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 | 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