The magnifying power of this telescope is found by dividing the focal distance of the object-glass by the focal distance of the eye-glass: the quotient gives the magnifying power, or the number of times that the object seen through the telescope, appears larger or nearer than to the naked eye. Thus, for example, if the focal distance of the object-glass be 28 inches, and the focal distance of the eye-glass 1 inch, the magnifying power will be 28 times. If we would enlarge the telescope and select an object-glass 10 feet, or 120 inches focus, an eye-glass of 2 inches focal length might be applied, and then the diameter of objects would be magnified 60 times, and their surfaces 3600 times. If we would use an object-glass of 100 feet, it would be necessary to select an eye-glass about 6 inches focus, and the magnifying power would be 200 times, equal to 1200 inches divided by 6. Since, then, the power of magnifying depends on the proportion of the focal length of the object and eye-glasses, and this proportion may be varied to any degree, it may seem strange to some that a short telescope of this kind will not answer that purpose as well as a long one. For instance, it may be asked why an object-glass of 10 feet focus, may not be made to magnify as much, as one of 100 feet focal length, by using an eye-glass of half an inch focus, in which case, the magnifying power would be 240 times? But it is to be considered, that if the power of magnifying be increased, while the length of the telescope remains the same, it is necessary to diminish the focal length of the eye-glass in the same proportion, and this cannot be done on account of the great distortion and colouring which would then appear in the image, arising both from the deep convexity of the lens and the different refrangibility of the rays of light. It is found that the length of common refracting telescopes must be increased in proportion to the square of the increase of their magnifying power; so that in order to magnify twice as much as before, with the same light and distinctness, the telescope must be lengthened four times; to magnify 3 times as much, 9 times; and to magnify four times as much, sixteen times; that is—suppose a telescope of 3 feet to magnify 33 times,—in order to procure a power four times as great, or 132 times, we must extend the telescope to the length of 48 feet, or 16 times the length of the other. Much likewise depends upon the breadth or aperture of the object-glass. If it be too small, there will not be sufficient light to illuminate the object; and if it be too large, the redundance of light will produce confusion in the image.

The following table, constructed originally by Huygens, and which I have re-calculated and corrected, shows the linear aperture, the focal distance of the eye-glass, and the magnifying power of astronomical telescopes of different lengths, which may serve as a guide to those who wish to construct telescopes of this description.

Focal distance of the object-glass.Linear aperture of the object-glass.Focal distance of the eye-glass.Magnifying power.
Feet.Inch.Dec.Inch.Dec.
10.5450.60520
20.760.8420.5
30.941.0434.6
41.081.1840
51.211.3345
61.321.4550
71.431.5853
81.531.6956.8
91.621.7860.6
101.711.8863.8
152.102.3078
202.432.6889.5
303.003.28109
403.433.76127
503.844.20142
604.204.60156
704.555.00168
804.835.35179
905.155.65190
1005.405.95200
1205.906.52220

In the above table, the first column expresses the focal length of the object-glass in feet; the second column, the diameter of the aperture[20] of the object-glass, the third column, the focal distance of the eye-glass, and the fourth, the magnifying power, which is found by reducing the feet in the first column to inches, and dividing by the numbers in the third column. From this table it appears that, in order to obtain a magnifying power of 168 times, by this kind of telescope, it is requisite to have an object-glass of 70 feet focal distance, and an eye-glass five inches focus, and that the aperture of the object-glass ought not to be more than about 4½ inches diameter. To obtain a power of 220 times requires a length of 120 feet.

The following is a summary view of the properties of this telescope. 1. The object is always inverted. 2. The magnifying power is always in the proportion of the focal distance of the object-glass to the eye-glass. 3. As the rays emerging from the eye-glass, should be rendered parallel for every eye, there is a small sliding tube next the eye, which should be pushed out or in till the object appears distinct. When objects are pretty near, this tube requires to be pulled out a little. These circumstances require to be attended to in all telescopes. 4. The apparent magnitude of an object is the same wherever the eye be placed, but the visible area, or field of view, is the greatest when the eye is nearly at the focal distance of the eye-glass. 5. The visual angle depends on the breadth of the eye-glass; for it is equal to the angle which the eye-glass subtends at the object-glass; but the breadth of the eye-glass cannot be increased beyond a certain limit, without producing colouring and distortion.

If the general principles on which this telescope is constructed be thoroughly understood, it will be quite easy for the reader to understand the construction of all the other kinds of telescopes, whether refracting or reflecting. A small astronomical telescope can be constructed in a few moments, provided one has at hand the following lenses:—1. A common reading-glass, eight or ten inches focal distance; 2. A common magnifying lens, such as watchmakers or botanists use, of about 1½ or 2 inches focus. Hold the reading-glass—suppose of ten inches focus—in the left hand opposite any object, and the magnifying lens of two inches focus, in the right hand near the eye, at twelve inches distance from the other in a direct line, and a telescope is formed which magnifies five times. I have frequently used this plan, when travelling, when no other telescope was at hand.

SECT. 3.—THE AERIAL TELESCOPE.

The Aerial is a refracting telescope of the kind we have now described, intended to be used without a tube in a dark night; for the use of a tube is not only to direct the glasses, but to make the place dark where the images are formed. It appears from the preceding table inserted above, that we cannot obtain a high magnifying power, with the common astronomical telescope, without making it of an extreme length, in which case the glasses are not manageable in tubes—which are either too slight and apt to bend, or too heavy and unwieldy if made of wood, iron or other strong materials. The astronomers of the seventeenth century, feeling such inconveniences in making celestial observations with long tubes, contrived a method of using the glasses without tubes. Hartsocker, an eminent optician, contrived to fix them at the top of a tree, a high wall, or the roof of a house; but the celebrated Huygens, who was not only an astronomer, but also an excellent mechanic, made considerable improvements in the method of using an object-glass without a tube. He placed it at the top of a very long pole, having previously enclosed it in a short tube, which was made to turn in all directions by means of a ball and socket. The axis of this tube he could command with a fine silken string, so as to bring it into a line with the axis of another short tube which he held in his hand, and which contained the eye-glass. The following is a more particular description of one of these telescopes. On the top of a long pole or mast ab (fig. 45), is fixed a board moveable up and down in the channel cd: e is a perpendicular arm fixed to it, and ff is a transverse board that supports the object glass enclosed in the tube i, which is raised or lowered by means of the silk cord rl; gg is an endless rope with a weight h, by which the apparatus of the object-glass is counterpoised; kl is a stick fastened to the tube i; m the ball and socket, by means of which the object-glass is moveable every way: and to keep it steady, there is a weight n suspended by a wire; l is a short wire to which the thread rl is tied; o is the tube which holds the eye-glass; q the stick fixed to this tube, s a leaden bullet, and t a spool to wind the thread on; u is pins for the thread to pass through; x the rest for the observer to lean upon, and y the lantern. Fig. 46 is an apparatus contrived by M. de la Hire for managing the object-glass; but which it would be too tedious particularly to describe. To keep off the dew from the object-glass, it was sometimes included in a pasteboard tube, made of spongy paper, to absorb the humidity of the air. And to find an object more readily, a broad annulus of white pasteboard was put over the tube that carried the eye-glass; upon which the image of the object being painted, an assistant who perceived it, might direct the tube of the eye-glass into its place.

figure 45.

fig 46.