eminent artists. In that article it fell not within our plan to treat scientifically of their magnifying powers; thefe can be explained only by the laws of refraction and reflection, which we fhall therefore apply to a few microfcopes, leaving our readers to make the application themselves to fuch others as they may chufe to analyze by optical principles. and f, till they come to the eye at k, where they will begin to converge by the refractive power of the humours; and after having croffed each other in the pupil, and paffed through the cryftalline and vitreous humours, they will be collected into points on the retina, and form the large inverted image AB thereon. 566. By this combination of lenfes, the aberration of the light from the figure of the glass, which in a globule of the kind above-mentioned is very confiderable, is in fome measure corrected. This appeared fo fenfibly to be the cafe, even to former opticians, that they foon began to add another lens. The inftrument, however, receives a confiderable improvement by the addition of a third lens; for, fays Mr MARTIN, it is not only evident, from the theory of this aberration, that the image of any point is rendered lefs confufed by refraction through two lenfes than by an equal refraction through one; but it alfo follows, from the fame principle, that the fame point has its image ftill lefs confufed, when formed by rays refracted through three lenfes than by an equal refraction through two;, and therefore a third lens added to the other two will contribute to make the image more diftinct, and confequently the inftrument more complete. At the fame time the field of view is amplified, and the ufe of the microscope rendered more agreeable by the addition of the other lens. Thus alfo we may allow à fomewhat larger aperture to the object lens, and thereby increafe the brightnefs of objects, and greatly heighten the pleasure of viewing them. For the fame reafon, Mr Martin made a fourglafs microfcope, which anfwers the purposes of magnifying and of diftinct vifion still more perfectly. 564. The firft and fimpleft of all microfcopes is nothing more than a very fmall globule of glafs, or a convex lens whose focal distance is extremely hort. The magnifying power of this microscope is thus afcertained by Dr SMITH: "A minute object pq, feen diftin&tly through a small glafs AE (fig. 5. and 6. pl. CCLIX.) by the eye put clofe to it, appears fo much greater than it would to the naked eye, placed at the leaft diftance qL from whence it appears fufficiently diftinct, as this latter diftance q L is greater than the former E; for, having put your eye close to the glafs EA, in order to fee as much of the object as poffible at one view, remove the object pq to and fro till it appear moft diftinctly, fuppofe at the diftance Eq. Then conceiving the glafs AE to be removed, and a thin plate with a pin-hole in it to be put in its place, the object will appear diftinct and as large as before, when feen through the glafs, only not fo bright. And in this latter cafe it appears fo much greater than it does to the naked eye at the diftance q L, either with the pin-hole or without it, as the angle p E q is greater than the angle pLq, or as the latter diftance 4 L is greater than the former q E. Since the interpofition of the glafs has no other effect than to render the appearance diftinct, by helping the eye to increase the refraction of the rays in each pencil, it is plain that the greater apparent magnitude is entirely owing to a nearer view than 567. The magnifying power of double microcould be taken by the naked eye. As the human fcopes is eafily underflood, thus: The glass L eye is fo conftructed, as, for reafons already next the object PQ (fig. 14, plate CCLVIII.) is affigned, to have diftinct vifion only when the very small, and very much convex, and confe rays which fall upon it are parallel or nearly fo; quently its focal diftance LF is very fhort; the it follows, that if the eye be fo perfect as to fee diftance LQ of the small object PQ is but a little diftinctly by pencils of parallel rays falling upon greater than LF: Greater it muft be, that the it, the diftance E q, of the object from the glafs, is rays flowing from the object may converge after then the focal distance of the glafs. Now, if the paffing through the glafs, and, croffing one another, glafs be a small round globule, of about one 15th form an image of the object; and it must be but of an inch diameter, its focal diftance E q, being a little greater, that the image pg may be at a three quarters of its diameter, is one 20th of an great distance from the glafs, and confequently inch; and if L be eight inches, the diftance at much larger than the object itfelf. This picture which we ufually view minute objects, this glo- q, being viewed through a convex glafs AE, bule will magnify in the proportion of eight to whofe focal diftance is q E, appears diftine as in a telescope. Now the object appears magnified upon two accounts; firft, becaufe, if we viewed its picture pq with the naked eye, it would appear as much greater than the object, at the fame diftance, as it really is greater than the object, or as much as Lq is greater than LQ: and, adly, because this picture appears magnified through the eye-glafs, as much as the leaft diftance, at which it can be feen diftinctly with the naked eye, is greater than qE, the focal distance of the eye-glafs. For example, if this latter ratio be five to one, and the former ratio of Lg to LQ be 20 to one, then, upon both accounts, the object will appear 5 times 20, or 100 times greater than to the naked eye. Fig. 1, Plate CCLX. reprefents the fection of a compound microscope with 3 lenfes. one 20th, or of 160 to 565. The DOUBLE or COMPOUND MICROSCOPE (fig. 13. plate CCLVIII) confifts of an object glafs cd, and an eye-glafs ef. The fmall object b is placed at a little greater diftance from the glafs cd than its principal focus; fo that the pencils of rays flowing from the different points of the object, and paffing through the glafs, may be made to converge, and unite in as many points between g and b, where the image of the object will be formed; which image is viewed by the eye through the eye-glafs ef For the eye-glafs being fo placed, that the image gb may be in its focus, and the eye much about the fame diftance on the other fide, the rays of each pencil will be parallel after going out of the eye-glafs, as at e By By the middle one GK the pencils of rays coming from the object-glafs are refracted fo as to tend to angle equal to ≈lx, which is as x mnPQ; and PQ appears under an angle PoQ which is as- and d therefore is magnified in the ratio of these angles, that is, of mnd to xl. a focus at Ŏ; but being intercepted by the pro-to the naked eye at the distance d from PQ, it per eye-glafs DF, they are brought together at I, which is nearer to that lens than its proper focus at L; fo that the angle DIF, under which the object now appears, is larger than DLF, under which it would have appeared without this additional glafs and confequently the object is more magnified in the fame proportion. Dr HOOKE tells us, that, in most of his obfervations, he made use of a double microscope, with this broad middle glass, when he wanted to see much of an object at one view, taking it out when he would examine the fmall parts of an object more accurately; for the fewer refractions there are, the more bright and clear the object appears. 568. Having given a practical account of the conftruction of Dr SMITH's double reflecting microscope in § 210, it is proper in this place to afcertain its magnifying power. This we shall do from the author himself, because his fymbols, being general, are applicable to fuch microscopes of all dimenfions; and though the mere practical reader may perhaps be at first fight puzzled by them, yet, if he will fubftitute any particular numbers for m and n, &c. he may afcertain with eafe the magnifying power of fuch a microscope of those particular dimenfions. 569. Between the centre E and principal focus T of a concave speculum ABC, (fig. 2. Plate CCLX.) whofe axis is EQTC, place an object PQ; (fig. 7. Plate CCLIX.) and let the rays flowing from it be reflected from the speculum AB towards an image pq; (fig. 2. Plate CCLX.); but before they unite in it, let them be received by a convex fpeculum abc, and thence be reflected, through a hole BC in the vertex of the concave, to a 2d image ax, to be viewed through an eye-glafs 1. The object may be fituated between the fpecula C, c; or, which is better, between the principal focus and vertex c of the convex one, a small hole being made in its vertex for the incident rays to pass through. In both cafes we have TQ, TE, Tq, continual proportionals in fome given ratio, fuppofe of 1 to n; and alfo tq, te, tx, continual proportionals in fome other given ratio, fuppofe of 1 to m. Then if d be the ufual distance at which we view minute objects distinctly with the naked eye, and xl the focal diftance of the leaft eye-glafs, through which the object appears fufficiently bright and diftinct, it will be magnified in the ratio of mnd to xl. For the object PQ, and its firft image pq, are terminated on one fide by the common axis of the fpecula, and on the other by a line PEp, drawn through the centre E of the concave ABC. Likewife the images pq and x are terminated by the common axis and by the line epa, drawn through the centree of the convex abc (Euclid. v. 12.). Hence, by the fimilar triangles axe, pqe, and alfo pq E, PQE, we have ex: pq:: xe: qe::m: 1, and pq: PQ:: qE: QE::n: 1; and confequently wx: PQ:: mn: I, whence x=mn x PQ. Now if x be the focal diftance of the eye-glafs 4, the points P, Q, of the object, are feen through it by the rays of two pencils emerging parallel to the lines, * respectively; that is, PQ appears under an 569. Corol. Having the numbers m, n, d, to find an eye-glafs which shall cause the microscope to magnify M times in diameter, take x/mnd M For the apparent magnitude is to the true as M: 1 :: mnd: xl. 570. We fhall conclude with the following eafy method of ascertaining the magnifying power of fuch microscopes as are most in ufe. The apparent magnitude of any object is measured by the angle under which it is feen; and this angle is greater or smaller according as the object is near to or far from the eye; and of confequence the lefs the diftance at which it can be viewed the larger it will appear. The naked eye is unable to diftinguish any object brought exceedingly near it: but looking through a convex lens, however near the focus of that lens be, there an object may be diftinctly seen; and the smaller the lens is, the nearer will be its focus, and in the fame proportion the greater will be its magnifying power. From these principles, it is easy to find the reafon why the firft or greateft magnifiers are fo extremely minute; and alfo to calculate the magnifying power of any convex lens employed in a fingle microfcope: For as the propor tion of the natural fight is to the focus, fuch will be its power of magnifying. If the focus of a convex lens, for inftance, be at one inch, and the natural fight at 8 inches, which is the common ftandard, an object may be seen through that lens at one inch diftance from the eye, and will appear in its diameter 8 times larger than it does to the naked eye: but as the object is magnified every way, in length as well as in breadth, we must fquare this diameter to know how much it really is enlarged; and we then find that its fuperficies is magnified 64 times. 571. Again, fuppofe a convex lens whofe focus is only one tenth of an inch distant from its centre; as in 8 inches, the common diftance of diftinct vifion with the naked eye, there are 80 fuch tenths, an object may be feen through this glafs 80 times nearer than with the naked eye. It will, of confequence, appear 80 times longer, and as much broader, than it does to common fight; and there. fore is 6400 times magnified. If a convex glais be fo small that its focus is only of an inch dif tant, we find that 8 inches contains 160 of these 20th parts; and of confequence the length and breadth of any object feen through fuch a lens will be mage nified 160 times, and the whole furface 25.600 times. As it is an eafy matter to melt a drop or globule of a much smaller diameter than a lei sein be ground, and as the focus of a globule is no latther off than a quarter of its own diameter, it ma of confequence magnify to a prodigious degree. But this exceffive magnifying power is much more than counterbalanced by its admitting to de Hhh 2 light light, want of diftinctness, and showing fuch a minute part of the objects to be examined; for which reafon, thefe globules, though greatly in vogue fome time ago, are now almost entirely rejected. Mr LEEUWENHOEK made ufe only of fingle microscopes confifting of convex lenfes, and left to the Royal Society a legacy of 26 of thofe glaffes. According to Mr FOLKES'S' defcription of thefe, they were all exceedingly clear, and fhowed the object very bright and diftin&t; "which (fays he) must be owing to the great care this gentleman took in the choice of his glafs, his exactness in giving it the true fi gure, and afterwards, among many, referving only fuch for his ufe as upon trial he found to be moft excellent. Their powers of magnifying are different, as different objects may require: and as, on the one hand, being all ground glaffes, none of them are fo fmall, or confequently magnify to fo great a degree, as fome of thofe drops frequently used in other microscopes; yet, on the other hand, the diftin&tnefs of these very much exceeds what I have met with in glaffes of that fort. And this was what Mr Leeuwenhoek ever propofed; rejecting all thofe degrees of magnifying, in which he could not fo well obtain that end. For he informs us in one of his letters, that though he had above 40 years by him glaffes of an extraordinary fmallnefs, he had made but very little ufe of them; as having found in a long courfe of experience, that the most confiderable difcoveries were to be made with fuch glaffes as, magnifying but moderately, exhibited the object with the greatest brightnefs and diftinctnefs." $72. In a fingle microscope, to learn the magnifying power of any glafs, no more is neceffary than to bring it to its true focus, the exact place whereof will be known by an object appearing perfectly diftinct and fharp when placed there. Then, with a pair of small compaffes, meafure, as nearly as poffible, the distance from the centre of the glafs to the object, and afterwards applying the compaffes to any ruler, with a diagonal fcale of the parts of an inch marked on it, you will eafily find how many parts of an inch the faid distance is. When that is known, compute how many times thofe parts of an inch are contained in 8 inches, and that will give the number of times the diameter is magnified; fquaring the diameter will give the fuperficies; and the folid contents will be fhown by multiplying the fuperficies by the diameter. 573. The fuperficies of one fide of an object only can be feen at one view; and to compute how much that is magnified, is most commonly fufficient: but fometimes it is fatisfactory to know how many minute objects are contained in a larger; as fuppofe we defire to know how many animalcules are contained in the bulk of a grain of fand: and to answer this, the cube, as well as the furface, must be taken into the account. For the fatisfaction of those who are not much verfed in thefe matters, we fubjoin the following 574. TABLE of the MAGNIFYING POWERS of CONVEX GLASSES, employed in Single Microscopes, according to the diftance of their focus; calculated by the fcale of an inch divided into foo parts: showing how many times the DIAMETER, the Su 575. The greatest magnifier in Mr Leeuwenhoek's cabinet of microfcopes, prefented to the Royal Society, has its focus, as nearly as can well be measured, at one 20th of an inch distance from its centre; and confequently magnifies the diameter of an object 160 times, and the fuperficies 25,600. But the greateft magnifier in Mr WILSON's fingle microscopes, as they are now made, has ufually its focus at no farther distance than about the goth part of an inch; whereby it has a power of enlarging the diameter of an object 400, and its fuperficies 160,000 times. 576. The magnifying power of the folar microfcope must be calculated in a different manner; for here the difference between the focus of the magnifier and the diftance of the screen or fheet whereon the image of the object is caft, is the propor tion of its being magnified. Suppofe the lens made ufe of has its focus at half an inch, and the fcreen is placed at the distance of five feet, the object will then appear magnified in the proportion of five feet to half an inch: and as in five feet there are 120 half inches, the diameter will be magnified 120 times, and the fuperficies 14,400 times; and, by putting the fcreen at farther diftances, you may magnify the object almoft as much as you please; but Mr Baker advises to regard diftinctnefs more than bignefs, and to place the fcreen just at that distance where the object is seen moft diftinct and clear. 577. With regard to the double reflecting microscope, Mr BAKER obferves, that the power of the object lens is indeed greatly increased by the addition of two eye-glaffes; but as no object lens can be used with them of fo minute a diameter, or which magnifics of itself near fo much as thofe that can be used alone, the glaffes of this microscope, upon the whole, magnify little or nothing more than thofe of Mr Wilfon's fingle one; the chief advantage arifing from a combination of lenfes |