James. That is readily done; by dividing 8 inches, the limit of distinct vision, by 4, 4, and

Charles. And to divide a whole number, as 8, by a fraction, as 4, &c. is to multiply the said number by the denominator of the fraction: of course, 8 multiplied by 4, gives 32; that is, the lens, whose radius is a 4 of an inch, magnifies the diameter of the object 32 times.

James. Therefore the lenses of which the radii are and will magnify as 8 multiplied by 8, and 8 multiplied by 20; that is, the former will magnify 64 times, the latter 160 times, the diameter of an object.

Tutor. You see, then, that the smaller the lens, the greater its magnifying power. Dr. Hooke says, in his work on the microscope, that he has made lenses so small as to be able, not only to distinguish the particles of bodies a million times smaller than a visible point, but even to make those visible of which a million times a million would hardly be equal to the bulk of the smallest grain of sand.

Charles. I wonder how he made them.

Tutor. I will give you his description: he first took a very narrow and thin slip of clear glass, melted it in the flame of a candle or lamp, and drew it out into exceedingly fine threads. The end of one of these threads he melted again in the flame till it run into a very small drop, which, when cool, he fixed in a thin plate of

metal, so that the middle of it might be directly over the centre of an extremely small hole made in the plate. Here is a very convenient single microscope.

James. It does not seem, at first sight, so simple as those which you have just now described.

Tutor. A (Fig. 39.) is a circular piece of brass, it may be made of wood, ivory, &c. in the middle of which is a very small hole, in this is fixed a small lens, the focal distance of which is ▲ D, at that distance is a pair of pliers DE, which may be adjusted by the sliding screw, and opened by means of two little studs a e; with these any small object may be taken up, and viewed with the eye placed at the other focus of the lens at F, to which it will appear magnified as at I M.

up.

Charles. I see by the joint it is made to fold

Tutor. It is; and may be put into a case, and carried about in the pocket, without any incumbrance or inconvenience. Let us now look at a double or compound microscope.

James. How many glasses are there in this? Tutor. There are two; and the construction of it may be seen by this figure; c d (Fig. 40.) is called the object-glass, and ef the eye-glass. The small object ab is placed a little farther from the glass cd than its principal focus, so that the pencils of rays flowing from the differ

ent points of the object, and passing through the glass, may be made to converge and unite in as many points between g and h, where the image of the object will be formed. This image is viewed by the eye-glass ef, which is so placed that the image g h may be in the focus, and the eye at about an equal distance on the other side, the rays of each pencil will be parallel after going out of the eye-glass, as at e and f, till they come to the eye at k, by the humours of which they will be converged and collected into points on the retina, and form the large inverted image a B.

Charles. Pray, sir, how do you calculate the magnifying power of this microscope?

Tutor. There are two proportions, which, when found, are to be multiplied into one another: (1.) As the distance of the image from the object-glass is greater than its distance from the eye-glass; and, (2.) as the distance from the object is less than the limit of distinct vision.*

Example. If the distance of the image from the object-glass be four times greater than from the eye-glass, the magnifying power of four is

* Dr. Vince gives the following rule for finding the linear magnifying power of a compound microscope: "It is equal to the least distance of distinct vision, multiplied by the distance of the image from the object-glass, divided by the distance of the object from the object-glass, multiplied by the focal length of the eye-glass,”

gained and if the focal distance of the eyeglass be one inch, and the distance of distinct vision be considered at seven inches, the magnifying power of seven is gained, and 7 multiplied by 4 gives 28; that is, the diameter of the object will be magnified 28 times, and the surface will be magnified 784 times.

James. Do you mean that an object will, through such a microscope, appear 784 times larger than by the naked eye?

Tutor. Yes, I do; provided the limit of distinct vision be seven inches; but some persons who are short-sighted, can see as distinctly at five or four inches, as another can at seven or eight: to the former the object will not appear so large as to the latter.

Ex. 2. What will a microscope of this kind magnify to three different persons, whose eyes are so formed as to see distinctly at the distance of 6, 7, and 8 inches by the naked eye; supposing the image of the object-glass to be five times as distant as from the eye-glass, and the focal distance of the eye-glass be only the tenth part of an inch?

Charles. As five is gained by the distances between the glasses, and 60, 70, and 80, by the eye-glass, the magnifying powers will be as 300, 350, and 400.

James. How is it 60, 70, and 80, are gained by the eye-glass?

Charles. Because the distances of distinct vi

sion are put at 6, 7, and 8 inches, and these are to be divided by the focal distance of the eyeglass, or by ; but to divide a whole number by a fraction, we must multiply that number by the denominator, or lower figure in the fraction: therefore the power gained by the distance between the two glasses, or 5, must be multiplied by 60, 70, or 80. And the surface of the object will be magnified in proportion to the square of 300, 350, or 400, that is as 90,000, 122,500, or 160,000.

Tutor. We now come to the solar microscope, which is by far the most entertaining of them all, because the image is much larger, and being thrown on a sheet, or other white surface, may be viewed by many spectators at the same time, without any fatigue to the eye. Here is one fixed in the window-shutter, but I can explain its construction best by a figure.

James. There is a looking-glass on the outside of the window.

Tutor. Yes, the solar microscope consists (Plate VI. Fig. 42.) of a looking-glass so without, the lens ab in the shutter du, and the lens nm within the dark room. These three parts are united to, and in a brass tube. The looking-glass can be turned by the adjusting screw, so as to receive the incident rays of the sun sss, and reflect them through the tube into the room. The lens ab collects those rays into a focus at nm, where there is another magnifier;