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I. The Figure of a Machine for grinding 
Lenfes fpherically , invented by Mr. Samuel 
Jenkins, and communicated by him to the 
Hon ble Sir Hans Sloane, Baf Tr. R. S. &c. 
SIR , 
T H E Advantage it would be to have Lenfes 
of the fpherical Kind, Segments of a true 
Sphere, hath occafioned the Invention of 
many Machines and Methods of Grinding, in order 
to produce fuch Segments : But nothing hitherto 
made public hath anfwered the End propofed. 
The beft Methods now in Ufe will only produce 
an Approximation to a truly fpherical Figure, but 
demonftrably not one, though the Artificer fhould 
employ the utmoft Skill and Care in the Ufe of the 
beft Machines hitherto invented : And indeed, at 
prefent, Gentlemen have nothing to depend on, that 
their Lenfes are nearly fpherical, but the Care and 
Integrity of the Workmen; in which how often they 
are deceived, is too obvious to every one who hath 
Occalion to ufe fuch Lenfes. 
I therefore beg Leave to fubmit to your Confidera- 
tion the EfFe&s of a Machine, of which the inclofed 
is a Reprefentation [Tab.I. Fig. i.] ; which, as it is 
contrived to turn a Sphere at one and the fame time 
on Two Axifes which cut each other at Right Angles, 
with equal Velocity and Preflure on each of them, 
I .conceive it is demonftrable, that (without any Skill 
or Care in the Workman) it will produce a Seg- 
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