A treatise of optics: containing elements of the science; in two books. by Joseph Harris, ... 1775
Harris, Joseph.
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SS > © „„ »Z + * wa. 4 * * © 00 — be * „e * 3 | 4 F Q 0 * * — 7 „ 3 6 0 v7 tics, * 3 , 5 — . — . ——— — 26323 A # _ Sect. IV. OF ODP-T1.6C8, #53 The lens being thus covered, place it ſo that its axis may point directly towards the ſun; then through the holes 3, 6, there will Hue the ſtreams of light gan, sn; the rays belonging to the upper and lower limb of the tun, having their focz reſpectively at the points u, . Now if a paper be held behind the lens, theſe ſtreams of light will form two white ſpots or circles upon it, which gradually approach nearer together, as the paper is moved toward v; at a certain point 4 their limbs will touch ; after this they will incroach one upon another, and the part common to each will be brighter than the reſt ; at « theſe circles will coincide; if the paper be moved farther, they will begin to ſeparate, and at / their limbs will juſt touch. But as it is difficult to determine preciſely, when the two circles are perfectly united; obſerve where their limbs are at a ſmall and equal diſtance aſunder, as at o and p; then biſecting op we ſhall have the focus v required. If that point be called x, where the lines da, hb a produced either way, as the caſe may require, would interſect ; it will be dv: V:: Xx q: x and ſo xd +> xb:xd:: db: dv. The holes a, &, ſhould be cloſe to the edge of that aperture which the lens is to have when applied to its uſe; and they ſhould be alto of a proper ſize ; not too ſmall, for then the white circles will be dark and ill defined; and to make them large would be diſadvantageous, as their centers muſt be nearer together. The experiment will ſucceed better, if the room be darkened. Inſtead of having the paper with the holes in it; the lens might be left open, and covered only with two round opaque circles : But the holes do better. By this method the focal length of a lens may be found, I think, more accurately than by either of the preceding ||. By making the experiment with the lenſes before mentioned of about 12, 8, and 44 feet focal lengths; I could determine theſe lengths reſpectiveiy within about , +, +5 or 2 of an inch. The limits betwixt the places where I could perceive the images to ſeparate, were reſpectively about 3 inches, 2 inches and 2 of an inch; and had the flatter lenſes been wider, theſe limits would have been more contracted. The focal length may be alſo found in the ſame manner, by ex- poſing the lens to the moon, and obſerving where its image is leaſt; or where the bright ſpots coalefce, if the lens is covered as above. But we cannot be ſo exact here as with the ſun, etpecially if the focal length + The incident ravs Ka, &; and Ja, 15; Other methods for finding the focal lengths proceed reſpectively from the upper and lower of the object. glaſtes, of teletcopes, and of mi- limbs of the ſun; 14, /b, being parallel to As, croſcopic lentes, will be ſhewcd in the nest and fa, &b to Ax. book. 3. VI. EA. 256 An apparatus | | for holding the lens. Fig. 93. A I REATI1SE Book II. length exceeds two or three feet; and if the lens be covered the holes muſt be large. 365. In making the above experiments ; the lens and the paper for receiving the images, ſhould have proper ſupports; ſo that they may remain fixed at any given ſtation, while the reſpective diſtances are meaſured. The annexed figure repreſents an apparatus, I made uſe of, for hold- ing lenſes of various fizes. A is the pillar of a wooden candleſtick, on which ſlides the wooden bar cd, which may be ſtayed at any height by means either of a ſpring or a wooden wedge at c, bearing againſt the pillar. The lens is to be placed between the upright and wooden pieces a, þ; the piece & being moveable on c d, till it touches the edge of the lens. The fore and inſide parts of a, &, and alſo the upper ſurface of c d, have narrow and thin ledges for the lens to bear againſt; and for confining it on the other ſide, are ſlips of wood ſlid- ing on the infide ſurfaces of a, ö. Theſe ſlips have a motion of about half an inch, on account of receiving a thick lens, or a lens in its cell; and they are confined at proper places, by a ſcrew in each going through flits made acroſs in a, &, and having a nut bearing againſt the out-ſide of the ſaid pieces 4, 6. This little apparatus I had made fo as to hold any lens not wider than fix inches: And that the lens might be ſo placed as directly to face any object, or that its axis might have any elevation ; the bar cd turns ſtifly in a round hole made in the ſocket ſliding on the pillar A; and as a guide to point it aright, there is a ſhort index fixed to the top of the immoveable piece a, having on it two ſights to guide the ęye, or to let the ſun ſhine through. An + ox-eye fixed to a window looking eaſterly or weſterly, ſo as it may face the ſun when he is low, will be very convenient for finding the focal lengths of ſuch lenſes as may be readily ſcrewed to it. Or a ſhort tube faſtened to the window, and having without a || plane ſpe- culum which may be ſo inclined as to reflect the ſun's rays directly upon the lens, will do ſtil] better. | The paper for receiving the light ſhould be parallel to the lens ; and how to ſupport it in this manner, there may be different methods, which it would be needleſs to deſcribe 7. To + See 297. of this. not exc2eJing two feet. Within about eight || See the deſcription of the ſolar microſcope inches of one end of a ſtrait wooden bar 32 in the next book. inches long, was fixed acroſs a ſhort bar, havin J Having miſlaid the above deſcribed ap- fliding checks, Sc. for confining lenſes of dit- paratus, I have ſince got made a more conve- ferent ſizes, like cd, a, 6, before deſcribed. nient one for finding the focal lengths of lenſes The long cnd of the bar had a groove in it, 3 an Al. a» , ei anc. Secr. IV, OF OPTICS. 257 To find the focal length of a concave lens. 366. Let the lens be covered with paper having in it two ſmall Fig. 93. circular holes, as at O, v; and on the paper for receiving the light, deſcribe two ſmall circles as a, 6, whoſe centers let be at twice the di- ” ſtance aſunder of the centers of O, v; and it will be beſt if their di- ameters are alſo double thoſe of O, v. Then moving the paper to or fro, till the middle of the ſun's light coming through the holes O, v, falls exactly on the middle of the circles a, 5; that diſtance of the paper from the lens will be the focal length required. For it is ma- niteſt that a6 : Ov:: aF : OF: Or whatever is the diſtance of a, 6, it will be, 45 — Ov: 4O :: OV: OF, the focal length of the lens. In- wy of the paper with the holes, ſmall patches may be ſtuck on the lens. 367. The focus may be alſo found by candle-light, thus: Let Q Focus found be the place of the flame; c, d, the bright ſpots upon the paper, and 1 the point where the lines vd. Oc produced backwards would inter- ſe. To find the point 9, it will be c - Ov: Ov :: Oc: Og. Then Qq: QO:: QO: Qa, and O2 is the focal length required. 225. J. 368. The focal length of a concave lens may be readily found, by By joining joining it to a convex one having a ſhorter focus. pda pea Let g be the image of any object formed by the convex lens A, of a deeper fixed at A; and let Q be the image of the ſame object, when the ſocus. concave lens O is joined to A. Having meaſured the diſtances Q 4, Fig. 95; 9O; to find the focal length OF of the concave lens, it will be, as in the preceding, Qq: QO:: QO: QF; then QF —QO= OF. WE. I. 8. 3. Of viſion when the object or the eye or both, are in a medium denſer than air. | 369. The appearances of objects placed in a denſe medium, whoſe | re fracting ſurface is plane, to a ſpectator in the common medium of | air, in which was a ſlider divided into inches and was fixed occaſionally a piece at right- angles, t parts; over both theſe was an upright piece which by moving the ſlider would touch the which moved the whole length, and which thickeſt part of the lens, and then the diviſions | might be readily fixed in any place. Ihe fide cut by the paper would ſhew the diitance be- of this piece facing the lens was covered with tween them. This apparatus was fixed occa- white paper, for receiving the ſun's image; and fionally to tlie top of a ſtand for carrying a ſmall for meaſuring the exact diſtance between the reflecting tel-{cope, by which it might be ele- paper and the lens, at one end of the long ſlider vated to any angle. LI 258 » 144. I. A TREATISE Boox IT. air, may be eaſily underſtood froni prop. V. and its coroll. of Book I. And I think the phenomena agree in all caſes with the theory, as it has been there explained. PROP. XXXVL 370. To explain the phenomena of viſion of ebjetts placed in @ ſpheri- cal denſe medium, to a ſpectator in the medium of air. Phnom, Objects placed in ſuch a medium to a ſpectator without, appear magnified, and that in different degrees according to their di- {tances from that part of the ſurface which is next the eye; thoſe that are in contact to that point of the ſurface not being magnified at all, whilſt at all other places they will be magnified, and that more. and more the farther they are from the ſaid point of the ſurface ; ſo that when an object is in contact with the remoteſt point of the ſur- face from the eye, it is magnified molt of all. Let AD O be the ſection of a refracting ſphere whoſe center is O; as for inſtance, the ſection of a decanter of water; the ſpectator being on the ſide A, and ſomewhere in the axis A. Let F be the focus of rays, coming from without parallel to the axis f OF, after their refrac- tion near A; or F the focus of thoſe rays ſuppoſing the medium con- tinued beyond F; and f the focus of rays within the ſphere parallet to the axis DOA, after their emerſion near A. And let QI, Q2, O3, Q4, Qs, Doe, be the diameter of an object, or the diameters of as many equal and ſimilar objects, ſituated at theſe reſpective places. Now to find the points ꝙ of the reſpective images q 1, 942, O3, 94, 95, 96; it will be, QF: OF :: AQ: Ag, Having thus found the reſpective points ; through the extreams 1, 2, &c. of the objects 1, Q 2, &c. draw the ſtrait lines Or, O 2, Sc. and produce them till they meet 71, 2, Sc. drawn parallel to the reſpective objects; and 91, q2, Cc. will be the geometrical images of the ſaid objects, or of their diame- ters. Or in this caſe, becauſe the objects are all equal and contained between the parallel lines AD, dv; their images, if we neglect the aberrations of the refracted rays, will be contained between the axis: * Conſt. f AF, and the line fd produced, as to 6. For f is the © focus of a ray. vd coming to d parallel to the axis; and ſo the rays coming to d from the extreams. 1, 2, Fc. of the ſeveral objects will be all retracted into df; whence the extreams 1, 2, Fc. of all the images are in the line d produced. Hence when Q is in A, or the object is in Ad; ꝙ is alſo in A, or the image is equal and coincident with the object. But as the object is * removed. Sger. IV. F OP TICS. 259 removed from A towards D v, its image increaſes, and that more and more as it advances towards D; the image being greateſt of all when the object is in Dv. All which are exactly agreeable to the pheno- mena. 2. E. D]. 371. Corol. 1. The refracting ſurface Ad remaining the ſame if the medium be indefinitely continued on the oppoſite part, the images will ſtill increaſe in magnitude as the object advances farther from A, until it has got to F. If the object be placed beyond F, viſion will be indiſtinct; becauſe then the refracted rays will enter the eye, placed near to A, converging. 372. Corol. 2. The denſer is the medium, the more it magnifies objects placed within it: For then the leſs is the focal diſtance Af; and conſequently the diameter of the object = Ad remaining the ſame, the greater is the angle Af d. 373. Schol. 1. Whilſt the object is between A and the center O, the image is nearer to A than the object; at O they both coincide, and the image is farther when the object is beyond O. And this is exactly agreeable to the phenomena ; the ſemi-diameter OA next the eye, ap- pearing much ſhorter than the ſemi-diameter OD, which ſeems ex- tended as far as the line 6. By covering the bottom of a decanter of water with ſmall objects, as peas, &c. the phenomena here explained will be very remarkable, and quite agreeable to the above theory, | if the eye is nearly in the ſame plane with the objects. But if the eye is much above that plane, ſo that the remoter objects are ſeen through the belly of the decanter, whilſt the nearer ones are ſeen through a ſmaller ſegment ; the remoter objects will appear accordingly ſo much the more remote: For OD, De are in a conſtant ratio ; that is, the greater is OD, the greater alſo in proportion will be D e, | 374. Schol. 2. The images of a given ſmall object placed at the All ſpheres oF centers, or at like diſtances in proportion to the radii from the re- de fame me- fraQting ſurfaces, of any ſpheres made of the ſame medium, are equal. «if objects Let O be the common center of the ſpherical refracting ſurfaces 133 AD, ad, and F, F their principal foci; and let Oy, the breadth of breadths, the given object placed any where between the parallel lines AB, DC, equally. be ſo ſmall, as not to differ ſenſibly from the tangents of the arches Fig. 97. AD, ad: I fay the images formed by the refracting ſurfaces AD, ad © will be equal, if the diſtance of the obje& in each ſphere from the reſpective ſurfaces AD, ad, be as the radii OA, Oa, L1 2 Through The lines Oab, QB, qB& are for illu- of the figures referred to in that propoſition, ſtrating the theory according to Prop. XXI. but nevertheleſs falling under the ſame rules. Book J. This being a different caſe, from eicher 260 A TREATISE Book II. 2 | Through the reſpective points D, d, draw the lines FDH, dh; 4 and where- ever the objects are placed in the reſpective ſpheres, their images will be contained between the lines FG, FH, and fg, Yb. Let the object placed within the ſphere ABO be called X, and its image x; and the object within the lefſer ſphere a5 O be called V, and its image y. Now becauſe, * Hypoth. FX: OF (::*fY : Of) :: AX: Ax (: : Y: ay), it will be, 144. J. Ax: ay :: AX: V:: FA: Va (:: Ax FA: ay+fa) :: Fx: fy. But, e 4. VI. Ex. FA: Fx :: AD: &; and fa: y :: ad: y; and becauſe, FA: F:: Fa : fy; it will be AD: x:: ad: y. But AD ad, and therefore x 2 y. 2. E. D. Thus, if the ſmall object be at the center, as Oy, its image in each ſphere will be Ox; and if it be at the peripheries bc, BC, its images will be g = GH, | 375. Schol. 3. When the object is ſo large, that the verſed fine av has a ſenſible magnitude; the image formed by the refraction of the | lefſer ſphere, will be leſs than that formed by the greater ſphere. | For ſuppoſing the object Oy to be at the center, for inſtance ; it will be, fv: O:; vd: Ox; and therefore the greater is the ratio of fv to / O, the greater will be the ratio of Oy toOx. And hence, equal objects having ſenſible magnitudes, appear ſomewhat more magnified _ the larger is the ſphere, Add to this, that the greater obſcurity of the thicker medium, may ſomewhat enlarge the apparent diſtance of the image; and this will proportionably increaſe the apparent magnitude. 376. Corel, And hence, from theſe two cauſes conſpiring together; the ſmall bores of capillary tubes, or ſuch as are uſed for mercu- rial thermometers, appear bigger in proportion the thicker are the tubes. 377. Schol. 4. A broad ruler with parallel ſides placed upright in the middle of a conical veſſel, as a glaſs of water, will at firſt ſight ap- pear broadeſt where the glaſs is narroweſt. This deception is chiefly owing, to the breadth of the ruler being referred to that of the glaſs; the diſtance that is obſerved between them, being partly attributed to the figure of each. But holding the glaſs even with the eye, and look- ing attentively, the apparent taperneſs of the ruler will ſoon vaniſh. c 0 Fig. 95. 373. Schol. 5. The greateſt proportion that the breadth of the . [ image of an object placed within a ſphere of water, can bear to the 1 0 breadth of the object, is that of 2 to 1. For the image is greateſt, i when the object is at the remoteſt ſurface BC. Let K be the prin- v cipal focus of rays coming from without upon the ſurface AD; and A »—= — ru — 0 — Stet. IV. OF OPTICS. 261 it will be, AB: AG:: fKB: KO::*2: 3 ::*AB: AF. Wherefore 144. I. FA:FG:1:2: AD: GH, But at firſt fight one is apt to ima- * Conſt. gine that the diameter of a round object, as a pea, is magnified much more than in the above proportion. We ſee that the whole bulk is greatly ſwelled ; the apparent magnitude in this caſe, being not much leſs, than as the cube of the diameter, as on account of the diſtance between our two eyes, we fee at once more than half the pea; and by ſo much as is ſeen, the idea of the inviſible part is readily ſug- geſted. And hence, the bulk and diameter are ſuppoſed at random, to be magnified in near the ſame proportion, We commit the ſame miſtakes in naked viſion, the reaſon indeed in both caſes being the very ſame. But if we attentively compare the breadth of the mag- nified pea, with the extent of two contiguous peas ſeen by naked viſion, we ſhall ſoon rectify our former miſtake. If the refracting ſphere is ſolid glaſs, then GH: AD :: 3: 1. If the object be at the center of a ſphere of water, its diameter will be to that of its image as 3 to 4; and if the ſphere is ſolid glaſs, the proportion between them will be as 2 to z. 379. To a ſpectator in a denſe medium, as for inſtance in water, Viſion in a all objects within that medium will be confuſed ; and the confuſion gente me: . . lum con- may be fo great, that one object cannot be diſcerned from another, as fuſed. in the caſe of a very flat eye that cannot diſcern any thing without ſpectacles, The caſe will be much the ſame, if the objects are with- out that medium, if its refracting ſurface is flat, as that of ſmooth water. | The reaſon of which is, that the refraction between the denſe me- dium, and the cornea and the aqueous humour, is leſs than between air and the cornea ; and ſo the rays not converging enough at their en- trance into the chryſtaline humour, are not united upon the retina, but have their focus's beyond it. If the refractive power of the denſe medium, is equal or greater than that of the cornea and aqueous hu- mour ; the ravs will accordingly proceed to the chryſtaline humour either unrefracted or more diverging, 380. The beſt way for divers is to ſuit themſelves with glaſſes by experiment; for according as they are /ong, common, or ſbort- ſighted; or as the refractive power of their + cornea may be greater or leſs in proportion to that of their chryſtaline humour, they will require glaſſes of greater or leſs convexities, But, if the focal length of the cornea in our natural element, air, is known; a lens which will reſtore diſtinct viſion in a given medium, may be found by the following prop. PR OP.. + By the refractive power of the cornea, is properly meant that of the aqueous humour behind 1; 262 Fig. 98,99. 1736. L 177, & 211. J. © 83. J. 938. 1. * 302, II. Fig. 99. 381. II. A TREATISE Book II, NOF. n. 38 1. The fecal length of a lens in one medium, being given; to find its focal length in any other given medium. Let the medium whereof the lens is made, be called G, one of the mediums wherein it is placed A, and the other medium W. Let the greater and leſſer of the fines of incidence and refraction between G and A, be reſpectively 2 and ; and between G and W, M and N; and the focal length of the lens in A be , and in W =F. And it will be, F: F:: — nearly, m—n NN 1. Let the lens be a plano-convex, with its plane fide to the inci- dent rays; Oà the radius of its convexity, af its focal length in the medium A, fig. 98; and aF its focal length in the medium W; to find which in the reſpective mediums, it will be accurately: Oa:af::*m—n:n; and Oa:aF::*M—N : N; whence O | af=—=; and aF= N; and therefore, m—x M—N ? af:aF: —: IG Q. E. D. If the lens be reverſed, its focal length in each medium will be ſtill the ſame, * reckoning that length the diſtance between the focus, and the neareſt focal center of the lens. And in all lenſes, whoſe ſides are both ſpherical, if we negle& their thickneſſes as inconſiderable, it will be, F: F:: —: NN. Therefore, Cc. 2. E. D. 382. Corol. Hence if the lens is glaſs; the medium A is air, and the medium W is water; it will be /: F:: 1: 4. For M— : n:: 1: 2; and M—N: N:: 1: 8; whence, — t 4335: 2:8) 513 4. 383. Schol. 1. Any lens being given ; we may find another lens which being joined to the former, both together ſhall have a given focal length in any given medium. Let AF be the focal length required of the two combined lenſes, in the given medium. 1. Find * the focal length of the given lens in the given medium W; if the lens has no + focus, that is, if it tranſmits the rays unrefracted ; then it is manifeſt that aF is the focal length of 4 ens + This cannot happen but when the medium medium W ; as is ſuppoſed to be caſe of the of the lens has the 4 refractive power as the aqueous humour of the eye and common water. —_—_— c Ak. +, ace af: Dos ow 05 —8 - ry — £? £3. Szer. IV. OF OPT 1GS: 55 lens required in this medium, whence its focal length in air is "_” 381. II. found. If the given lens has a real focus, as g; then ſay, gF: ga :: ga: gG; or if its focus is G, that is, if it tranſmits pa- rallel rays diverging as from G; it will be, GF: Ga:: G4: GH; 227. J. and aG or 4 H will be accordingly, the focal length in the medium W of the lens required. Whence in all caſes, its focal length in air may be found. 384. Scbol. 2. Hence having the focal length of the cornea in air, A proper lens we may alſo have its focal length in any other given medium; and fo, “et. from the preceding, ſuit ourſelves with a lens that will reſtore diſtinct viſion in that medium. Thus, if the focal length of the cornea in air is = 4 F, and its re- fractive power be the ſame with that of water; a lens that will pro- cure diſtinct viſion in water, will have its focal length therein =aF; and if the lens is glaſs, its focal length in air will be =* + AF. If * 382. II. the focus of the cornea a, when under water be g, or G; the focal length in water of a lens that will reſtore diſtinct viſion, will be ac- cordingly a G, or a H. 385. Schol. 4. If the cornea be not concerned in the change made in the eye, for procuring diſtinct viſion at different diſtances ; the lens above found will enable the eye to ſee diſtinctly in water, at all ſuch diſtances as it can in air : But if the cornea 1s concerned in that change of configuration of the eye, as moiſt probably it is; the. latitude of diſtinct. viſion through the above lens in the denſe medium, will not be ſo extenſive as it is to the naked eye in air. 386. Schal. 4. Hence again, if a perſon under water had ſufficient light, and was exactly fitted with a lens for ſeeing an object at a. given diſtance diſtinctly; we might from thence find pretty nearly the focal length of the cornea in air: And if the faid perſon could alſo determine, how. much farther and nearer than the faid given di- {tance, he could alto ſee diſtinctly ; we might alſo. make an eſtimate of: the ſhare, which the cornea has in the change of configuration of the eye. But the want cf light, and of ability of ſtaying at eate any time under water, are difficulties that would render very precari— ous, the concluſions drawn from the abſervations of a.perton under theſe circumſtances. A TREATISE Book II. $. 4. Of camera-obſcura's. The theory in general of the camera-ob/cura has been already ex- plained in Book I. art. 243 to 246. I am here to add ſome farther particulars, not there taken notice of, with a deſcription of different contrivances for forming the dark chamber. 387. The pictures exhibited in the camera-obſcura are very enter- taining ; eſpecially if they repreſent objects in motion, as carriages either by land or water, people walking, the wafting of the boughs and leaves of trees, &c. And it all circumſtances are favourable ; the pictures ſeem to appear more lively and diſtinct, than the objects do to a naked eye looking at them, from the place where the lens for form- ing theſe pictures or images was fixed, For, the picture being dimi- niſhed, the rays forming it are condenſed; and ſo the colours, ſhades, Sc. are proportionally brighter and more vivid. The picture being alſo a near object, is ſeen free from that faint hue wherewith objects without doors are commonly tinged ; thoſe rays that occaſion theſe ap- pearances, being as it were abſorbed in the picture, or becoming too teeble, after they are there diſperſed, to be perceived, Objects ata 388. All other circumſtances being alike, the pictures of objects moderate di- ee that are near, as within 5, 10, or 20 yards, appear more vivid than the beſt pic- thoſe of objects that are more remote. And univerſally, the pictures ture. will be more diſtinct and pleaſant, when the objects are at ſuch mo- derate diſtances in proportion to the focal length of the lens, as to ex- hibit ſmall parts, as the features of a perſon's face, the bricks and tyles of houſes, &c. If the light without is favourable, and the ſpec- tator has been ſome time in the dark; it is ſurprizing how diſtinct and bold the pictures of ſmall objects will appear, that are diminiſhed at leaſt 20 or 3o times; and a perſon may be known, when his fea- tures are no bigger than in that proportion. The lights, ſhades and tints being here exquiſitely delicate and perfectly juſt, at the ſame time, that the picture is diminiſhed ; the re/zevo's of objects are ſur- prizingly bold, and when the natural ones are but moderate, thoſe in the picture ſeem to come up to the real ſize. A diſtant proſpect ap- pears perfect enough, though it does not make ſo entertaining a picture. 1 389. The room wherein the picture is formed ſhould be as dark mould be as as poſſible; that is, all light ſhould be excluded from it but what 3 as off Comes thro' the lens; for in proportion as the field about is darker, the objects will appear brighter, as the ſtars do in a dark night. And for this purpoſe, the lens, beſides having its aperture properly limited, ſhould E 1 — * + a. + Fo 7 — 4 85 : 18 &. * : ; b 3 2 j — 1 % © 5 5 Jv © 0 — ts — wo gw * * 21 5 +. + - * * * N. ZH p 5 .. ”"2 5 4 * IN AS "x 2 wi Ger IV. OF OPFICS 265 ſhould have a ſhort tube before it, ſuch as will exclude all light but what is contained in the field intended to be taken into the picture. . This tube ſhould be black on the inſide; and it would do ſo much . the better, if the whole inſide of the dark room was alſo black Te ſpectator himſelf, at leaſt whilſt he looks at the picture, ſhould be 13 alſo in the dark; for by this means, the pupils of his eyes will en- 35 large, and as they do enlarge, the apparent brightneſs of the picture will increaſe, and being alſo free from extraneous light, the impreſſions upon the retina's will be the more vivid and ſenſible. | 390. The objects ſhould be alſo well enlightened ; otherwiſe, not- And the ob- withſtanding all the above requiſites have been taken care of, if the feu! 8 weather is dark, or the objects are in the ſhade, the picture will be : obſcure, dull, and no ways agreeable. This phenomenon therefore of the camera-obſcura, ſhould never be attempted but in a clear day; and it 1s beſt of all when the ſun ſhines upon ho objects from the oppoſite coaſt ; that is, if the proſpect is weſtern, the phenomena will be beſt in the morning or forenoon ; if eaſtern, in the afternoon ; if northern, about noon. A ſouthern aſpect is the worſt of any for the camera- obſcura, becauſe the ſun is never oppoſite to it; and in this caſe, the experiment will ſucceed beſt either betimes in the morning, or late in the evening; that is, when the ſun ſhines moſt directly upon the ob- jets. In all caſes, a great deal of light is ſtopped by lenſes, as is manifeſt from the vividneſs of the images of objects ſeen in them by reflection: And in the preſent caſe, the light impinging upon the paper, or whatever the obſtacle be at which the picture is formed, is there diſperſed, ſo as to be much rarified before it comes to the eye. And hence it is, that the chamber requires to be very dark, and the objects well illuminated. 391. The lens, uſed for this purpoſe, ſhould have a proper aper- Proper aper- ture. If the aperture be too ſmall, the picture will be dark and ob- (res of lentes ſcure, and upon that account indiſtint and unpleaſant ; and if it wet Dong be too large, the picture will be indiſtin& on account of the aber- rations of the extream rays, and alſo becauſe the room will be too much enlightened by adventitious light entering into it ; and this laſt cauſe has no ſmall ſhare in marring the pictures, as it proportionably renders them more obſcure : But when the aperture of the lens is moderate, the vitious rays on account of the aberrations are, in the preſent caſe, at their entrance into the eye very dilute and rare, and therefore ſcarce ſenſible. But the apertures here will admit of ſome latitude ; and they may be a little narrower or wider, according as the objects are more or leſs illuminated; and according as they are nearer M m or 266 A TREATISE Book II. or farther, It is beſt therefore to leave the aperture of the lens, juſt wide enough for the darkeſt weather it.is to be uſed in, and to have a-narrow ring to clap on occaſionally. By making obſervations as carefully as I could, in a pretty clear day, the objects being at about 150 yards diſtance, and the ſun ſhin- ing obliquely upon them : A lens of 18 inches focal length, I thought did beſt with an aperture of about 1 inch or 1+ inch in diameter, ac- cording as the weather varied ; and the weather being overcaſt, an aperture of 1+ inch ſeemed to do better than a leſs: And had the ob- jets been nearer with the ſun bright upon them, I doubt not but that an aperture of ſomewhat leſs than an inch would have been beſt. This lens when open was 2+ inches wide, and it ſeemed then to form a picture pretty diſtin ; but on clapping to it a ring having a proper aperture, the difference was very conſiderable. The ſun ſhining upon the objects; a lens whoſe focal length was about 30 inches, required an aperture at the leaſt of 1+ inch; and it would bear at moſt, one of about 1+ inch. The picture was thrown into a. box placed in a light room; but had the room itſelf been dark, thoſe apertures would have bore, and even required to have been, conſiderably leſs. In this laſt cafe, an aperture of 1+ inch ſeemed to ſuit very well with a lens of eight foot focus. | | From theſe obſervations, an eſtimate might be made of the proper aperture of a given lens, the object being under given circumſtances. But as the focal lengths of the lenſes are increaſed, there will be no great nicety required in ſettling theſe apertures; only I think they ſhould not be taken much wider, if any, than in the ſubduplicate pro- portion of thoſe lengths : And let us do what we can, the apparent brightneſs of the picture will decreaſe nearly, as the ſquare of the focal length of the lens is increaſed. For this apparent brightneſs will be nearly, as the denſity of the light in the picture, divided by the denſity of the adventitious light in the room. And whatever is the fo- cal length of the lens, the denſity of the adventitious light in the toom, will be nearly as the ſquate of the linear aperture of the lens; and to preſerve the ſame denſity of the light in the picture, the linear aperture muſt be as the focal length of the ſame lens. Wherefore, if the ſame aperture be retained, that is, if the adventitious light in the room remains the ſame ; the apparent brightneſs of the picture, which in this caſe is as the denſity of the rays that form it, will be reci— procally as the ſquare of the focal length of the lens: The apparent brizhtneſs of the picture will be alto in the faid proportion, if the denſity of the light upon it be preſerved the ſame ; that is, . the inear Srcr. IV. OF OPTICS, linear aperture of the lens be taken as its focal length ; for in this caſe, the adventitious light will be directly as the ſquare of the focal length. And in ſettling the linear apertures of different lenſes, we ſhall not much mend the matter, by taking any proportion between the ſimple and ſubduplicate of their focal lengths ; the apparent bright- neſs being here, I think, the chief thing to be regarded, the aber- rations not being ſenſible ; and this brightneſs, as near as I could eſti- mate, is nearly in the propoction above aſſigned. 392. And hence, without ſome method of “ preventing the adventi- Limit of the tious light, from diminiſhing in ſo great a degree the apparent bright- ture be received upon paper, a lens of about 8 foot focus, I take upon the whole to be preferable to one that is longer ; this will repreſent objects in a landſkip, larger than we commonly ſee them in pictures; and the picture will be much brighter, diſtincter and pleaſanter, than if the lens had been flatter. A lens of about 8 foot focus, in the preſent caſe, has manifeſtly a very conſiderable advantage above a lens of 12 foot, and more ſtill proportionably above a lens of a longer focus. As we decreaſe in our focal length, the images will appear brighter, ſharper, and rather more diſtinct and pleaſant, till we come to a certain limit; after this, the picture will be leſs pleaſant and ſeemingly leſs diſtinct, becauſe we ſhall loſe ſome of the ſmaller parts of the objects. This limit as to the leaſt focal length, I do not take to be leſs than 2 or 3 feet ; eſpecially if the picture be received upon paper within a room, for in that caſe, there will not be a convenient ſpace for the ſpectator to view it in, if the lens be ſhorter than as above. Upon the whole, I take it, that a lens from. about 4 to 6 or 8 foot focal length, is the beſt ſize of any for the camera-obſcura, But in ſome caſes, a lens of a yet, longer focus will do better ; and in ſome others we may deſcend to fo ſmall a length as 12 or 8 inches focus, and the picture will be pleaſant enough. 393. In ſome caſes, the breadth of the picture may be about two- thirds of its diſtance from the lens, and even more if the paper for a field or angle of near forty degrees. But in moſt caſes when the field is ſo wide, the middle half of the picture will be diſtincter than towards the extreams ; and therefore generally it is beſt not to take in a larger angle than about 20 or 30 degrees. | M m 2 e * How this may be partly remedied will be ſeen a little farther on. , mm . of lenſes for neſs of the picture; we ſhall ſoon come to a limit, beyond which it the camera- would be uſeleſs to extend the focal lengths of our lenſes. If the pic- obſcura. Extent of the field that may be taken in receiving it be made a little concave ; that is, the picture may take in the pifure. | 267 lengths 268 Glaſs poliſh- ed only on one fide for receiving the images. The pheno- mena farther explained. Fig. 100. A TREATISE Bock II. 394. If inſtead of the white paper or cloth for receiving the pic- ture, be placed a glaſs having both its ſides ground flat and parallel, and poliſhed only on one ſide; a ſpeCtator behind the glaſs will ſee the images vaſtly more vivid, diſtin& and bright, than by the reflec- tion from the paper. The rays of light in their paſſage through the rough ſurface of the glaſs, are there broke and diſperſed, after the ſame manner as they were by the paper, and ſo as to paint there as it were the images ot the objects from whence they came. But here the rays tranſmitted are not ſo much diſſipated, as they are by the reflection of an opaque ſurface ; and ſo the rays being denſer, the ſpectator be- hind receives a greater quantity in each pencil, than when he ſees the picture upon the paper *. In this caſe, the ſpectator is alſo leſs of- tended with extraneous light, and it would be eaſy to exclude from him all ſuch light, excepting what falls on the glaſs itſelf, and is tranſmitted through it; and hence, from theſe two concurring cauſes, we may have a good picture by a much ſhallower or a much deeper lens, than when the rays are reflected from the paper. 