PROCEEDINGS OF SECTION A. 367 
and supported upon two bearings. For its proper performance it 
is necessary that the axis be placed horizontal and truly east and 
west, that the line of collimation of the telescope be exactly at 
right angles to the axis, and that the circle give a definite and 
known reading when the line of collimation is horizontal. That 
these conditions may be always complied with, it is desirable that 
all parts of the instrument be rigid, or, in other words, remain 
invariable in form. Now, a rigid substance, though often 
postulated by lecturers on physics, does not exist innature. All 
known solid materials are more or less elastic, and change their 
form to a greater orlessextent. Thus the telescope of the transit 
instrument may be straight when vertical, but when placed in a 
horizontal position the ends will droop, and this effect will take 
place, though to a less degree, in positions intermediate to the 
horizontal and vertical. Similarly, the axis will droop, but its 
flexure will be the same, provided the material is homogeneous in 
all positions of the telescope. 
Now, did both ends of the telescope and axis bend equally, no 
harm would be done, as the effect of flexure would simply 
move the line of collimation to a position parallel to and a 
minute distance from that which it would occupy were there no 
flexure. Unfortunately, however, this equality or symmetry of 
flexure does not appear to exist; hence, errors arise, and the 
performance of the instrument is impaired. 
In all transit instruments known to us, the telescope tube is 
of circular section, consisting of two slightly conical portions 
united by a central cube, or sphere, and the axis consists of two 
other conical parts. Now, this section is suitable for a beam 
exposed to bending moments equally in the direction of all its 
diameters, but is totally unsuitable to the case in point, in which 
the bending moment is all in one plane, that in which gravity 
acts. What would be thought of an engineer who employed a 
circular tube as a girder for a bridge? Why, he would be an 
object of ridicule to the whole profession. The transit telescope, 
equally with the bridge-girder, is a beam always flexed in the 
same plane, and, in the interests of both strength and rigidity, 
should be made so that its cross section has as large a moment of 
inertia as possible about its central axis. In this respect iy 
differs essentially from the telescope of an equatorial, upon which 
gravity may act in any plane. The section, then, of a transit 
telescope should be rectangular instead of circular, and the bulk 
of the material should be concentrated in the top and bottom, 
the sides being as thin as practical considerations permit. The 
best depth of the beam or tube cannot, I think, be determined by 
the methods of maxima and minima, but will be as great as 
practical conditions allow, as the flexure of a beam made as 
described varies inversely as the depth. In side elevation the 
tube will have the form of a lozenge, the greatest depth being at 
