The nature of the corrections which take place in the doublet is explained in the annexed diagram (Fig. 5), where L O L´ is the object, P a portion of the pupil, and D D the stop, or limiting aperture. Now, it will be observed that each of the pencils of light from the extremities L L´ of the object is rendered eccentrical by the stop, and of consequence each passes through the two lenses on opposite sides of their common axis O P; thus each becomes affected by opposite errors, which to some extent balance and correct each other. To take the pencil L, for instance, which enters the eye at R B, R B; it is bent to the right at the first lens, and to the left at the second; and as each bending alters the direction of the blue rays more than the red, and, moreover, as the blue rays fall nearer the margin of the second lens, where the refraction, being more powerful than near the centre, compensates in some degree for the greater focal length of the second lens, the blue and red rays will emerge very nearly parallel, and of consequence colorless to the eye. At the same time the spherical aberration has been diminished by the circumstance that the side of the pencil which passes one lens nearest the axis passes the other nearest the margin. This explanation applies only to the pencils near the extremities of the object. The central pencil, it is obvious, would pass both lenses symmetrically; the same portions of light occupying nearly the same relative places on both lenses. The blue light would enter the second lens nearer to its axis than the red, and being thus less refracted than the red by the second lens, a small amount of compensation would take place, quite different in principle and inferior in degree to that which is produced in the eccentrical pencils. In the intermediate spaces the corrections are still more imperfect and uncertain; and this explains the cause of the aberrations which must of necessity exist even in the best-made doublet. It is, however, infinitely superior to a single lens, and will transmit a pencil of an angle of from 35° to 50° without any very sensible errors. It exhibits, therefore, many of the usual test-objects in a very beautiful manner. [Illustration: Fig. 5.] [Illustration: Fig. 6.]