. 
We can therefore easily find the various positions of one of the 
lines. | 
Now for the position of the other line, viz. the line proceeding 
from the same point in the object, and drawn parallel to the 
