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 | Linear aperture Focal distance | Magnifying of the | of the of the | power. object-glass. | object-glass. eye-glass. | ---------------+-----------------+----------------+----------- Feet. | Inch. Dec. | Inch. Dec. | 1 | 0. 545 | 0. 605 | 20 2 | 0. 76 | 0. 84 | 28.5 3 | 0. 94 | 1. 04 | 34.6 4 | 1. 08 | 1. 18 | 40 5 | 1. 21 | 1. 33 | 45 6 | 1. 32 | 1. 45 | 50 7 | 1. 43 | 1. 58 | 53 8 | 1. 53 | 1. 69 | 56.8 9 | 1. 62 | 1. 78 | 60.6 10 | 1. 71 | 1. 88 | 63.8 15 | 2. 10 | 2. 30 | 78 20 | 2. 43 | 2. 68 | 89.5 30 | 3. 00 | 3. 28 | 109 40 | 3. 43 | 3. 76 | 127 50 | 3. 84 | 4. 20 | 142 60 | 4. 20 | 4. 60 | 156 70 | 4. 55 | 5. 00 | 168 80 | 4. 83 | 5. 35 | 179 90 | 5. 15 | 5. 65 | 190 100 | 5. 40 | 5. 95 | 200 120 | 5. 90 | 6. 52 | 220
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 4-1/2 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.