66 GrupBp—On a New Form of Equatorial Telescope. 
of a perfect plane; and, in fact, the skill of such might be estimated by the size of 
the plane surface which he could produce. For this reason, and keeping in view 
the fact that no perfect plane of a large size has ever yet been made, I have 
hesitated to recommend this form of instrument for large sizes until the idea 
occurred to me of reducing the necessary dimensions of the plane by the combina- 
tion of the dialyte telescope and siderostatic mounting, as described above. ‘The 
French, however, seem to have no such fears, for not only have they a mirror 
inside the tube, but another outside the objective, and the full size of same. A 
little reflection will show that, assuming any given degree of skill of the optician, 
the difficulties of construction of the French form are, at least, nine times that of 
the form above described ; or, putting it in another way, assuming a given degree 
of accuracy of the optician, the residual error and its effect on the image will be, 
at least, nine times as great; for it must be acknowledged, I think, that the diffi- 
culties of producing an accurate plane surface vary, at least, as the area, 7.e., as the 
square of the aperture. (Probably nearer to the cube.) Therefore the difficul- 
ties in making the mirror outside the objective are four times that of the mirror 
inside, as it is about double the diameter: and again, as the rays have twice as far 
to travel from this to the focus as from the small mirror, the effect of any error 
will be again doubled, so that the difficulties of making the large mirror will be 
eight times that of the smaller, or, any given error will have eight times the effect 
on the image. Now the above form has only the inside mirror and none outside. 
So the effect of any given amount of error will be as 9 to 1. 
This is what I meant when I said in an early part of the Paper that I believed 
enormous sacrifices have been made in the attempt to combine universality and 
precision in the French instrument. Again, it is clearly for very large instru- 
ments, in which the labour of working is great, that this form would be pre-emi- 
nently useful. In reading M. Loewy’s Paper I imagined that the French instrument 
must have been of some great size, for speaking of working such telescopes he says :— 
‘“‘The rotatory movement of the earth changes at every instant the apparent 
position of the star which one observes. There follows from this a. corresponding 
change of place for the observer: not a simple movement of his chair to right or 
left, but a further change of place in height. It is necessary, indeed, to elevate or 
depress his seat, according to the case. Further, since the telescope is enclosed 
under a dome which shelters it, and in which is provided a large slit from summit 
to base, in order to make observations possible, it is necessary to move this opening 
or slit, in front of the telescope. The dome can in reality turn upon itself The 
observation then necessitates the movement of the telescope, that of the observer, 
and that of the dome, not to speak of the principal movements. If one adds to 
this that the observer is obliged to seat himself or to stretch himself in a horizontal 
position, sometimes in a most inconvenient manner, one understands that it may be 
truly laborious. 
