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accurate purposes, is that the eye cannot he adapted to distinct 
vision for three different distances at the same time. We cannot 
see the notch, the vise, and the object aimed at, all distinctly. 
The invention of the telescope effected a complete change in the 
apparatus for the precise measurement of angles. By it the arrange- 
ment of the plain-sight was reversed ; the eye-hole was expanded to 
admit the object-glass, and the image was received at the plane of 
the cross-wires. 
These two are the only improvements which have hitherto been 
made in the art of pointing. Hadley’s quadrant, the invention of 
which has almost created nautical astronomy, is a contrivance for 
indicating the difference between the directions of two objects ; it 
does not show the direction of either. 
The pointer used in the catadioptric theodolite is thus the third 
of its class ; it contains, literally within the compass of a nut-sliell, 
the means of determining the direction of an object true to within 
half a minute of a degree. 
About the years 1815, 1816, the late Rev. Edward Irving gave 
to his class of young geometers as an exercise, “To construct 
graduated squares with plummets attached, by help of which the 
tangents of angles of elevation may be observed.” Some of us used 
pasteboard, some wood ; and it happened that, having broken my 
school slate, which was a thick one, the idea came into my head to 
make my square out of the larger fragment. Armed with these 
little instruments, we attacked and carried most of the surrounding 
heights. The weather-cock on the top of the church steeple was, as 
a matter of course, one of our targets. On bringing the upper edge 
of my slate-square to bear upon it, that upper edge having been 
ground flat and pretty well smoothed, I saw the inverted image of 
the weather-cock. It then occurred to me that, if I could bring the 
image to agree with the weather-cock itself, the plane of the upper 
edge would be accurately pointed. At the same time it was obvious 
that when the plane passed through the object there could be no 
reflection. 
Here, then, was a problem “ To obtain a reflection such that the 
reflected can be collated with the direct image, and afford a test of 
accurate pointing.” The pointer used in the catadioptric theodolite 
exhibits a complete solution of this problem. It is a piece of glass cut 
in the form of an isosceles tetrahedron, of which two faces form an 
