-------+--------------------+---------------------+------------------- Focal | Convex lens of | Concave lens of | Convex lens of length.| crown glass. | flint glass. | crown glass. -------+--------------------+---------------------+------------------- Inches |Inc. Dec. Inc. Dec. |Inc. Dec. Inc. Dec. |Inc. Dec Inc. Dec. 6 | 4. 54 3. 03 | 3. 03 6. 36 | 6. 36 0. 64 9 | 6. 83 4. 56 | 4. 56 9. 54 | 9. 54 0. 92 12 | 9. 25 6. 17 | 6. 17 12. 75 | 12. 75 1. 28 18 | 13. 67 9. 12 | 9. 12 19. 08 | 19. 08 1. 92 24 | 18. 33 12. 25 | 12. 25 25. 50 | 25. 50 2. 56 30 | 22. 71 15. 16 | 15. 16 31. 79 | 31. 79 3. 20 36 | 27. 33 18. 25 | 18. 25 38. 17 | 38. 17 3. 84 42 | 31. 87 21. 28 | 21. 28 44. 53 | 44. 53 4. 48 48 | 36. 42 24. 33 | 24. 33 50. 92 | 50. 92 5. 12 54 | 40. 96 27. 36 | 27. 36 57. 28 | 57. 28 5. 76 60 | 45. 42 30. 33 | 30. 33 63. 58 | 63. 58 6. 40
The following table contains the proportions of curvature, said to be employed by the London opticians.
--------+-----------------------+-------------+------------------------ | | | | | Radius of | | | both the | Focal | Convex of crown | surfaces of | Convex lens of length. | glass. | the concave | crown glass. | | of flint | | | glass | --------+-----------------------+-------------+------------------------ | | | | | Inches. | Inc. Dec. | Inc. Dec. | Inc. Dec. | Inc. Dec. | Inc. Dec. 6 | 3. 77 | 4. 49 | 3. 47 | 3. 77 | 4. 49 9 | 5. 65 | 6. 74 | 5. 21 | 5. 65 | 6. 74 12 | 7. 54 | 8. 99 | 6. 95 | 7. 54 | 8. 99 18 | 11. 30 | 13. 48 | 10. 42 | 11. 30 | 13. 48 24 | 15. 08 | 17. 98 | 13. 90 | 15. 08 | 17. 98 36 | 22. 61 | 26. 96 | 20. 84 | 22. 61 | 26. 96 42 | 26. 38 | 31. 45 | 24. 31 | 26. 38 | 31. 45 48 | 30. 16 | 35. 96 | 27. 80 | 30. 16 | 35. 96 54 | 33. 91 | 40. 45 | 31. 27 | 33. 91 | 40. 45 60 | 37. 68 | 44. 94 | 34. 74 | 37. 68 | 44. 94
From this table it appears, that the two convex lenses, have the same radii of their respective sides and that the concave flint lens has its two surfaces equally concave, so that a triple object-glass formed according to these proportions, would require only three pair of grinding tools. The following are the curves of the lenses of one of the best of Dollond’s achromatic telescopes, the focal length of the compound object-glass being 46 inches. Reckoning from the surface next the object--the radii of the crown-glass were 28 and 40 inches: the concave lens 20.9 inches, and the inner crown-glass lens, 28.4 and 28.4 inches. This telescope carried magnifying powers of from 100 to 200 times.