per, the light of the fun refracted through alglobe or cylinder of glass filled with water. If the paper is held parallel to the axis of the cylinder, and clofe to it, the illuminated part will be bounded by two very bright, parallel lines, where it is cut by the curve; and these lines will gradually approach each other as the paper is withdrawn from the veffel, till they coalefce into one very bright line at F, or near it. If the paper be held with its end touching the veffel, and its plane nearly perpendicular to the axis, the whole progress at the curve will be diftinétly feen.

544. As fuch globes were ufed for burning glaffes, the point of greatest condensation (which is very near but not exactly in F) was called the focus. When these curves were obferved by Mr TCHIRNHAUSS, he called them cauftics; and thofe formed by refraction he called diacauftics, to diftinguifh them from the catacauftics formed by reflection. It is fomewhat furprifing, that thefe curves have been fo little ftudied fince the time of Tchirnhaufs. The doctrine of aberrations has indeed been confidered in a manner independent on their properties. But whoever confiders the progrefs of rays in the eye-piece of optical inftruments, will fee that the knowledge of the properties of diacauftic curves determines directly, and almoft accurately, the foci and images that are formed there. For let the object-glafs of a telescope or microscope be of any dimenfions, the pencils incident on the eye-glaffes are almost all of this evanefcent bulk. These advantages will be shown in their proper places: we proceed at prefent to confider the aberrations of parallel incident

rays.

544. From the instance represented by the figure, it is evident that the cauftic will touch the furface in a point, so fituated that co:=m:n. The refracted ray will touch the furface, and will cross the axis in, the nearest limit of diffufon along the axis. If the furface is of smaller extent, as PV, the cauftic begins at ƒ, when the extreme refracted ray Pƒtouches the cauftic and croffes the axis in F', and the oppofite branch of the cauftic in K. If there be drawn an ordinate KO k to the cauftic, it is evident that the whole light incident on the furface PV п paffes through the circle whofe diameter is K k, and that the circle is the smallest space which receives all the re fracted light.

546. It is of great importance to confider the manner in which the light is diftributed over the furface of this circle of fmalleft diffufion; for this is the representation of one point of the infinitely diftant radiant object. Each point of a planet, for inftance, is reprefented by this little circle; and as the circles reprefenting the different adjacent points muft interfere with each other, an indiftinct nefs muft arife, fimilar to what is obferved when we view an object through a pair of fpectacles which do not fit the eye. The indiftinctnefs must be in proportion to the number of points whofe circles of diffufion interfere; that is, to the area of thefe circles, provided that the light is uniformly diffuffed over them: but if it be very rare at the circumference, the impreffion made by the circles belonging to the adjacent points must be efs fenfible. Accordingly Sir ISAAC NEWTON,

fuppofing it incomparably rarer at the circumference, than towards the centre, affirms, that the indiftinctness of telescopes, arifing from the spheri cal figure of the object-glafs. was fome thousand times less than that arifing from the unequal refrangibility of light; and therefore, that the attempts to improve them by diminishing or removing this aberration were needlefs, while the indif tinctness from unequal refrangibility remained. It is furprifing, that a philofopher fo eminent for fas gacity and for mathematical knowledge fhould have made fuch a mistake, and unfortunate that the authority of his great name hindered others from examining the matter, trufting to his affertion, that the light was fo rare at the border of this circle. His miftake is furprising, because the very nature of a cauftic fhould have fhowed him, that the light was infinitely denfer at the borders of the circle of fmalleft diffufion. The first perfon who detected this oversight of the British philosópher was the Abbe BOSCOVICH, who, in a differtation publifhed at Vienna in 1767, fhowed, by a very beautiful analyfis, that the diftribution was extremely different from what Newton had afferted, and that the fuperior indiftinctness arifing from unequal refrangibility was incomparably lefs than he had faid. We fhall attempt to make this delicate and interesting matter conceivable by thofe who have but small mathematical preparation.

547. Let the curve DVZCI c z v d(fig. 2. Pl. CCLIX.) be the caustic (magnified), EI its axis, I the focus of central rays, B the focus of extreme rays, and IB the line containing the foci of all the intermediate rays, and CO e the diameter of the circle of smallest diffufion. It is plain, that from the centre O there can be drawn two rays OV, Ov, touching the cauftic in V, v. Therefore the point O will receive the ray EO, which paffes through the vertex of the refracting furface, and all the rays which are incident on the circumfe rence of a circle defcribed on the refracting furface by the extremity of the ray OV, or O v. The denfity of the light at O will therefore be indefinitely great. From the point C there can be drawn two rays; one of them CX touching the cauftic in C, and the other C, touching it at d on the oppofite fide. The rays which touch the cauftic in the immediate vicinity of Cy, both in the arch CV and the arch CI will cut OC in points indefinitely near to each other; because their distance from each other in the line OC will be to their uniform diflapce on the refracting furface, as the distance between their points of contact with the cauftic to the distance of these points from the refracting furface. Here therefore at C the density of the light will also be indefinitely great. From any point H, lying between O and C, may be drawn three rays. One of them, LHT, P, touching the arch CD of the cauftic in T, cutting the refracting furface in P, and the axis in L: ano. ther t Hp, touching the arch CI of the cauftic în t. The third is HT, touching the arch c d of the oppofite branch of the caustic in 7.

548. It will greatly affift our conceptions of this fubject, if we confider a ray of light from the refracting surface as a thread attached at I of this figure, or at F of fig. 1. Pl. CCLIX, and gradually

unlapped

unlapped from the cauftic DNCI on one fide, and then lapped on the oppofite branch Icvd; and attend to the point of its interfection with the diameter QC of the circle of fmalleft diffufion. Therefore, 1. let the ray be firft supposed to pals through the refracting furface at F, the right hand extremity of the aperture. The thread is then folded up on the whole right hand branch ICVD of the cauftic; and if the ftraight part of it FD be produced, it will cut the diameter of the circle of fmallelt diffufion in the oppofite extremity c. Or suppose a ruler, in place of the thread, applied to the cauftic at D and to the refracting furface at F, the part of it Dc, which is detached from the cauftic, cuts CO in the point c. 2. Now fup pofe the ruler to revolve gradually, its extremity moving across the arch FAƒ of the refracting furface, while the edge is applied to the cauftic; the point of contact with the cauftic will fhift gradually down the branch DV of the cauftic, while its edge paffes across the line e C; and when the point of contact arrives at V, the extremity will be at Y on the refracting furface, and the interfection of the edge will be at O. 3. Continuing the motion, the point of contact shifts from V to Z, the extremity from Y to Q', and the interfection from OC2 O to Q, fo that OQ' as will prefently appear. 4. After this, the point of contact will shift from 2 to C, the extremity from Q' to X, halfway from F to A, as will foon be shown, and the interfection from Q to C. 5. The point of contact will now fhift from C down to I, the extremity will pafs from X to A, and the interfection will go back from C to O. 6. The ruler muft now be applied to the other branch of the cauftic Iezvd, and the point of contact will afcend from I to c, the extremity will pafs from A to , half way to ƒ from A, and the interfection from O to C. 7. The point of contact will afcend from C to z, the extremity paffes from x to q', and the interOca fection from Ċ to g, Oq' being

2

2

8. While

the contact of the ruler and cauftic shifts from to v, the extremity fhifts from q' to y, and the interfection from q to O. 9. The contact rifes from vto d, the extremity paffes from y to f, and the interfection from O to C; and then the motion across the refracting furface is completed, the point of contact fhifting down from D to I, along the branch DVZCI, and then afcending along the other branch Iczvd, while the interfection pafies from c to C, back again from Ctor, and then back again from c to C, where it ends, having thrice paff ed through every intermediate point of c C.

549. We may form a notion of the DENSITY of the LIGHT in any point H, by fuppofing the incident light of uniform denfity at the refracting furface, and attending to the conftipation of the rays in the circle of smallest diffufion. Their vicinity may be eftimated both in the direction of the radii OH, and in the direction of the circumference defcribed by its extremity H, during its revolution round the axis; and the denfity muft be conceived as proportional to the number of originally equidiftant rays, which are collected into a spot of given area. These have been collected from a cor

refponding fpot or area of the refracting furface; and as the number of rays is the fame in both, the denfity at H will be to the denfity of the refracting furface, as the area occupied of the refracting furface to the correfponding area at H. The vicinity of the rays in the direction of the radius depends on the proportion between PT and TH. For the ray adjacent to PTH may be fupposed to crofs it at the point of contact T; and therefore the uniform diftance between them at the furface of that medium is to the diftance between the fame rays at H as the distance of T from the refracting furface to its diftance from H. Therefore the number of rays which occupy a tenth of an inch, for example, of the radius AP, is to the number which would occupy a tenth of an inch at H as TH to TP; and the radical density at P, is to the radical denfity at H alfo, as TH to TP.-In the next place, the circumferential denfity at P is to that at H, as the radius AP to the radius OH. For fuppofing the figure to turn found its axis AI, the point P of the refracting furface will defcribe a circumference whose radius is AP, and H will defcribe a circumference whose radius is OH; and the whole rays, which pass through the firft circumference, pafs alfo through the laft; and therefore their circumferential denfities will be the inverfe proportion of the spaces into which they are collected. Now the radius AP is to the radius OH as AL to OL; and circumferences have the fame proportion with their radii. Therefore the circumferential density at P is to that in H as AL to OL inversely; and it was found, that the radical denfity was as AN to ON inversely, being as TH to TP, which are very nearly in this ratio. Therefore the abfolute denfity (or number of rays collected in a given space) at P will be to that at H, in the ratio compounded of thefe ratios; that is, in the ratio of ONXOL to ANX AL. But as NL bears but a very small ratio to AN or AL, ANXAL may be taken as equal to AO without any fenfible error. It never differs from it in telefcopes rooth part, and is ge nerally incomparably smaller. Therefore the denfity at H may be confidered as proportional to ONXOL inverfely. And it will afterwards appear that NS is 3 L. Therefore the density at His inverfely as ONX NS.

the

and draw NT cutting the circumference Ne*= 550. Now defcribe a circle on the diameter OS, NXNS, and the density at H is as No inverfely. This gives us a very eafy eftimation of the denfity, viz. draw a line from the point of contact of and the denfity is the inverfe fubduplicate ratio ray which touches the part VC of the cauftic, of the part of this line intercepted between the axis and the circumference SpỖ. It will afterwards appear that the denfity correfponding to all the three: or a better expreffion will be had this ray is one half of the denfity correfponding to for the denfity at H by drawing R& perpendicular to R, and so perpendicular to ß, making 4 R in o; then e o is as, or is proportional to the denfity, as is evident. When H is at O, N is at S, and is infinite. As H moves from O, N defcends, and diminishes, till H comes to Q, and T to z, and p to, and o to R. When H

I

་ moves

moves from Q towards C, T defcends below 2; 90 again increases, till it is again infinite, when H is at C, Tat C, and N at O. Thus it appears, without any minute confideration, that the light has a den. fity indefinitely great in the centre O; that the denfity decreases to a minimum in fome intermediate point Q and then increafes again to infinity at the margin C. Hence it follows, that the indiftin&tnefs arifing from the fpherical figure of the refracting furfaces is incomparably greater than Newton fuppofed; and that the valuable difcovery of Mr Dol lond of achromatic lenfes, must have failed of anfwering his fond expectations, if his very method of producing them had not, at the fame time, enabled him to remove that other indiftinctnefs, by employing contrary aberrations. And now, fince the difcoveries by Dr BLAIR of fubftances which difperfe the different colours in the fame proportions, but very different degrees, has enabled us to employ much larger portions of the fphere than Mr Dollond could introduce into his object glaffes, it becomes abfolutely neceffary to ftudy this matter completely, in order to difcover and afcertain the amount of the errors which perhaps unavoidably remain.

551. This flight fketch of the moft fimple cafe of aberration, namely, when the incident rays are parallel, will ferve to give a general notion of the fubject; and the reader can now fee how contrary aberrations may be employed in order to form an ultimate image which fhall be as diftinct as poffi ble. For let it be propofed to converge parallel rays accurately to the focus F,(fig. 3. pl. CCLIX.) by the refraction of fpherical furfaces of which is the vertex. Let PV be a convex lens of fuch a form that rays flowing from F, and paffing through it immediately round the vertex V, are collected to the conjugate focus R, while the extreme ray FP, incident on the margin of the lens P, is converged to r, nearer to V, having the longitudinal aberra: tion Rr. Let pV be a plano concave lens, of fuch fphericity that a ray Ap, parallel to the axis CV, and incident on the point p, as far from its vertex V as P in the other lens is from its vertex, is difperfed from r, the diftance V being equal to TV, while the central rays are difperfed from P, as far from Vas R is from V. It is evident, that if thefe lenfes be joined as in fig. 4. a ray A'p, parallel to the common axis CV, will be collected at the dif, tance VF equal to VF in fig. 4. and that rays paf fing through both lenfes in the neighbourhood of the axis will be collected at the fame point F.

SECT. III. Of OPTICAL INSTRUMENTS. 553. For the conftruction of optical inftruments. See TELESCOPE. Or the mechanifm of thefe inftruments particular accounts are given in this work under their refpective denominations. But as it belongs to the fcience of optics to explain, by the laws of refraction and reflection, the feveral pheno mena which thefe inftruments exhibit, we must in this place enumerate the inftruments themselves, omitting entirely, or ftating very briefly, fuch facts as are stated at large in other places. In this enumeration we begin with the multiplying glass, not because it is firft in importance, but that it may not intervene between inftruments, more useful, and which have a mutual relation to one another.

SI. Of the MULTIPLYING GLASS. 554. THE multiplying glafs is made by grinding down the round fide bik (Fig. 7. Pl. CCLVIII.) of a plano-convex glafs AB, into feveral flat furfaces, as h b, bid, dk. An object C will not appear magnified when feen through this glafs by the eye at H; but it will appear multiplied into as many different objects as the glafs contains plane furfaces. For, fince rays will flow from the object C to all parts of the glafs, and each plane furface will refract thefe rays to the eye, the fame object will appear to the eye in the direction of the rays which enter it through each furface. Thus, a ray giH, falling perpendicularly on the middle furface, will go through the glafs to the eye without fuffering any refraction; and will therefore fhow the object in its true place at C: whilft a ray ab flowing from the fame object, and falling obliquely on the plane furface & b, will be refracted in the direction be, by paffing through the glafs; and, upon leaving it, will go on to the eye in the direction e H; which will caufe the fame object C to appear alfo at E, in the direction of the ray H e, produced in the right line Hen. And the ray 4, flowing from the object C, and falling obliquely on the plane furface dk, will be refracted (by paffing through the glafs, and leaving it at f to the eye at H; which will canfe the fame object to appear at D, in the direction HfmmIf the glafs be turned round the line g, as an axis, the object C will keep its place, because the furface bld is not removed; but all the other objects will feem to go round C, becaufe the oblique planes, on which the rays a b c d fall, will go round by the turning of the glass.

556. Let AB (fig. 8, pl. CCLVIII.) be an object before the reflecting furface ghi of the plane mirror CD and let the eye be at o. Let Ah be a ray of light flowing from the top A of the object, and falling upon the mirror at h, and hm be a perpendicular to the furface of the mirror at h; the ray Ah will be reflected from the mirror to the eye at o, making an angle 'm ho equal to the angle Ahm: then will the top of the image E appear to the eye in the direction of the reflected ray ob produced to E, where the right line ApE, from the top of the object, cuts the right line ob E, at E. Let Bi be a ray of light proceeding from the foot of the object at B to the mirror at i; and ni a perpendicular to the mirror from the point i, where the ray Bi falls upon it: this ray will be reflected in the line io, making an angle nio equal the angle Bin, with that perpendicular, and enter. ing the eye at o; then will the foot F of the image appear in the direction of the reflected ray oi, produced to F, where the right line BF cuts the reflected ray produced to F. All the other rays that flow from the intermediate points of the object. AB, and fall upon the mirror between and i, will be reflected to the eye at o; and all the intermediate points of the image EF will appear to the eye in the direction of these reflected rays produ. ced. But all the rays that flow from the object, and fall upon the mirror above h, will be reflected back above the eye at o; and all the rays that flow from the object, and fall upon the mirror below i, will be reflected back below the eye at o; fo that none of the rays that fall above h, or below i, can be reflected to the eye at o; and the dif. tance between h and i is equal to half the length of the object AB. Hence it appears, that if a man fees his whole image in a plane looking-glafs, the part of the glafs that reflects his image muft be juft half as long and half as broad as himself, let him ftand at any diftance from it whatever; and that his image muft appear juft as far behind the glafs as he is before it. Thus, the man AB (fig. 9. pl. CCLVIII.) viewing himself in the plane mirror CD, which is just half as long as himself, fees his whole image as at EF, behind the glass, exactly equal to his own fize. For a ray AC proceeding from his eye at A, and falling perpendicularly upon the furface of the glafs at C, is reflected back to his eye, in the fame line CA; and the eye of his image will appear at E, in the fame line produced to E, beyond the glafs. And a ray BD, flowing from his foot, and falling obliquely on the glafs at D, will be reflected as obliquely on the other fide of the perpendicular a b D, in the direc tion DA; and the foot of his image will appear at F, in the direction of the reflected ray AD, produced to F, where it is cut by the right line BGF, drawn parallel to the right line ACE. Juft the fame as if the glafs were taken away, and a real man food at F, equal in fize to the man ftanding at B: for to his eye at A, the eye of the other man at E would be feen in the direction of the line ACE; and the foot of the man at F would be feen by the eye A, in the direction of the line ADF. If the glafs be brought nearer the man AB, as fuppofe to tb, he will fee his image as at CDG: for the reflected ray CA (being perpendi

cular to the glafs) will show the eye of the image as at C; and the incident ray Bb, being reflected in the line 6 A, will how the foot of his image as at G; the angle of reflection ab A being always equal to the angle of incidence Bba: and fo of all the intermediate rays from A to B. Hence, if the man AB advances towards the glass CD, his image will approach towards it; and if he recedes from the glafs, his image will alfo recede from it. 557. If the object be placed before a common looking-glafs, and viewed obliquely, three, four, or more images of it, will appear behind the glass. To explain this, let ABCD (fig. 10. pl. CCLVIII.) reprefent the glafs; and let EF be the axis of a pencil of rays flowing from E, a point in an object fituated there. The rays of this pencil will in part be reflected at F, fuppofe into the line FG. What remains will (after refraction at F, which we do not confider here) pass on to H; from whence (on account of the quickfilver which is spread over the fecond furface of glaffes of this kind, to prevent any of the rays from being transmitted there) they will be ftrongly reflected to K, where part of them will emerge and enter an eye at L. By thefe means one reprefentation of the faid point will be formed in the line LK produced, fuppofe in M; Again, another pencil, whose axis is EN, first reflected at N, then at O, and afterwards at P, will form a second reprefentation of the fame point at Q: And thirdly, another pencil, whofe axis is ER, after reflection at the feveral points R, S, H, T, V, fucceffively, will exhibit a third representation of the fame point at X; and fo on in infinitum. The fame being true of each point in the object, the whole will be reprefented in the like manner; but the reprefentations will be faint, in proportion to the number of reflections the rays fuffer, and the length of their progrefs within the glafs. We may add to these another representation of the fame object in the line LO produced, made by fuch of the rays as fall upon O, and are from thence reflected to the eye at L. This experiment may be tried by placing a candle before the glafs as at E, and viewing it obliquely as from L.

158. Of CONCAVE and CONVEX MIRRORS. The effects of thefe in magnifying and diminishing objects have been already in general explained; but for the better understanding the nature of reflecting telescopes, it will fill be proper to fubjoin the following particular defcription of the effects of concave ones.

559. When parallel rays (fig. 11, pl. CCLVIII.) as dfa, Cmb, ele, fall upon a concave mirror AB (which is not tranfparent, but has only the furface AbB of a clear polifh), they will be reflected back from that mirror, and meet in a point m, at half the distance of the furface of the mirror from C, the centre of its concavity; for they will be reflected at as great an angle from a perpendi cular to the furface of the mirror, as they fell up on it with regard to that perpendicular, but on the other fide thereof. Thus, let C be the centre of concavity of the mirror AbB; and let the parallel rays dfa, Cm b, and ele, fall upon it at the points a, b, and c... Draw the lines Cia, Cmb, and Che, from the centre C to thefe points; and all these lines will be perpendicular

to

to the furface of the mirror, because they proceed thereto like so many radii or spokes from its centre. Make the angle Cah equal to the angle da C, and draw the line a mh, which will be the direction of the ray dfa, after it is reflected from the point a of the mirror; fo that the angle of incidence da C is equal to the angle of reflection Cab; the rays making equal angles with the perpendicular Cia on its oppofite fides. Draw alfo the perpendicular Che to the point c, where the ray ele touches the mirror; and having made the angle Cei equal to the angle Cce, draw the line e mi, which will be the courfe of the ray elc, after it is reflected from the mirror. The ray Cmb paffing through the centre of concavity of the mirror, and falling upon it at b, is perpendicular to it; and is therefore reflected back from it in the fame line bm C. All these reflected rays meet in the point m; and in that point the image of the body which emits the parallel rays da, Cb, and ec, will be formed; which point is diftant from the mirror equal to half the radius bm C of its concavity.

560. The rays which proceed from any celeftial object may be efteemed parallel at the earth; and therefore the image of that object will be formed at m, when the reflecting furface of the concave mirror is turned directly towards the object. Hence the focus m of parallel rays is not in the centre of the mirror's concavity, but half way between the mirror and that centre. The rays which proceed from any remote terrestrial object are nearly parallel at the mirror; not ftrictly fo, but come diverging to it, in feparate pencils, or as it were bundles of rays, from each point of the fide of the object next the mirror; and therefore they will not be converged to a point at the diftance of half the radius of the mirror's concavity from its reflecting furface, but into feparate points at a little greater diftance from the mirror. And the nearer the object is to the mirror, the farther thefe points will be from it; and an inverted image of the object will be formed in them, which will feem to hang pendant in the air; and will be seen by an eye placed beyond it (with regard to the mirror) in all refpects like the object, and as distinct as the object itself.

361. Let AcB (fig. 12. pl. CCLVIII.) be the reflecting furface of a mirror, whofe centre of concavity is at C; and let the upright object DE be placed beyond the centre C, and fend out a conical pencil of diverging rays from its upper extremity D, to every point of the concave furface of the mirror Ac B. But, to avoid confufion, we only draw three rays of that pencil, as DA, Dc, DB. From the centre of concavity C draw the three right lines CA, Cc, CB, touching the mirror in the fame points where the forefaid rays touch it; and all these lines will be perpendicular to the furface of the mirror. Make the angle CA d equal to the angle DAC, and draw the right line Ad for the courfe of the reflected ray DA: make the angle Ced equal to the angle DC, and draw the right line ed for the courfe of the reflected ray Dd: make alfo the angle CBd equal to the angle DBC, and draw the right line Bd for the course of the reflected ray DB. All thefe reVOL. XVI. PART II.

flected rays will meet in the point d, where they will form the extremity d of the inverted image ed, fimilar to the extremity D of_the_upright object DE. If the pencil of rays Ef, Eg, Eh, be alfo continued to the mirror, and their angles of reflection from it be made equal to their angles of incidence upon it, as in the former pencil from D, they will all meet at the point e by reflection, and form the extremity e of the image e d fimilar to the extremity E of the object DE. And as each intermediate point of the object, between D and E, fends out a pencil of rays in like manner to every part of the mirror, the rays of each pencil will be reflected back from it, and meet in all the intermediate points between the extremi tiese and d of the image; and fo the whole image will be formed, not at i, half the diftance of the mirror from its centre of concavity C, but at a greater diftance, between and the object DE; and the image will be inverted with respect to the object.

562. When the object is more remote from the mirror than its centre of concavity C, the image will be less than the object, and between the object and mirror; when the object is nearer than the centre of concavity, the image will be more remote and bigger than the object. Thus, if ED be the object, de will be its image: for, as the object recedes from the mirror, the image approaches nearer to it; and as the object approaches nearer to the mirror, the image recedes farther from it, on account of the leffer or greater divergency of the pencils of rays which proceed from the object; for the lefs they diverge the fooner they are converged to points by reflection; and the more they diverge, they farther they must be reflected before they meet. If the radius of the mirror's concavity, and the diftance of the object from it, be known, the diftance of the image from the mirror is found by this rule: Divide the product of the distance and radius by double the diftance made lefs by the radius, and the quotient is the diftance required. If the object be in the centre of the mirror's concavity, the image and object will be coincident, and equal in bulk. If a man places himself directly before a large concave mirror, but farther from it than its centre of concavity, he will fee an inverted image of himfelf in the air between him and the mirror, of a lefs fize than himfelf. And if he holds out his hand towards the mirror, the hand of the image will come out towards his hand, and coincide with it, of an equal bulk, when his hand is in the centre of concavity; and he will imagine he may fhake hands with his image. If he reaches his hand farther, the hand of the image will pafs by his hand, and come between his hand and his body; and if he moves his hand towards either fide, the hand of the image will move towards the other; fo that whatever way the object moves, the image will move the contrary. All the while a bystander will fee nothing of the image, becaufe none of the reflected rays that form it enter his eyes,

III. Of MICROSCOPES.

563. Under the article MICROSCOPE a copious detail has been given of the conftruction of those inftruments, as they are now made by the most Hhh eminent