figure 74.

figure 75.figure 76.

Aberration of lenses.—In connection with the above descriptions, the following statements respecting the spherical aberration of lenses may not be inappropriate. Mr. John Dollond, in a letter to Mr. Short, remarks, that ‘the aberration in a single lens is as the cube of the refracted angle; but if the refraction be caused by two lenses, the sum of the cubes of each half will be ¼ of the refracted angle, twice the cube of 1 being ¼ the cube of 2. So three times the cube of 1 is only one ninth of the cube of 3.’ &c. Hence the indistinctness of the borders of the field of view of a telescope is diminished by increasing the number of lenses in an eye piece. Sir J. Herschel has shown that if two plano-convex lenses are put together as in fig. 75, the aberration will be only 0.2481, or one fourth of that of a single lens in its best form. The focal length of the first of these lenses, must be to that of the second as 1 to 2.3. If their focal lengths are equal, the aberration will be 0.603, or nearly one half. The spherical aberration, however, may be entirely destroyed by combining a meniscus and double convex lens, as shown in fig. 76, the convex sides being turned to the eye when they are used as lenses, and to parallel rays, when they are used as burning glasses. Sir J. Herschel has computed the following curvatures for such lenses.

Focal length of the convex lens+10.000
Radius of its first surface+5.833
Radius of its second surface-35.000
Focal length of the meniscus+17.829
Radius of its first surface+3.688
Radius of its second surface+6.294
Focal length of the compound lens+6.407

On the general principles above stated, a good astronomical eye-piece may be easily constructed with two proper lenses, either according to the plan of Huygens or that of Ramsden; and, from what has been now stated it is demonstrably certain, that, in all cases where two glasses are properly combined, such an eye-piece is superior to a single lens, both in point of distinctness, and of the enlargement of the field of view. I lately fitted up an eye-piece, on Ramsden’s principle, with two lenses, each about 3 inches focal length, and 1⅜ inch diameter, placed at half an inch distant, with their convex surfaces facing each other as in fig. 74, which forms an excellent eye-piece for an achromatic telescope, 6 feet 8 inches focal distance, and 4 inches aperture, particularly for viewing clusters of stars, the Milky Way, and the large nebulæ. The field of view is large, the magnifying power is only between 50 and 60 times, and the quantity of light being so great, every celestial object appears with great brilliancy, and it is in general much preferable, when applied to the stars than any of the higher powers. When applied to Presepe in Cancer, it exhibits that group at one view, as consisting of nearly a 100 stars which exhibit a beautiful and most striking appearance.

It may appear a curious circumstance that any eye-piece which is good with a short telescope, is also good with a long one, but that the reverse is not true; for it is found to be more difficult to make a good eye-piece for a short than for a long focal distance of the object-glass.

Celestial eye-pieces are sometimes constructed so as to produce variable powers. This is effected by giving a motion to the lens next the eye, so as to remove it nearer to or farther from the field lens; for at every different distance at which it is placed from the other lens, the magnifying power will either be increased or diminished. The greatest power is when the two lenses are nearly in contact, and the power diminishes in proportion to the distance at which the glass next the eye is removed from the other. The scale of distance, however, between the two lenses, cannot be greater than the focal distance of the field, or inner glass; for if it were, the lenses would no longer form an eye-piece, but would be changed into an inverting opera-glass. For effecting the purpose now stated, the eye-glass is fixed in a tube which slides upon an interior tube on which is marked a scale of distances, corresponding to certain magnifying powers; and, in this way an eye-piece may be made to magnify about double the number of times, when the lenses are in one position than when they are in another—as, for example, all the powers from 36 to 72 times may be thus applied, merely by regulating the distance between the two lenses. When the glasses are varied in this manner the eye-piece becomes sometimes a positive eye-piece, like Ramsden’s, and sometimes a negative one like that of Huygens.

Diagonal eye-pieces. The eye-pieces to which we have now adverted, when adapted to refracting telescopes, both reverse and invert the object, and therefore are not calculated for showing terrestrial objects in their natural position. But as the heavenly bodies are of a spherical form, this circumstance detracts nothing from their utility. When the celestial object, however, is at a high altitude, the observer is obliged to place his head in a very inconvenient position, and to direct his eye nearly upwards; in which position he cannot remain long at ease, or observe with a steady eye. To remedy this inconvenience, the diagonal eye-piece has been invented, which admits of the eye being applied at the side—or at the upper part of the eye-piece, instead of the end; and when such an eye-piece is used, it is of no importance in what direction the telescope is elevated, as the observer can then either sit or stand erect, and look down upon the object with the utmost ease. This object is effected by placing a flat piece of polished speculum-metal at an angle of 45 degrees in respect to the two lenses of the eye-piece, which alters the direction of the converging rays, and forms an image which becomes erect with respect to altitude, but is reversed with respect to azimuth;—that is, in other words, when we look down upon the objects in the field of view, they appear erect; but that part of an object which is in reality on our right hand appears on our left; and if it be in motion, its apparent is opposite to its real motion; if it be moving towards the west, it will seem to move towards the east.

There are three situations in which the diagonal reflector in this eye-piece may be placed. It may be placed either 1. before the eye-piece,—or 2. behind it,—or 3. between the two lenses of which the eye-piece consists. The most common position of the reflector is between the lenses; and this may be done both in the negative and the positive eye-pieces; but as the distance between the two lenses is necessarily considerable, to make room for the diagonal position of the reflector, the magnifying power cannot be great; otherwise, a diagonal eye-piece of this construction remains always in adjustment, and is useful in all cases where a high power is not required. The following is a description and representation of a diagonal eye-piece of this kind in my possession.