light, he altered their pofition till the papers in the two holes appeared to be equally enlightened. This being done, he computed the proportion of their light by the fquares of the diftances at which the luminous bodies were placed from the objects. If, for instance, the distances were as 3 and 9, he concluded that the light they gave were as 9 and 81. Where any light was very faint, he fometimes made use of lenfes to condense it; and he inclofed them in tubes or not as his particular application of them required.

526. To measure the intenlity of light proceeding from the heavenly bodies, or reflected from any part of the sky, he contrived an inftrument which refembles a kind of portale camera obfcura. He had two tubes, of which the inner was black, faftened at their lower extremities by a hinge C, (fig. 5. pl. CCLVIII.) At the bottom of thefe tubes were two holes, R and S, 3 or 4 lines in diameter, covered with two pieces of fine white paper. The two other extremities had each of them a circular aperture, an inch in diameter; one of the tubes confifted of two, one of them fliding into the other, which produced the fame effect as varying the aperture at the end. When this inftrument is ufed, the obferver has his head and the end of the inftrument C fo covered, that no light can fall upon his eye befides that which comes through the two holes S and R, while an affiftant manages the inftrument, and draws out or fhortens the tube DE, as the obferver directs. When the two holes appear equally illuminated, the intenfity of the lights is judged to be inverfely as the fquares of the tubes. In ufing this inftrument, the object fhould fubtend an angle larger than the aperture A or D, feen from the other end of the tube; for, otherwife, the lengthening of the tube has no effect. To avoid, in this case, making the inftrument of an inconvenient length, or making the aperture D too narrow, he has recourfe to another expedient. He conftructs an inftrument, (fee fig. 6.), confifting of two object-glaffes, AE and DF, exactly equal, fixed in the ends of two tubes fix or feven feet, or, in fome cafes, 10 or 12 feet long, and having their foci at the other ends. At the bottom of these tubes B are two holes, 3 or 4 lines in diameter, covered with a piece of white paper; and this inftrument is ufed exactly like the former.

527. If the two objects to be obferved by this inftrument be not equally luminous, the light that iffues from them must be reduced to an equality, by diminishing the aperture of one of the objectglaffes; and then the remaining furface of the two elaffes will give the proportion of their lights. But for this purpose, the central parts of the glafs must be covered in the fame proportion with the parts near the circumference, leaving the aperture fuch as is reprefented, (pl. CCLVII. fig. 15.), because the middle part of the glafs is thicker and lefs tranfparent than the reft. If all the objects to be obferved lie nearly in the fame direction, he obferves, that these two long tubes may be reduced into one, the two object-glaffes being placed clofe together, and one eye-glafs fufficing for both. The inftrument will then be the fame with that of which he published an account in 1748, and which he called a HELIOMETER, or ASTROMETER.

528. He obferves, that it is not the abfolute quantity, but only the intenfity of the light that is measured by these two instruments, or the number of rays, in proportion to the furface of the luminous body; and it is of great importance that thefe two things be diftinguifhed. The intensity of light may be very great, when the quantity and its power of illuminating other bodies may be very small, on account of the finallnefs of its furface; or the contrary may be the cafe, when the furface is large. To thefe methods which he took to measure the proportions of light, we subjoin a few examples of his application of them.

529. When a perfon ftands in a place where there is a furong light, he cannot diftinguish objects that are placed in the fhade; nor can he fee any thing upon going immediately into a place where there is very little light. It is plain. therefore, that the action of a strong light upon the eye, and alfo the impreffion which it leaves upon it, makes it infenfible to the effect of a weaker light, M Bouguer endeavoured to afcertain the proportion between the intenfities of the two lights in this cafe; and by throwing the light of two equal candles upon a board, he found that the fhadow made by intercepting the light of one of them, could not be perceived by his eye, upon the place enlightened by the other, at little more than eight times the difiance; whence he concluded, that when one light is 8 times 8, or 64 times less than another, its prefence or abfence will not be per ceived. He allows, however, that the effect may be different on different eyes; and fuppofes that the boundaries in this cafe, with refpect to different perfons, may lie between 60 and 80.

530. Applying the two tubes of his inftrument, to measure the intensity of the light reflected from different parts of the fky, he found, that when the fun was 25° high, the light was four times ftronger at the diftance of 8° or 9° from his body, than it was at 31° or 32°. But what fruck him the moft was to find, that when the fun is 15° or 20° high, the light decreases on the fame parallel to the horizon to 110° or 120°, and then increafes again to the place exactly oppofite to the fun. The light of the fun, he obferves, is too ftrong, and that of the ftars too weak, to determine the variation of their light at different altitudes; but as, in both cafes, it must be in the fame proportion with the diminution of the light of the moon in the fame circumftances, he made his obfervations on that luminary, and found, that its light at 19° 16', is to its light at 66° 11', as 1681 to 2500; that is, the one is nearly two thirds of the other. He chofe thofe particular altitudes, because they are thofe of the fun at the two folftices at Croific, where he then refided. When one limb of the moon touched the horizon of the fea, its light was But this proportion he acknowledges must be 2000 times lefs than at the altitude of 66° 11'. fubject to many variations, the atmosphere near the earth varying fo much in its denfity. From this obfervation he concludes, that, at a medium, light is diminished in the proportion of about 2500 to 1681, in traversing 7469 toifes of denfe air. Laftly, he applied his inftrument to the different parts of the fun's difk, and found that the centre is confi derably more luminous than the extremities of it.

'As

As near as he could make the obfervation, it was more luminous than a part of the difk ths of the femidiameter from it, in the proportion of 35 to 28; which is more than in the proportion of the fines of the angles of obliquity. On the other hand both the primary and fecondary planets are more luminousat their edges than near their centres. 531. The comparifon of the light of the fun and moon is a fubject that has often exercifed the thoughts of philofophers; but we find nothing but random conjectures, before our author applied his accurate measures. In general, the light of the moon is imagined to bear a much greater propor tion to that of the fun than it really does; and not: only are the imaginations of the vulgar, but thofe of philofophers also, imposed upon with respect to it. M. De la Hire could not, by the help of any burning mirror, collect the beams of the moon in a fufficient quantity to produce the leaft fenfible heat. Other philofophers have fince made the like attempts with mirrors of greater power, without greater fuccefs.

532. To folve this curious problem, M. BouGUER Compared the light of each luminary to that of a candle in a dark room, one in the day-time, and the other in the night following, when the moon was at her mean diftance from the earth; and, after many trials, he concluded that the light of the fun is about 300,000 times greater than that of the moon; which is such a difproportion, that, it can be no wonder, that philofophers bave had fo little fuccefs in their attempts to collect the light of the moon with burning-glaffes. For the largest of them will not increafe the light 1000 times; which will ftill leave the light of the moon, in the focus of the mirror, 300 times lefs than the intenfity of the common light of the fun.

533. Dr SMITH made an eftimate of the quantity which would have been tranfinitted to us from the opaque body, if it reflected all the light it receves; and thought that he had proved, that the light of the full moon would be to our day-light as i to about 90'900, if no rays were loft at the moon. For his calculation on this conjecture, we refer the reader to his work, as it is tedious, and on the whole uncertain.

534. Mr MICHELL made a fimilar computation in a more fimple and caly manner. Confidering the distance of the moon from the fun, and that the denlity of the light muft decrease in the proportion of the fquare of that diftance, be calculated the dentity of the fun's light, at that diftance, in proportion to its denfity at the furface of the fun; and thus found, that if the moon reflected all the light it receives from the fun, it would only be the 45,000th part of the light we receive from the luminary. Admiting, therefore, that moonlight is only a 300,000th part of the light of the fun, Mr Michell concludes, that it reflects no more than between the 6th and 7th part of what falls upon it.

SECT. II. Of ABERRATION.

535. THE great practical ufe of the fcience of optics is to aid human fight; but in conftructing dioptrical inftruments for this purpofe, great difficulties arife from the aberration of light. It has been shown, 273, 274, &c. how to determine

the concourfe of any refracted ray PF with the ray RVCF (figs. 5, 6, &c. Plate CCLII.) which paffes through the centre C, and therefore falls perpendicularly on the spherical furface at the vertex V, and fuffers no refraction. This is the conjugate focus to R for the two rays RP, RV, and for another ray flowing from R and falling on the furface at an equal distance on the oppofite fide to P. In fhort, it is the conjugate focus for all the rays flowing from R, and falling on the fphe rical furface in the circumference of a circle, defcribed by the revolution of the point P round the axis RVCF; that is, of all the rays which occupy the conical furface defcribed by the revolution of RP, and the refracted rays occupy the conical furface produced by the revolution of PF. But no other rays flowing from R are collected at F; for it appeared in the demonftration of that propofition, that rays incident at a greater distance from the axis RC were collected at a point between C and F; and then the rays which are incident on the whole arch PC, or the spherical surface generated by its revolution round RC, although they all crofs the axis RC, are diffused over a certain portion of it, by what has been called the aberration of figure. It is called alfo (but improperly) the aberration from the geometrical focus, by which is meant the focus of an infinitely flender pencil of rays, of which the middle ray (or axis of the pencil) occupies the lens RC, and fuffers no refrac tion. But there is no fuch focus. But if we make m RV-n RC: m RV=VC: VF, the point F is called the geometrical focus, and is the remotest limit from C of all the foci (equally geometrical) of rays flowing from R. The other limit is easily determined by conftructing the problem for the extreme point of the given arch.

536. It is evident from the construction, that while the point of incidence P is near to V, the line CK increases but very little, and therefore CF diminish little, and the refracted rays are but little diffufed from F; and therefore they are much denfer in its vicinity than any other point of the axis. It will foon be evident that they are incomparably denfer. It is on this account that the point Fhas been called the conjugate focus narv, to R, and the geometrical focus and the diffution has been called aberration. A geometrical point R is thus reprefented by a very fmall circle (or phyfical point, as it is improperly called) at F, and F has drawn the chief aftention. And as, in the performance of optical inftruments, it is necessary that this extended reprefentation of a mathematical point R be very fmall, that it may not fenfibly interfere with the reprefentations of the points adjacent to R, and thus cause indiftinct vifion, a limit is thus fet to the extent of the refracting furface, which must be employed to produce this reprefentation. But this evidently diminishes the quantity of light, and renders the vifion obfcure, though diftinct. Artifts have therefore endeavour. ed to execute refracting furfaces of forms not fpherical, which collect accurately to one point the light iffuing from another, and the mathematicians have furnished them with forms having this property; but their attempts have been fruitless. Spherical furfaces are the only ones which can be executed with accuracy. All are done by grinding Ggg &

the

I:T, I, diff.: T, I; but Pfp: PCp= PR: Pf, DR: DB (because DP is parallel to Bf by conftruction) tan. CPRtan. CPI: tan. CPI. Now CPI is the angle of incidence; and therefore CPR is the angle properly correfponding to it as an angle of refraction, and the point fis properly determined.

540. Hence the following rule: As the diffe. rence of the tangents of incidence and refraction is to the tangent of incidence, fo is the radius of the furface multiplied by the cofine of refraction to the diftance of the focus of an infinitely Gender pencil of parallel incident rays.