402 FHILOSOPHICAL TRANSACTIONS. [aNNO 1753. 



to Mr. Dollond to write to him, showing him the mistake, and desiring to know 

 his reasons for that hypothesis ; and therefore I desire, that this letter of Mr. 

 Dollond's to me may be kept among the Society's papers, till Mr. Eiiler has had 

 a sufficient time to answer Mr. Dollond's letter to him. 



Letter II. From Mr. John Dollond to James Short, A. M., F. R. S. concerning 

 a Mistake in M, Eulers Theorejii for Correcting the Aberrations in the Object- 

 glasses of Refracting Telescopes. Dated March \ I, 1752. p. 289. 



The famous experiments of the prism, first tried by Sir Isaac Newton, suffi- 

 ciently convinced that great man, that the perfection of telescopes was impeded 

 by the different refrangibility of the rays of light, and not by the spherical figure 

 of the glasses, as the common notion had been till that time ; which put the 

 philosopher on grinding concave metals, in order to come at that by reflexion, 

 which he despaired of obtaining by refraction. For, that he was satisfied of the 

 impossibility of correcting the aberration by a multiplicity of refractions, appears 

 by his own words, in his treatise of Light and Colours, Book i. part 2, prop. 3. 

 " I found moreover, that when light goes out of air through several contiguous 

 mediums, as through water and glass, as often as by contrarj' refractions it is so 

 corrected, that it emerges in lines parallel to those in which it was incident, con- 

 tinues ever after to be white. But if the emergent rays be inclined to the inci- 

 dent, the whiteness of the emerging light will by degrees, in passing on from the 

 place of emergence, becomes tinged in its edges with colours." 



It is therefore somewhat strange, that any person should now attempt to do 

 that, which so long ago has been demonstrated impossible. But, as so great a 

 mathematician as Mr. Euler has lately published a theorem * for making object- 

 glasses, that should be free from the aberration arising from the different refran- 

 gibility of light, the subject deserves a particular consideration. I have there- 

 fore carefully examined every step of his algebraic reasoning, which I have found 

 strictly true in every part. But a certain hypothesis in p. 285 appears to be des- 

 titute of support either from reason or experiment, though it be there laid down 

 as the foundation of the whole fabric. This gentleman puts m : 1 for the ratio 

 of refraction out of air into glass of the mean refrangible rays, and m : 1 for that 

 of the least refrangible. Also for the ratio of refraction out of air into water of 

 the mean refrangible rays he puts nil, and for the least refrangible n : 1 . As 

 to the numbers, he makes m = 4-l, m = x^, and n = 4; which so far answer 

 well enough to experiments. But the difficulty consists in finding the value of n 

 in a true proportion to the rest. 



Here the author introduces the supposition above-mentioned ; which is, that 



• Vide Meraoires of the Royal Acad, of Berlin for the year 1747.— Orig. 



