124 Transactions. 
the concave one, and thus by simply turning the plane reflector on its axis we 
are saved the cumbrous alternative of moving the whole tubular length of the 
telescope in order that it may point to the object to be observed. In large 
instruments this must be a very important desideratum. Let us suppose a 
telescope twenty feet in diameter : ordinarily this would require tubing at 
least 120 feet in length, and provision would be required for its sweeping 
through 300 feet of motion ; whereas with the horizontal speculum, a circular 
building thirty feet in diameter and about sixty feet high would furnish 
ample space, and also allow the observer, without changing his position, to 
work entirely under shelter. ; 
In such an instrument the friction is reduced to a minimum by perfecting 
the bearing of a single axis, consequently little power is required for continu- 
ing its rotation. 
I may remark that I have used, with good effect, the regular flow of water 
through a small turbine, in order to impart to the speculum an equal angular 
velocity. By merely altering the velocity we are enabled to shorten or 
lengthen the telescope, and in a few seconds the mercury attains its equilibrium, 
and not only the parts near the vertex are parabolic, but those also which 
extend to the parameter, and to any distance we like to go above, leaving out 
of consideration a very slight deviation caused by the earth’s sphericity, which 
would impart a slight tendency to the hyperbolic curve, but which, even in 
immense instruments, would be so minute as to be within the power of ` 
correction by the eye-piece of the telescope. 
It also follows that the focus can be observed by looking upwards, if the 
vertex of the curve be removed, and those parts only used which are above its 
parameter. 
As it is of immense importance that we should be able to concentrate a 
large beam of light for examination of the distant nebulz, and especially for 
Spectroscopic investigations, it is not improbable that the use of such an 
instrument, constructed on a large scale, would extend our knowledge of the 
natural heavens, for notwithstanding all the discoveries made in the great 
cosmic problems of creation, still, that we may be enabled to travel further 
` into what is as yet the dark profound, and to gaze with bodily eye on what 
now form the manifold mysteries of the universe, must be the ardent wish of 
every lover of science. : 
Nore.—That the above expressions are the dynamical measures of gravity 
and centrifugal force is thus shown :— 
In circular motion the centripetal and centrifugal forces are everywhere 
equal. Let the are AB be described in one second ; draw BE perpendicular to 
AS ; then in one second the body originally at A will have fallen from its 
wonted straight path, AM, a distance = AE towards the attractive force at- 
