we repeat the same construction for the other extremity S', we shall find its focus f' in the axis S'A produced; and in the same way we obtain all the foci of the intermediate points; whence we have ƒƒ' an inverted image of the object. The image is inverted because the foci are formed beyond the point where the axes of the pencils cross each other.

This image will become sensible if it is received upon a screen of white pasteboard or ground glass placed in ff'; it may also be seen immediately, if the eye be situated beyond this point, at the proper distance for seeing distinctly a real object occupying the same place.

54. If the luminous object SS', be situated at a very great distance, the image will fall on the opposite side of the lens, near the principal focus F. This furnishes us with the means of determining experimentally the focal distance of converging glasses. As the object approaches the lens, the image recedes from it increasing at the same time in magnitude. When the object is removed only by a quantity double the principal focal distance, Fig. 51. the image will be of the same magnitude; if it be brought nearer, the image will be removed, the dimensions being increased; finally, when it arrives at the principal focus the image will be Fig. 52. removed to an infinite distance. This result might be easily foreseen, since the object and image may always be made to change places; if the object, placed at an infinite distance, has its image in the principal focus; reciprocally, when the object is placed in the focus, the image will be at an infinite distance. Between these two limits, the image is always inverted.

The object, being brought nearer continually, will fall at length between the principal focus and the surface of the lens. Then Fig. 53. the image, according to our general construction, passes to the same side of the lens. It is now larger than the object, more distant and erect; as the object approaches the lens, the image approaches also, the size being diminished; till finally the image' and object unite and coincide throughout upon the surface.

55. These are the results of theory, and they are completely confirmed by experiment. Take, for example, any converging lens, as the object lens of an opera-glass, and look through it at an object which we will at first suppose at a great distance relative to the focal distance of the lens. Then, plac- Fig. 50. ing the eye properly we shall see an inverted image of this

object, which, as has already been remarked, we can render sensible by receiving it upon a screen of pasteboard or ground glass. But although this image really falls on the same side of the lens with the observer, yet it is referred by him to the opposite side, and conceived to be at a greater or less distance than the object, according to the circumstances by which his judgment is influenced in other cases.

56. When we are thus placed at the point where the image is most distinctly seen, if we measure the distance of the eye from the lens, we shall find that it is equal to the focal distance of parallel rays, plus the ordinary distance of distinct vision for the eye of the observer, This is another proof that the eye is placed so as to view the image as if it were a real object; and it receives from the image similar impressions. This opinion is every way confirmed; for if the eye be removed further from the glass, the image appears diminished and its minute parts are less easily distinguished, like those of a real object which is removed from us. If, on the contrary, we approach the image, it becomes irregular and confused, like that of an object which is brought too near the eye. In this last case, the image appears to be increased in size, like an object seen very near; and we are led to believe that it is brought nearer. It finally becomes altogether confused and indistinct when the eye arrives at the focus itself. But, which is very remarkable, as we approach still nearer the glass, the image is formed again, erect and very much confused. Its direction is not again changed as the distance of the eye from the glass diminishes, but it becomes less indistinct, and at length we see the object tolerably well, with its natural outlines and dimensions, when the eye is at the surface of the glass; especially if we contract the aperture of the pupil by looking through a small hole made in a card.

In these last experiments the rays are convergent when they approach the eye; and since the image is still perceived, it is a proof that vision may also take place in this way, though with incomparably less distinctness than when it is produced by divergent rays.

57. But it may here be asked why the image appears erect and becomes less confused as the eye approaches nearer to the glass, To resolve these different questions clearly, let us first take the simple case where the radiating object is reduced to a

luminous point very far removed. This takes place, for example, when we look through a converging lens at Venus, or any very brilliant star.

In this case, if the eye is first placed in OO, beyond the focus Fig. 54. of parallel rays, and at a proper distance for distinct vision, we shall see a very clear well defined image of the star. This sensation is produced by a cone of divergent rays which has its vertex at F, and OO, the aperture of the pupil, for its base. As the eye approaches the lens, the base of this cone remaining always of the same magnitude, it intercepts a greater number of rays, and of rays which form among themselves a greater angle. On account of this divergency the eye is unable to collect them all into the same focus on the retina; and consequently, they form upon this membrane a small circular image, such as a luminous circle would produce placed without the eye. The image of the star is thus gradually enlarged, and forms a disc which increases in size as the eye approaches the focus. Finally, when the eye arrives at O'O', that is, at the focus, this disc is equal in magnitude to the lens itself, because the aperture of the eye then admits all the rays which the lens has refracted. But as the eye approaches still nearer the glass a certain portion of the rays are lost; and those which first escape, being those which depart farthest from the axis of the lens, they are also the most convergent. Hence, when the eye is very near the glass, the only rays which can enter the pupil have very little convergence, and consequently the object begins to appear less confused. This being applied successively to all the points of an extended object, we perceive why it appears more distinct as the eye approaches the glass. The position is erect, since the luminous pencils do not cross each other before they enter the eye.

58. Having thus verified the results of theory for very distant objects, we shall now consider those which are placed at a less distance. In this case we also verify the other phenomena indicated by theory, and we find them the same, whichever of the faces of the lens is presented to the incident rays.

It will hence be readily understood what advantage is derived from the use of converging lenses by long-sighted persons who see near objects confusedly. For, if the object SS' be too near Fig. 55. the eye 00 to allow the rays, proceeding from it, to come to a focus upon the retina, we have only to interpose the convex lens

MAM, so near the object as to bring it within the principal focal distance AF of parallel rays, and having such a convexity as to throw back the images of the points S, S', to the foci ƒ, f', precisely at the distance ƒ 0, f' O, where the eye sees most distinctly. This is the way in which convex glasses enable long-sighted persons to see near objects distinctly. They are particularly im-, portant to aged persons, who are commonly long-sighted, and who are able by means of this useful invention to read, write, and in general to execute any kind of work which requires to be placed near the eye, as if the focus of vision was not affected by age. But they are obliged to dispense with these glasses in looking at distant objects, because they make the rays converge too fast, and thus occasion indistinctness of vision, as we have already shown.

Of Magnifying Glasses and Simple Microscopes.

59. THE expedient above mentioned is useful also to watchmakers, engravers, and generally to those persons whose business requires much care directed to small objects. In this case, however, it is not to remedy defects of sight, but to magnify the objects, Fig. 56. and render the minute parts more perceptible. To understand this use of lenses, let OO be the eye, and SS' the object which we wish to see distinctly and in large dimensions. If the latter condition were the only one sought, it might be fulfilled by simply bringing the object nearer the eye, for the visual angle subtended increases as the distance diminishes. But the image would appear confused since the object is brought within the limits at which distinct vision naturally takes place. To remedy this inconvenience, we have only to place close to the eye a convex lens, and to bring the object within the focal distance of the glass precisely so far that its image shall be thrown back to the distance Of, Of', of distinct vision. This is always possible; for the distance of the image from the glass may vary from nothing to infinity, according to the distance of the object. When we have found by several trials this proper distance, the image ff' will be seen distinctly; and, moreover, the visual angle ƒAƒ',

which it subtends at the eye placed in contact with the glass, is equal to the angle SAS' under which the object would appear to the naked eye, if it could be seen distinctly at so small a distance as AP. We shall thus obtain the double advantage of seeing the object distinctly, and of seeing it under a larger angle. But from the very circumstance of never having seen it in this way, the judgment which we form of its real magnitude is not modified by any previous experience of the ratio of the distance to the visual angle; and as we see it under a much greater angle than it subtends to the naked eye, although at the same distance at which we endeavour to place it in order to see it distinctly, it must appear to be magnified in all its dimensions. And this is constantly found to be the case. Convex lenses fitted to

produce the effect in question, are called magnifiers.

60. The magnifying power is evidently determined by the ratio of the absolute magnitudes of the image and object; and this ratio is the same, by the construction of the figures, as that of their distance from the glass, since they are both comprehended between the sides of the same angle of ƒAƒ. Thus the enlargement takes place because the image is formed at a greater distance from the glass than the object, and on the same side of it. These two conditions cannot be fulfilled, except with converging lenses.

61. We have supposed the eye to be very near the surface of the glass. This position renders our considerations more simple; and affords a wider field, that is, it allows us to take in with the same glass, a larger extent of objects. But after what we have said, it is evident that this condition is not indispensable to the obtaining of magnified images. Indeed, whenever the image, although larger and more distant than the object, is too near the glass for distinct vision, by removing the eye we can always find the exact point where it may be clearly and distinctly

seen.

Large magnifying glasses are sometimes employed in this way by aged persons placed at some distance from the eyes, which enable them to read. They are also used in examining the minute parts of maps. It is obvious that these glasses must be very large that both eyes may look through them at once. It is necessary, moreover, that the focal distance should be so great that the axes of the luminous pencils proceeding from the same