Se Lalas 
TRANSACTIONS OF THE SECTIONS. 181 
gular lever 1s of such proportions, in respect to the length of its arme, that if the 
points O and N be conceived to be joined by the lineO QN, the distance PM is ex- 
actly double of P Q, because the aggregate pressure upon the two points O N requiring 
to be counterpoised by the pressure upon the single point M, the lever PM must ne- 
cessarily be twice the length of PQ. A simple inspection of this arrangement will 
suffice to show that the six portions of equal area are rigidly counterbalanced and in 
equilibrio,—and, extending it to the whole speculum, that it is equally supported in 
eighteen points. Theoretically, the speculum is supposed to be so supported, that if it 
were imagined to be really cut up into the eighteen portions marked out by the di- 
visions while resting upon the discs and levers, it would still retain its normal shape 
and figure. 
Fig. 1. 
| Ὶ 7 
ῃ Π] 
ἀμ 
Ι 7. 
! 
L 
Practically, I find that this mode of support prevents all sensible bending when 
the telescope is directed to the zenith or to very high altitudes, and when there 
is no change of temperature.- But when the temperature has altered considerably 
since the speculum was placed on its supporting levers, there is often indisputable 
evidence, on turning the telescope on a star, that some distortion of the mirror has 
taken place ; which is I believe thus to be explained. The levers being of iron, ex- 
pand and contract by variations of temperature, differently from the speculum, and 
therefore the equal expansions and contractions of the speculum are controlled and 
disturbed by the incommensurate ones of the iron bars; which, from the amount of 
cohesion or stickage between the points of support and the back of the speculum, 
sensibly distort the figure. This defect I have in some measure removed by making 
the discs of support as smooth as possible, so that the speculum may slide upon 
them with the utmost practicable ease. With a view to remove entirely this cause 
of distortion, I now propose to make the supporting levers of the metallic alloy de- 
scribed by Lord Rosse in Phil. Trans. 1840, Part II., which has (sensibly) the same 
expansion as speculum tmetal. ἔ : 
.- Another cause of distortion, however, perhaps more difficult to remove, exists in the 
change of bearing which the speculum necessarily takes when directed to various alti-\., 
tudes—the more so when the altitudes are low. In the latter case, it is evident that 
the method of equal support at high altitudes almost totally fails : the speculum then 
only depends for its uniformity of figure upon the greater stiffness that it necessarily 
possesses when resting upon its edge. Such, however, is the perfection of figure 
required, that-in this position of the mirror there is generally some indication of a 
change of form in a greater or less degree, and I have hitherto endeavoured to remedy 
it by supporting the speculum in a thin semicircular iron hoop, secured at the ends 
of a horizontal diameter, which, supporting its edge in the greatest possible number 
