CHEMICAL NEWS Jan. 18, 1862. Royal Institution of Great Britain. with other bodies, the terms large and small will be found to be capable of infinite extension either way, until it becomes evident that in the physical universe the properties which they are supposed to represent have no existence, but are merely artificial distinctions called into being by the imperfections of our senses. We have been led into these reflections by some theoretical and experimental inquiries which have come under our notice respecting the constitution of matter; and some of the results obtained in the endeavour to ascertain the limits of mechanical divisibility of bodies are so curious, and illustrate so forcibly the above remarks, that we are induced to place them at once before our readers. 33 Having now obtained a continuous metallic film of gold upon a plate of glass (and that it is continuous and metallic has been amply proved by Faraday), let us see how far it is possible to subdivide it by mechanical means. From an examination of Nobert's test plate, it is seen that it is possible to rule lines with a diamond point on glass so close together, that upwards of 90,000 of them are comprised in the space of one inch. The apparent limit of vision in the best microscopes, as tested by De la Rue, Quekett, and Ross, does not, however, reach beyond lines separated the 1-80,000th of an inch. Let us, therefore, cut our square inch of gold on the glass plate, with lines this distance apart, and crossing each other at right angles. The whole inch The divisibility of matter is a subject which has been will, therefore, be divided into 6,400,000,000 squares, frequently treated of and reasoned upon; indeed, each of which is capable of being distinctly seen under in most works on physics or chemistry, illustrations are adequate microscopic power. What now is the weight given of the extraordinary degree of subdivision to of each piece? The square inch of gold weighed at the which bodies may be brought by mechanical means. commencement the I-57th of a grain. By the action of One of the best illustrations of this is to be found in cyanide of potassium, it was diminished in thickness Miller's "Elements of Chemistry," part I., page 4, where until it only weighed the 1-600th of a grain. This has the author shows to what a minute state of division it now been cut up into 6,400,000,000 separate pieces, is possible to bring the metal gold. All these illustra- each of which therefore weighs no more than the tions have, however, stopped far short of the limit attain-1-3,840,000,000,000th of a grain; or, in other words, a able by mechanical means, and indeed have been merely given to illustrate extreme subdivision without pushing the subject to its legitimate extent. The following experimental illustration shows what infinitesimally minute quantities the natural philosopher is capable of working with and rendering evident to the senses (or rather sense, for sight alone can appreciate them), and will also show how conventional are the ordinary ideas of magnitude. single grain of gold-a fragment about as large as a good-sized pin's head-has been divided into three billion, eight hundred and forty thousand million separate pieces, each distinctly visible to the eye! The mind is quite unable to attach any definite significance to these figures without artificial assistance, but it may, perhaps, enable our readers to form some faint idea of the minuteness of the subdivision, when we state that each square bears about the same proportion to the original grain of gold that a thimbleful of water does to a building five times the size of St. Paul's. How insignificant do our ideas of great and small appear in the contemplation of such overwhelming figures as these! In the eloquent words of Dr. Nicoll, "Great and little, in truth, seem in creation alike terms expressing merely relation to us, and vanish in the universe of the Infinite God." A PROCEEDINGS OF SOCIETIES. ROYAL INSTITUTION OF GREAT BRITAIN. Course of Six Lectures on Light' (adapted to a Juvenile We will start with a sheet of gold leaf. This consists of metallic gold beaten out into a film of about the 1-282,000th of an inch in thickness, measuring 3375 inches square and weighing about the 1-5th of a grain. A single square inch therefore weighs 1-57th of a grain. Now, Faraday in his beautiful researches on the relations of gold to light' has shown that it is possible by chemical means to reduce this thickness very considerably, still preserving the metallic continuity of the film. This is readily effected by breathing on a clean plate of glass and then gently placing it on a piece of gold leaf; the latter will adhere to it, and if distilled water be immediately applied at the edge of the leaf, it will pass between the glass and gold, and the latter will be perfectly stretched upon now draining the water out, the gold-leaf will be left well extended, smooth, and adhering to the glass. If, after the water is poured off, a weak solution of cyanide of potassium be introduced beneath the gold, the latter will be gradually dissolved away, becoming thinner and thinner; but at any moment the process may be stopped, the A ray of light falling through a vacuum as a perpendicular on the cyanide washed away by water, and the attenuated gold surface of any transparent solid or liquid, goes straight into the solid film left on the glass. If towards the end, a washing be or liquid-But if the ray strike the surface obliquely, it is bent on made with alcohol, and then with alcohol containing a entering the solid or liquid; and it is so bent as to approach the perpendicular Conversely, a ray of light issuing from the solid or little varnish, the gold film will be left cemented to the liquid would go straight forward if it struck the surface perpendicuglass. By this means the thickness will have become larly; but if it strikes it obliquely it is bent from the perpendicularThis bending of the ray on passing from one medium into another is reduced to about one-twelfth part of what it was called Refraction-Gases, liquids, and solids all refract light. The originally, weighing (in round numbers) about the quivering observed over a heated surface is due to refraction by the 1-600th of a grain to the square inch, and being only actually rises; and refraction causes his disk to be slightly flattened air-By the refraction of our atmosphere we see the sun before he about 1-3,000,000th of an inch in thickness. The film when near the horizon. in this condition, although consisting of pure gold, presents none of the ordinary appearances of the metal, being perfectly transparent, and resembling a delicate film of pale green varnish more than a dense metallic body. 3.46 'Experimental Researches in Chemistry and Physics," p. 394. LECTURE II. (Dec. 28, 1861.) NOTES TO THE LECTURE :— The Eye sees an object from which a ray issues in the direction of the ray as it enters the eye. In consequence of this, and of refraction, the bottom of a lake or river appears lifted up, the water seeming to bo shallower than it really is-Hence, if we thrust a straight obliquely into water, its immersed end will appear bighe really is, the stick being apparently bent upward where it o water-The bending of the stick must be carefully distinguish 1 Reported verbatim by special permission. stars. large sphere, and forms our concave mirror. Now with the bending of the rays; they are in opposite directions-Bodies refract light in very different degrees; the refraction produced by water regard to the manner in which images are formed by this is much greater than that produced by air, while the refraction by mirror. I will draw the outline of the mirror (a e 6), in glass or turpentine is greater than that produced by water. With one exception the diamond is the most powerful refractor known, and to this way (see Fig.); and suppose the curvature of this its power in this respect its brilliancy is due-The angle inclosed by mirror completed, so as to form a sphere; then when I the direct ray and the perpendicular is called the angle of incidence; the angle inclosed between the refracted ray and the perpendicular is speak of the centre of the sphere of which the mirror is a called the angle of refraction. However these angles may vary in size, part, I mean a point (c) about this distance from the there is for each individual substance a fixed relationship between surface of the mirror. You must bear in mind that them-The older boys will understand this relation. It is this: the there is a particular distinction and emphasis laid upon sine of the angle of incidence, divided by the sine of the angle of refraction, is a constant quantity for each particular medium. In glass this quotient rays of light which are called parallel rays which run is about 1. No matter, then, how the obliquity of a ray falling from side by side perfectly parallel without crossing each other a vacuum upon glass may vary, the sine of the angle of incidence is always as long and a-half as the sine of the angle of refraction. This-such rays for example as we get from the sun and the is a celebrated law, and ought, if possible, to be understood. The constant quotient is called the index of refraction. In glass, as just stated, the index is about 1, in water it is about 1, while in diamond If two bodies refract a ray of light equally, one of them cannot be seen within the other. The eye-ball of an ox, for example, vanishes if plunged into water, the refraction produced by both substances being the same. In this case there is no reflection at the common surface of the two media-Reflection always accompanies refraction, and the greater the refraction the more copious is the reflection; hence the wonderful power of the diamond as a reflector of light-Hence, when it is stated in the first note of this day's Lecture, that a ray of light goes straight into a transparent solid or liquid, the portion of the ray which has escaped reflection is meant - If a ray of light pass obliquely through a transparent plate with parallel surfaces, the refraction suffered on entering is exactly undone by the refraction suffered on quitting the plate, and the ray afterwards pursues a direction parallel to its original one-If the refracting surfaces be not parallel, the original direction is not restored. It is not restored, for example, in the case of prisms or lenses. it amounts to 2}.] Lenses are divided into two great classes, called convergent and divergent lenses-A double convex lens is an example of the former class; divergent rays have their divergency diminished, parallel rays are rendered convergent, and convergent rays have their convergency augmented by passing through a double convex lens. In lenses, as in mirrors, the focus of parallel rays is the principal focus-A double concave lens is an example of the divergent class: convergent rays are rendered less convergent, parallel rays are rendered divergent, and divergent rays have their divergency augmented by a double concave lens-If the divergent rays produced by the refraction of a parallel beam by a double concave lens be produced backward, they will cut in a point on that side of the lens from which the parallel beam comes. This point is the principal focus of the concave lens-Thus, in the case of the double convex lens, the rays actually cut each other on the side opposite to that from which the parallel beam comes; the focus is therefore real. In the case of the double concave lens the rays do not actually cut-the focus is imaginary. In a spherical lens the refraction near its edge is greater than at its centre; the central rays and the circumferential rays do not therefore converge to one and the same point-This difference between the refraction of the central and edge rays is called the spherical aberration of the lens-Convergent lenses produce real images which may be either larger or smaller than the object. Divergent lenses produce no real images-If a luminous object be placed at the principal focus of a convergent lens, its rays after passing through the lens do not intersect; they are parallel-If the object be placed between the focus and the lens the rays do not intersect; they are still divergent, though less so than before they entered the lens-1f the object be placed beyond the focus, the rays, after passing through the lens, intersect; and an inverted image of the luminous object is formed where they cut-The images of the magic-lantern and camera-obscura are thus produced. We concluded our last Lecture by some experiments showing the action of two different kinds of mirrors upon light. We allowed light to fall, first upon what we called a convergent mirror-the concave mirror-and we found that when the light fell upon the face of it, it was gathered up and projected and converged into a cone. I then interposed a screen where the cone came to a point, and there we found an image of the light from which the rays which fell upon the mirror emanated. We found on the other hand, in the case of the convex mirror, that when the beam of light fell upon it, the rays, instead of being converged to a point, were scattered widely in all directions and appeared as if they came from a point behind the mirror. I will just make one or two experiments with the concave mirror to-day in order to finish what I have to say upon the subject of the last lecture. Here is the same mirror we had on that occasion. You must figure to yourselves that concave mirror as a slice of a hollow sphere. If you supposed this mirror continued round, it would make a very large sphere of glass; but that small slice is, as it were, taken off that Now supposing a bundle (ff) of these parallel rays to fall upon the mirror in this way, they will be reflected to a point (d), midway between the centre (c) This point of the sphere, and the surface of the mirror. midway between the centre of the sphere and the surface of the mirror is therefore called the principal focus-it is the focus for parallel rays. But if I bring the light nearer here, 'for instance, and allow the rays to fall upon the mirror, they will also be reflected, but will meet at some point between the centre and the focus. And if instead of having a point of light there, I had an object -an arrow for instance, that arrow would be so reflected as to form a little arrow at the focus, and if I draw this arrow (a) with the point bending downwards and the feather end up, we should on examination find the image of it with the point bent upwards and the feather end downwards (6) the arrow being inverted and diminished. Now, what I want you to bear in mind is this:-if you put a little arrow here (b) making that the object, then this arrow (a) becomes its image. This (a) being the object, that (b) is its image, and that (6) being the object, this (a) is the image; one being changed for the other; the image becoming the object, and the object the image. You also see now that if you put your luminous point in front of the mirror (d), the rays, reflected from that point, and striking upon the mirror, will go from it parallel, without intersecting at all; and if the rays come from a point between this principal focus and the surface of the mirror, when the rays strike the mirror from that point they are caused to diverge,-they are reflected outwards. Now, with regard to an object; you have seen that if I place an arrow there (at a) the image of the head of the arrow would be upwards and the feather end of the arrow downwards, there (at b); and I find this to be precisely the case if I go near to this mirror myself. When I stand near it, between the centre and the mirror, I see an upright and enlarged image of myself. I am quite a giant, looking into that mirror. But if I go beyond the focus, what do I see? I see an inverted image of myself in the air :-there I stand with my head downwards; the hand of the image moves with mine like a spectre or a ghost-for there it is It does as plainly as possible in the air in front of me. exactly the same to me as I do to it, and when I point a stick at it it is so like a man driving a stick into my face that I can hardly strike out without winking my eyes. Our fingers are actually mingled; I am now shaking hands with the fingers of the spectre. There, it is grasping mine, as plainly as I grasp it. And just in accordance with what I have been saying to you, if I could stand upon my head there in the air-which, however, I cannot do, and which none pretend to do but those people who call them elves spiritualists, who regard the laws of this glorious CHEMICAL NEWS,} Jan. 18, 1862 Royal Institution of Great Britain. nature by which we are surrounded as nothing at all (for those people who absolutely have never taught us anything about these things, who are altogether ignorant of the laws and constitution of nature, pretend to be able to do things that we confess we cannot do)-however, if I could stand there with my feet in the air, resting upon nothing, then what would take place? Why, you would see upon the screen a magnified and upright image of myself. Now, as I profess my inability to stand with my feet in the air, resting upon nothing, I must ask you to accept a substitute. I will place a person just there, where the spectre stands who is shaking his stick in my face, and I will illuminate his face, and will try if I cannot actually cast an image of his face upon the screen. And will this image be erect or inverted? will it be upright or downward? It will be inverted, no doubt of it, let us try it now. We have our light simply for the purpose of illuminating this man's face. [The experiment was then performed, and the face of the assistant illuminated by the electric light, being placed between the principal focus and the centre of the mirror, an enlarged and inverted image of the face was projected upon the screen.] You may make all these experiments for yourselves with a much smaller apparatus. Here is a very small concave mirror, and when I look close into it, I see myself upright, and when I hold it at a distance I see myself inverted; and I will try and project an image with it to show that it may be made use of in that way also. Here are two medals which I will illuminate by means of the electric light, and will then throw an image of them by means of this concave mirror upon the screen. Taking the copper one first, I hold it, as you see, with the head downwards, but by virtue of the action of the mirror it is inverted, and you see we get an upright image. Here I have a silver medal, the image of which you also see on the screen. You can take a candle and try these experiments by means of it, and you will find the candle will be turned upside down by a little mirror of this kind-the flame will go downwards when the image is thrown clearly upon the screen. I have now to go on to another and very distinct portion of the subject, and I must try and make this perfectly clear to you by a somewhat gross image. I ask you to imagine the particles of light being shot off, so to say, from a luminous body: when those particles of light strike against a rough surface they are like elastic balls shot against a rough wall, such as this unpolished surface. Anybody who has ever played in a racket court will know that there is no dependence to be placed upon a ball that strikes a rough wall; it is reflected back, but it rebounds in any direction, and does not obey the law of the angle of incidence being equal to the angle of reЯection; so that when the particles of light strike a rough wall, they are, as I have said, scattered in all directions. If on the contrary the elastic balls strike a perfectly polished or smooth wall, they are reflected according to the same law as light. Well now, suppose you drop a body into the water a heavy body-a stone if you will; it strikes the water, and goes right down through it without turning to the right or to the left. But cast it from the hand thus [obliquely], every boy present ought to know that the earth pulls that stone downwards, and that its path is therefore not straight, but bent; (for even a cannon ball fired upwards is pulled down by the earth.) Well now, figure to yourselves-and this is merely an image that I put before you-figure to yourselves the little particles of light-(though I do not believe they are particles at all, and I shall tell you my reasons for not believing this, in a future lecture)-fix your thoughts upon the particles of light falling obliquely upon a surface of glass. When they fall obliquely upon the surface, the piece of glass appears to exert an attractive force and pull them down, just like the influence which is exerted by the earth when a stone is thrown from the hand. This is exactly 35 the way the great Sir Isaac Newton imagined that when light struck obliquely, it was pulled down in its course. What is the consequence of that? the consequence is this that if you take a ray of light and allow it to fall exactly plumb upon a surface of that kind, it goes straight through it without deviation either to the right or to the left; but if you allow it to fall obliquely, when it comes nearly to the surface-a little before it enters the medium, it begins to be bent-instantly bent, at the point where the ray enters the glass. Here, then, I have a piece of 10 glass (a b) with two parallel sides; if, as I have said, the ray of light falls upon this perpendicularly, it goes straight through; but if it strikes obliquely (cf) the consequence is that when it comes very close to the surface of the medium, it is pulled down towards it and goes through in that direction (fg); but when it wants to get out again, however, the attraction of the lower surface tends to pull it back again and it goes off in that direction (gh); so that in a case of this kind, there are two bendings. There is a bending (at f) where the ray enters the glass from the air; it is there bent towards this perpendicular (cd) and when it quits the glass (at g) and gets into the air again, it is bent away from the perpendicular. The original direction of the ray is thus perfectly restored, and it goes along exactly in the same direction as that in which it entered the medium; but instead of going straight along in a line with the original ray, which it would do if the glass were not there, it takes a course parallel to the first ray. In order that you may satisfy yourselves of this fact, take a piece of glass, the thicker the better, and make two dots with ink upen paper close together. Upon looking straight down at one of those dots through the glass, it does not alter in position at all with regard to the other; but when looked at obliquely, the moment you bring the glass between your eye and the dot, it immediately appears to have shifted its position. They are no longer in the same straight line. I will now show you the refraction of light-for that is the term that is used. This bending of the ray downwards and upwards by the glass plate is called refraction. I will refract a bean of light by means of this piece of glass, which you see is very thick and has perfectly parallel surfaces. I have here the electric lamp; 1 will first get a beam of light quite horizontal and will interpose a slit in front of the lamp. Here you see is the exact position of the image of the slit marked on the screen by a pointer. I beg your attention to this beam, look along it, not only upon that image, but along the path of the rays of light. You see the beam tracking itself along the dust of the room. If I now interpose this piece of glass so that the beam shall go right plumb through it, you will find that there is no deviation in the direction of the beam upon the screen; but if I now twist the glass on one side so as to cause the beam to pass through it obliquely, and then you will find an immediate shifting of the image. There, you see, it shifts in one direction away from the pointer, and then as I twist the glass in the other direction, the beam shifts accordingly. This is caused by the bending of the rays on entering the glass and the restoration of them to a straight line parallel to their first position when they quit the glass. I will now take instead of this thick slab of glass, a bar of glass such as I have here in my hand. It is simply a rod of glass with two plane polished surfaces. I will interpose this bar across the slit, and when I allow the light from the slit to pass through the bar at right angles, you will find there is no deviation,-the light wil pass straight through from beginning to end; but when I hold it so that the beam shall fall on the glass obliquely. you then find that a portion of it is deflected, either to the right when I hold it in this way, or to the left when I hold it in the opposite direction. Here is our bar of glass; you see there is no change produced as long as I hold it far, plumb, over the beam. But as I now twist it so as to cause the beam of light to strike it obliquely, you see the middle portion of the beam is deflected on one side; and if I allow it to pass through in the other direction you see it is deflected to the other side. This is caused by the refraction by the piece of glass. Instead of that, I can take an object such as I have here, an arrow, and project its image upon the screen. If I allow my bar or plate, of glass to go straight across the path of the light there is no deviation whatever. But if I cause it to twist aside you know very well what takes place: a portion of the arrow must be now twisted on one side owing to the refraction. It I bring it straight again so as to allow the light to pass through perpendicularly, there is no deviation no shifting at all of the arrow. This is an example of what we call refraction-the bending of the rays of light when they pass through a transparent substance obliquely. We have hitherto been dealing with a body possessing parallel surfaces; and I hope you all remember what I have said regarding a body of this kind: when the light enters obliquely there is a bending of it towards h perpendicular, and when the light quits the me ium it is bent from the perpendicular. But, instead of taking a piece of glass with two parallel surfaces, suppose I now take a piece of glass with unparallel surfaces. In the case of a piece of glass with two parallel surfaces, the bending produced upon entering the glass was immediately undone upon the ray quitting the glass. This is no longer the case when we take a piece of glass with the two surfaces not parallel. Here I have a little bit of glass shaped in the form of a wedge with the two surfaces not parallel; and you will find that the refraction is greater than in the case of the parallel surfaces; and here also I have two pieces of window glass put together so as to form a wedge-shaped figure, and if I have a little water poured into it, you see I have a wedge of waterwhat is called a prism, in fact, and now you will see what the effect of that wedge of wa er will be upon a beam of light issuing from our lamp. Unfortunately, this is not so nice and foggy a day as the day when we last met; and, therefore, the beam is not so clearly defined: still I would ask your attention to the beam, such as it is, marked along the dust of the room. It is perfectly clear to many of you, I dare say-a beautiful slice of light, so to say, falling thus upon the screen. Now I take the prism of water, and when I introduce it (a) you will see what takes place. It you watch the path of the light (bc) you will see how the beam behaves-how it jerks up, down, up, down, up, down, up [inserting the wedge in and out of the path of light]-this being produced by the refraction or the bending of the light by the prism of water. The track of the beam through the room is, perhaps, more instructive than the image itself. You see how the beam jumps up the moment the wedge of water is interposed. Instead of a weage of water I will now take a wedge of glass-one of these small prisms, and I will make a beautiful sun-like spot of light on the screen. Now, if you observe the track of the beam, you will find that it is jerked up also. There it goes-up, up, up,-and when I turn the wedge in this way the image goes down, down, down. If I turn it in this way, he image goes to the left, and in this other way to the right. Thus you see the ray is bent as it enters and quits this prism. Now, having learnt generally the nature of what we always call refraction if it were not called refracti n I would not use such a difficult word, I want to use the most simple words possible for my present audience; I would not therefore use an unnecessarily learned word, but this word refraction must be remembered; it is the word always used to express this bending of the ray of lis ht, having learnt generally the nature of refraction when a ray of light falls upon glass out of air. I want you to remember that the same would o cur if the ray of light fell into water out of air. Supposing this to be a vessel of water, and suppose an object, say a white pebble, to be at the bottom there, a ray of light quit ing that pebble would go in a certain direction, but on quitting the water and getting into the air it does not go straightforward, but is bent away from the perpendicular. What is the consequence of this? Supposing the eye to be placed at a point above the water; it sees the light along this line; instead of seeing the pebble in its real place, it sees it higher up; in fact the whole bottom of the basin is apparently raised up by the water and is rendered thereby in appearance much shallower than it really is. I have often found this to my great discomfort when I was learning to swim. Many a time I have imagined that I should be only up to my breast, and have really found myself up to the chin. I will take a basin of this kind and put a penny piece there at the bottom; it I place my eye here, this edge of the basin when it is empty cuts off the penny piece altogether from my eye. You know, in point of fact, that this quite intercepts the light coming from the pennypiece. Supposing this basin to be now filled with water; the bottom appears to be raised up, and in that position I can see the penny-piece very clearly, it being brought within the range of my eye. This is an experiment which I dare say some of you have made already, but which I want to make for the benefit of all. I dare say the smallest of my hearers will testify that he cannot see the penny. piece at the bottom of this basin. Evidently he would have to stand up to see it. Now I ask you to notice the effect produced by the water; it will be apparently to lift up the bottom of the vessel and bring it in view. [Water was then poured into the basin.] Here you see the bottom is raised up; and thus this action of the water, which has often disappointed me when a boy, is perfectly explained by the refraction of light. I will no take that pennypiece away, and I dip this rod straight down into the water, and there is no effect produced upon it; it does not appear to be bent at all. But look what takes place when put it in obliquely. The bottom is raised up, and thus that end of the rod which dips into the water appears higher than it ought to be, and as a consequence the rod will actually appear bent up at the point where it enters the water. I During the last few years I have been very much in the habit of examining people, not boys, exactly, but young CHEMICAL NEWS, Royal Institution of Great Britain. men, and I bave very often asked them to explain this effect. I have asked them to draw how the stick would be bent on being thrust obliquely into water; and I believe in nine cases out of ten they have drawn first of all a line through the water and then they have drawn the stick going off in the opposite direction to what actually takes place. They have mistaken the bending of the rays for the bending of the stick. They have drawn the way the ray of light issuing from the vessel is bent: the ray of light is so bent that the bottom seems to be lifted up, and because the bottom is lifted up, the stick is bent altogether in the opposite direction to the ray; so that you see they were quite wrong in ascribing that to the stick which belonged to the ray. This is an experiment well worthy of your attention, and it may be made with instruction when you go home. Well now, I have introduced to you these little bits of glass prisms as they are sometimes called-cut into the shape of wedges. I have here two of these wedges. If a beam of light falls upon one of these prisms, it strikes the surface a little obliquely and is bent towards the perpendicular on entering the surface and from the perpendicular on qui'ting it and goes on in an oblique direction. I will now take both these wedges and hold them edge to edge. Now, a ray of light striking upon these will on entering be bent towards the perpendicular, and on I pass on from this to a very interesting and important subject. It is a very difficult subject, but it is well worthy of all the care which you can bestow upon it. Let me reverse the position of my prisms. Suppose I put them with their bases truching (see Fig.); then if a ray of light falls upon them it will be bent on entering the prisms and on leaving, and the rays of light will be converged to a point instead of being scattered abroad as they were when we placed our prisms edge to ed.e. I then come to a figure similar to this, but bounded by a curved line in that way, and this is exactly the shape of a section of those spectacle glasses used by old people. We shall see the reason why by-and-by. Here is such a double convex lens; it is bulged out on both sides, and when we cause the rays of light to fall upon it, it will squeeze them together and bring them to a point behind the lens which is called the principal focus of the lens. I have here two such spectacles-a pair of boy's spectacles for short sight, and an old man's spectacles which might suit myself, for instance-for long sight. I pass these in front of the lamp and allow the 37 light to fall through both before falling on the screen, and I think you will find that one will sque ze the light together and produce a spot of light in the midale; whereas the other will scatter the light abroad and leave the lens in a state of shade, and cause a rim of light to fall around the circumference of the spectacle. When I put these before the lamp I will ask you which is convex and which is concave, and if you cannot answer me correctly, it must be ecause I have not made my subject sufficiently clear. I hold these glasses before the beam of light without actually knowing to which class each belongs; but now tell me, are they convex or concave? Why, they are convex, for concave lenses diverge the light, and here we have a squeezing together of it. You see there the difference between these two classes of lenses. I have shown you the boy's lens, and there »s I have said we have the old man's lens. You see the squeezing of the light in the middle; and here on the other hand you see the divergence of the light-the scattering of the light forming a luminous rim round about the lens. This is concave, and the first one was of course convex. How beautiful I have stated in the list of memoranda of to-day's Lec- see a marked distinction between the two. The |