VOL, L.] PHILOSOPHICAL TRANSACTIONS. 2^7 



cording to the number of teeth in the pinion. The number of teeth in the 

 great wheel moved by the lever is 66 ; but need not have teeth above half way 

 round. The wheel fixed to the rochet has 33 teeth, and its pinion 11. The 

 wheel fixed on the arbor on the outside, has 24 teeth, and its pinion l6. The 

 wheel which turns the fly has go teeth, and the pinion turned by this wheel 10. 

 The greater the number of teeth in the rochets, the better. This machine 

 may also be applied to other useful purposes at mines ; and it may be easily made 

 to turn a mill to grind corn ; or to turn a wheel to raise coals, or whatever else 

 is wanted to be raised from the mines. 



XCF^III. Of some Experiments concerning the Different Refrangibility oj 

 Light. By Mr. John Dollond. With a Letter from James Short, M. A., 

 F.R.S. p. 733. 



Mr. Short's introductory letter is as follows : 



I have received the inclosed paper from Mr. Dollond, which he desires may 

 be laid before the Royal Society. It contains the theory of correcting the errors 

 arising from the different refrangibility of the rays of light in the object-glasses 

 of refracting telescopes ; and I have found on examination, that telescopes made 

 according to this theory are entirely free from colours, and are as distinct as re- 

 flecting telescopes. The following by Mr. Dollond : 



It is well known, that a ray of light, refracted by passing through mediums of 

 different densities, is at the same time proportionally divided or spread into a 

 number of parts, commonly called homogeneal rays, each of a different colour ; 

 and that these after refraction, proceed diverging : a proof that they are diffe- 

 rently refracted, and that light consists of parts that differ in. degrees of refran- 

 gibility. Every ray of light passing from a rarer into a denser medium, is re- 

 fracted towards the perpendicular ; but from a denser into a rarer one, from the 

 perpendicular ; and the sines of the angles of incidence and refraction are in a 

 given ratio. But light consisting of parts which are differently refrangible, each 

 part of an original or compound ray has a ratio peculiar to itself; and therefore 

 the more a heterogene ray is refracted, the more win the colours diverge, since 

 the ratios of the sines of the homogene rays are constant ; and equal refractions 

 produce equal divergencies. That this is the case when light is refracted by one 

 given medium only, as suppose any particular sort of glass, is out of all dispute, 

 being indeed self-evident ; but that the divergency of the colours will be the same 

 under equal refractions, whatever mediums the light may be refracted by, though 

 generally supposed, does not appear quite so clearly. 



However, as no medium is known which will refract light without diverging 

 the colours, and as difference of refrangibility seems thence to be a property in-^ 

 herent in light itself, opticians have on that consideration, con(;luded, that equal 



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