TELESCOPE. 



was now u-nclianged, as was expefted, the compound rays 

 had not all ti.e fame divergence. The fhape of the wedges 

 was then modified, fo that the colours difappcai-cd by a due 

 oppoCtion of their refpeftive difperilons ; and when this was 

 effeiited, the refraftive powers of the two wedges were 

 four.d nearly 2:3; and, confequently, the fines of half 

 their angles, 19 : 33 ; which ratio is nearly 4 : 7. In this 

 fjtuation of the wedges, the rays which enter parallel emerge 

 alfo parallel, while they are equally deflefted from the points 

 of emergence. Thefe refults may be obtained very (Irikiiigly 

 by d.n union of four wedges, or pair of compound wedges, 

 as reprefented in Jig. 4, where tlie crown receives the rays 

 firft, and where the rays, at equal diftances from the central 

 line of union, meet always at the fame point. This, (here- 

 fcre, pointed out the conftruftion of a double objciil-glafs, 

 fuch as is reprefented in Jig. 5, in which the convex curve 

 of the crown-glafs is to the concave curve of the flint of 

 given qualities nearly as 7 : 4, or nearly in the ratio of their 

 refpeftive difperfive powers. But to avoid the too great 

 cffeft of fpherical aberration, arifing from the quick curves, 

 the fingle convex lens of crown-glafs was made into a double 

 convex, with double the radius of convexity ; and alfo the 

 fingle concave might be made double, with a fimilar increafe 

 in its radius of concavity, to anfwer the fame purpofe as the 

 combination laft defcribed. But, in this cafe, the con- 

 vexity of one glafs would not fit the concavity of the other, 

 fo as to come nearly in contadf throughout : it appeared ne- 

 cefTary, therefore, that while the internal faces fitted each 

 other, the external concavity of the flint-glafs Ihould be 

 eight times lefs, or of longer radius than before propofed, 

 in order to maintain the balance of oppofite difperfions ; or 

 otherwife, as in Jig. 6, if the double concave faces of flint- 

 glafs remain as above ftated, the front convexity of the 

 crown-glafs muft be five-fevenths of the due curvature, as 

 propofed above ; while the inner furface remains in perfeft 

 contaft with the concavity of the other. In thefe com- 

 binations, the fuperior refraftion of the convex lens, being 

 diminiflied one-third part by the oppofing refraftive power 

 of the concave lens, required this convex to be ground and 

 poliflied to a focus three times fliorter than would be required 

 for the fame lens ufed fingly ; and the option, that is af- 

 forded the artift:, of varying the curves at pleafure, provided 

 the combined effedf of the compound lens fliall produce a 

 proper effeft in banifliing the colours, admits of a modifica- 

 tion that will correft the fpherical aberration alfo, in a great 

 meafure. Telefcopes on this achromatic principle were firft 

 conftrufled in the year 1758, and when their merit was 

 once acknowledged, the great number that the inventor and 

 his fucceffors have had occafion to make, both for fale 

 among their cuftomers, and for exportation, have afforded 

 them the eafy means of trying a variety of concave and con- 

 vex glaffes together in fuccelTion, before they were finally 

 paired ; fo tliat their fuccefs not only originated in, but has 

 been continued by, the aid of experiments, which no one 

 but the Dollonds has had the power of executing to fo great 

 an extent. See Dollond. 



Nor was J. DoUond's fuccefs confined to the manipula- 

 tion of objedl -glaffes alone ; he had previoutly contrived and 

 conftrudfed the improved fyftem of eye-glaffes, in which 

 object he was followed by his fon-in-law, Ramfden. 



This improvement confifted in extending the ufual number 

 of eye-glaffes to five, fo fyftematically arranged, that by 

 dividing the errors of fpherical aberration, they reduced 

 their amount to an inconfiderable quantity. 



The value of this arrangement will be befl underftood 

 from his own words, which we will extraft from his 

 letter, publifhed in the Pliilofophical Tranfaftions of the 



year 1753. " If any one," fays he, " would have the 

 vifual angle of a tclefcope to contain 20 degrees, the ex- 

 treme pencils of the field muft be bent or refradcd in an 

 angle of 10 degrees; which, if it be performed by one eyc- 

 glafs, will caufe an aberration from the figure in propor- 

 tion to the cube of that angle; but if two glaffes are fo 

 proportioned and fituated, as that liie refraaion may be 

 equ.illy divided between tlicm, they will each of them pro- 

 duce a refradion equal to half tlie required angle; and, 

 therefore, the aberration being in proportion to the cube 

 of half tile angle taken twice over, will be but a fourth 

 part of that, which is in proportion to the cube of the 

 whole angle ; bccaufo twice the cube of one, is but one-fourth 

 the cube of two ; fo the aberration from the figure, where 

 two eye-glaffes are rightly proportioned, is but a fourth of 

 what mull unavoidably be, where the whole is performed 

 by a fingle eye-glafs. By the fame way of reafoning, when 

 tlie refraiSion is divided between three glaflcs, the aberration 

 will be found to be but the ninth part of what would be 

 produced from a fingle glafs ; becaufe three times the cube 

 of one, is but one-ninth the cube of three. Whence it 

 appears, that by increafing the number of eye-glaffes, the 

 indifKnftnefs which is obferved near the borders of the field 

 of a telefcope, may be very much diminithed, though not 

 entirely taken away." 



We have given this quotation at full length to fhew, that 

 in liis adoption of feveral glaffes in an eye-piece, the inge- 

 nious mechanic was not entirely indebted to his experiments, 

 unafTifled by reafoning and mathematical inferences, and 

 accordingly the Royal Society rewarded his fkilful labours 

 with Copley's medal. John Dollond was fucceeded in his 

 bufinefs by his no lefs ingenious and induftrious fon, Peter 

 Dollond, who improved the achromatic objeft-glafs IHII 

 further, by placing a double concave flint-glafs between two 

 convex ones of crown-glafs, as in ^g. 7. and by enlarging 

 the aperture to 31^ inches in a 45-inch telefcope ; of thefe, 

 a great number has been manufaftured, and feveral of five- 

 feet focal length. His calculations of the radii of convexity 

 and of concavity were never pubhcly made known ; and 

 perhaps conftituted a fecret, on which the continuance of 

 his celebrity depended, when the time of his father's patent 

 had expired. The bufinefs is now fuccefsfuUy condufted 

 by G. Dollond, the nephew, to whom we are indebted for 

 much liberal information ; but at no period had any of the 

 Dollonds an agent in Paris, as is faid in the new Supple- 

 ment to the Encyc. Britannica. For feveral years from the 

 time of the eldeff Dollond's death, the foreign TranfaAions 

 were crowded with differtations and memoirs on the combi- 

 nations of achromatic lenfes mathematically determined, and 

 tlie fubjeft afforded ample fcope for the geometrical and 

 analytical refearches of an Euler, a Clairaut, and a D'Alem- 

 bert, as well as for Bofcovich, Klingenflierna, Ksftner, 

 and Hennert : but in this, as in fome other fpeculative in- 

 vefligations, the labours of the profound mathematician 

 have not much benefited the practical advancement of the 

 art to which thefe labours have been direded ; nay, they 

 have tended to keep at a diflance from each other the mathe- 

 matician and the mechanic. 



Bofcovich's eye-piece, however, may be confidered as 

 conflituting an exception to the preceding remark, and de- 

 ferves here to be particularly noticed. According to one 

 of his theorems, an eye-piece free from colours may be 

 compofed of two fimilar lenfes of the faine glafs, provided 

 they be placed from each other juft one-half of the fum of 

 their focal diftances ; which is very fimilar to the eye-glafs 

 now commonly adopted, in preference to a fingle lens, ia 

 the common allronoinical rcfrafting telefcope, the only dif- 



fcrcnce 



