a Art. 350. without changing the eye-glafs, the brightness would be increased too, greater ; 357. But one may ask this question, fince by fubftituting an eye-glass of a longer focal diftance, the apparent indiftinctness hitherto examined is diminished, why may not the aperture of the object-glass be so far increased, till the fame degree of indiftinctness returns again as belongs to a telescope regulated by the table? For from hence more light is gained and the diftinctness is not altered. The answer is this, which I hinted b Art. 351. before, that the mist arifing from Newton's aberration, though the fame in quantity, becomes more fenfible in proportion to the brightness of the image. For the brightnefs of the mift increases at the fame time. And we find by experience, that as foon as the apertures of those day-light telefcopes are increased, the mift arifing from the aberrations of a brighter object begins to be troublesome. The apertures therefore must not be al tered. 358. Again one may ask, if a telescope fitted for Saturn be applyed to the Moon, which is 100 times brighter (I mean in each equal parts, though not in the whole, as being 10 times nearer to the Sun ;) one may aik I fay whether the breadth of the aperture and the focal distance of the eyeglass may not both be leffened in the fame proportion, to make the regions of the moon no brighter than thofe of faturn, but much greater in appearance than before. For instance, in a 30 foot telescope, if 3 inches, the breadth of the aperture be reduced to 2 of an inch, which is fomewhat less than (or) a third part of the former, and also the focal diftance of the eye-glafs be fhortened in the fame proportion; the proportion of the apparent brightness in these two telescopes, the object being Art. 350. the fame, would be quadruplicate of 3 toy that is as 100 to 1; and fince the regions in the noon are 100 times brighter in themselves than thofe in faturn, the moon would appear in the darker telescope just as bright as faturn did in the lighter. But the apparent indiftinctnefs hitherto confidered would alfo be the fame in both, and the amplification of the moon would be greater than that of faturn in the ratio of 3 to V., which is more than triple. So that this reduction of the aperture and eyeglafs feems very advantageous; but in reality it is quite otherwife; and that for two reasons. First because the minute parts of the moon may be better difcerned when all the light remains in the telescope, than when it is reduced to an 100th part, though not in the fame proportion. The other reason is that when the aperture is too much contracted, the out-lines that circumfcribe the pictures in the eye become confused; which is carefully to be minded, and also what are the limits of this confufion. This is certain that as the aperture is contracted, the flender pencils or cylinders of rays, that emerge from the eye-glafs into the eye, are also contract a Art. 350. c Art. 120. ed ठ ed in the fame proportion. Now if the breadth of one of these pencils be lefs than or of a line, that is lefs than or part of an inch, the out-lines of the pictures are spoiled, for fome unknown reafon in the make of the eye, whether in the choroid, or in the retina, or in the humors it is uncertain. For by looking through an hole, in a thin plate, narrower than or of a line, the edges of objects begin to appear confufed and fo much the more as the hole is made narrower. Now it is eafy to fhew in the last mentioned telescope that the cylinder of rays is too flender. For by adding of the aperture to it felf, the focal diftance of the eye- a Art. 355glafs becomes 2+, that is of an inch; and by fimilar triangles fubtended at the common focus q by the aperture and cylinder fought, it is as the focal distance of the object-glass, to the focal diftance b Fig. 181. of the eye-glass, fo the breadth of the aperture, to the breadth of the cylinder; that is as 30 feet or 360 inches to V2 inches, fo is √ of an inch to inch or almoft of a line; which is much less than. But in the telescope regulated in the table, it is as 360 to 3 fo 3 to 1 of an inch or almost of a line for the breadth of that cylinder; which 13 can poffibly do no harm. Hence we learn that the breadth of the aperture and focal distance of the eye-glafs cannot be contracted much more than of themselves; for even then the breadth of the cylinder at the eye will not much exceed of a line. The fame is to be understood of telescopes of all lengths regulated as in the table, the breadth of the cylinder being the fame in all. For by the proportion juft mentioned it equals the breadth of the aperture multiplied into the focal distance of the eye-glass and divided by the focal distance of the object-glafs, and confequently it is proportionable to the linear aperture directly and the linear amplification inversely; which two ratios muft compound a ratio of equality to preferve the fame apparent brightness, by art. 349. 4 14 I I 359. Hence though we transferred one of these telescopes from Saturn to Venus which is 225 times brighter, being 15 times nearer to the Sun, yet the breadth of the aperture muft not be contracted above part of the whole; and if too much light ftill remains, it must be diminished by darkening the eye-glafs with the fmoak of a candle. For a greater contraction of the aperture is hurtful for another reason, that all the little bubbles and veins in the eye-glafs become more confpicuous by intercepting the whole or a greater part of thofe little cylinders above mentioned, and confequently the particles of the object they came from. 360. Upon the whole I conclude we may lengthen our telescopes at pleafure, according to the laws of the table, with good fuccefs; fince not only the brightnefs and diftinctnefs remain unaltered, but alfo the breadth of the pencils that enter the eye. Laftly to obferve exceeding small stars and especially the Satellites of Jupiter and Saturn, the best way is to increase very much both the aperture and focal distance of the eye-glass. T For For fince they appear like points even through the telescope, there is nothing gained by endeavouring to increase their diameters; but their brightnefs must be increafed as much as poffible; and this is chiefly done by increafing the aperture. By doubling its breadth, the light received into it becomes quadruple, and then by doubling alfo the focal distance of the 3.rt. 347. eye-glafs, the diftinctness returns to the fame as at first. But ftill the brightness will not become 16 times greater, according to cor. 2. prop. 3, but only 4 times; because as I faid the picture of the star upon the retina is but a fenfible point, whofe brightness cannot therefore be increafed by a diminution of its breadth, but only by an addition of new light. The cafe is different when we view the moon and primary planets through the fame telescope, whose several parts receive 16 times more light than before. Thus by widening the apertures we very much increase the power of the telescope for finding out fmall ftars and the fatellites of Saturn, fo that perhaps with a 30 foot glass, whofe aperture is 6 inches or double the ufual one, as much may be done as with another of 120 foot whofe aperture by the table is alfo 6 inches. So far from Hugens. Art. 353. Art. 349. PROPOSITION VI. 361. In reflecting telescopes of various lengths a given object will appear equally bright and equally distinct, when their linear apertures and also their linear amplifications are as the fquare-fquare roots of the cubes of their lengths: and confequently when the focal distances of their eye-glasses are also as the fquare-fquare roots of their lengths. Put A for the linear aperture of the reflecting concave, L for its focal diftance or the length of the telescope, F for the focal diftance of the eyeglafs; and when the diftinctness is given A3 is as FLL*; and when the brightness is given the amplification or is as 4*, that is Fisas, There L3 A or fore when the distinctness and brightness are both given, A3 is as L F 362. In the reflecting telescope made and defcribed by John Hadley Efq; F.R. S. in the Philofophical Tranfactions No. 376 and 378, L=621 inches, For or of an inch. For he ufes 3 eye-glaffes and as many apertures for the reflecter whose breadths are 41, 5, 51 inches. Hence the linear amplifications or are 1871, 208, 227 L F respectively. Ta king the middle eye-glafs and aperture for a standard I computed the following table for telescopes of other lengths by this Rule. Call the number of inches in the length of any telescope L, and the focal distance of its eye glass will be equal to 60 10 L in thousandth parts of an inch. The 4 quotient of L divided by 604, 10 Lor Fgives the amplification', which a Art. 125. multiplied by 24 will always give the linear aperture in thoufandth parts of an inch. For by the propofition 4 L is as F; that is 4 62 or 4 125 2 or 300 millefimals in the given eye glafs, to the millefimals in the correspondent eye-glass or in F= 60 4 10 L. And the aperture being as the amplification by the propofition, fay, as the amplification given or 208 is to the amplification found, 3 L 5 fo is 5 inches, the aperture given, to the aperture fought= X 2081 363. Were it not for the unequal refrangibility of rays, refracting telescopes, though not fo fhort as thefe', would also be proportioned by b Art. 341. this rules: which not agreeing with experience, fhews again that the ab- e Art. 333, erration arifing from the spherical figure are inconfiderable in comparison to the other aberrations arifing from the unequal refrangibility of the rays. 338 |