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the preceding to answer in practice. It gives a circular motion to the tool, 
while the part carrying the glass has an eccentric motion, or towrnotement, 
and also another motion in consequence of its being loose in the circle 
which carries it. The description is accompanied by a report of Cassini, 
de Mairan, and de la Chevaleraye, who say that they have examined the 
glasses produced by this machine, and that several of them seem to be 
good. 
I find also in a catalogue of works on this subject, the title of a 
‘ Description of a new invented and very convenient machine for grinding 
optical glasses,” this is in the Berlin Journal for the Diffusion of Infor- 
mation, tom. 1V. p. 92. 
With respect to parabolic, elliptic, and hyperbolic figures, we find 
also very early pretences to the art of grinding them. In 1668, Smethwick 
in England, and De Sons at Paris, claimed the possession of the means 
of doing this. In the Philosophical Transactions for Nov. 1669, is a 
method, given by Sir Christopher Wren, for grinding hyperbolic glasses ; 
which is theoretically a most elegant application of a theorem of solid 
geometry, discovered by that great mathematician, though practically it 
would probably not succeed, being exposed to the same objection which 
we have already mentioned as applicable to Hooke’s. In 1726, in the 
Miscellanea Berolinensia, (tom. Ill.) we find Hertel’s method of grinding 
parabolas, ellipses, and hyperbolas, which consists only in making the 
glass or mirror revolve upon its axis, while it is cut by means of a tool 
directed by a gage to the proper form. This it is obvious could never 
produce a figure free from annular inequalities. 
In 1777, a valuable paper of Mr. Mudge, on grinding specula, appears 
in the Philosophical Transactions, in which however no machinery, pro- 
perly speaking, is used. He there gives a method of producing a parabolic, 
