Page:Dictionary of National Biography volume 33.djvu/354

Rh In the following year similar anomalous appearances were recorded. Thus, on one occasion, on using in combination a triple glass of Tulley's, free from coma and otherwise excellent, and a double plano-convex in which, when used alone, the spherical aberration was rather under-corrected, and an outward coma presented itself, the combination proved to have the spherical aberration rather over-corrected, and showed an inward coma. Again, a bi-convex glass of Herschel's construction, consisting of a biconvex of plate with a flint meniscus, when used alone with the flint surface foremost had little or no coma, but when combined with a triple 9/10 free from coma showed a ‘bur much inwards.’ The same glass used alone with the plate side foremost showed a ‘bur inwards,’ but when it was combined with the triple, which had before had the effect of inducing an inward coma, the bur inwards was changed to a ‘bur slightly outwards.’

Lister did not despair of finding an explanation of these perplexing and apparently inconsistent results, and in November 1829 a set of five plano-convex glasses manufactured by Utzschneider and Fraunhofer, very similar to those of Chevalier, but uncemented, having been placed freely at his disposal by Robert Brown, the botanist, he earnestly set to work to solve the difficult problem. His experiments he recorded in a series of tables, the first of which gives an accurate description of each of the five new glasses, and also of those of Chevalier, and of their performance when used singly. The others give the effects of various combinations of those glasses upon the chromatic and spherical aberrations and upon coma. He had previously observed in 1827 that in a particular combination of two glasses the coma was diminished by separating the glasses. And in these tables the performance of each combination is given, both when the glasses are close and when they are separated a certain distance from each other. The tables supply abundant evidence of the great effect produced upon coma and upon spherical aberration by the distance between the glasses; but the effects appear altogether inconsistent, and indeed contradictory.

Yet out of this apparent confusion Lister educed a principle which reconciled all the conflicting appearances, and formed the basis upon which all fine combinations for high powers of the microscope have since rested. He found that in a plano-convex lens, constructed like those above described, in which a double convex of plate has its colour corrected for a moderate aperture by a plano-concave of flint, the effect of the flint lens upon the spherical error caused by the plate lens varies remarkably according to the distance of the luminous point from the glass. If the radiant is at a considerable distance, the rays proceeding from it have their spherical error under-corrected; but as the source of light is brought nearer to the glass, the flint lens produces greater proportionate effect, and the under-correction diminishes till at length a point is reached where it disappears entirely, the rays being all brought to one point at the conjugate focus of the lens. This, then, is an aplanatic focus. If the luminous point is brought still nearer to the glass, the influence of the flint lens continues for a while to increase, and the opposite condition, of over-correction, shows itself; but on still greater approximation of the radiant, in consequence apparently of a reversal of the relations to each other of the angles at which the rays of light meet the different curves of the lens, the flint glass comes to operate with less effect, the excess of correction diminishes, and at a point somewhat nearer to the glass vanishes, and a second aplanatic focus appears; and from this point onwards under-correction takes the place of over-correction, and increases till the object touches the surface of the glass. Such a lens, then, has two aplanatic foci; for all points between these foci it is over-corrected, but under-corrected for points either nearer than the shorter, or more distant than the longer focus.

In a paper in the ‘Philosophical Transactions,’ read 21 Jan. 1830, Lister showed how a knowledge of these facts would enable the optician to combine a pair of compound achromatic lenses with perfect security against spherical error. ‘The rays,’ he wrote, ‘have only to be received by the front glass from its shorter aplanatic focus, and transmitted in the direction of the longer correct pencil of the other glass.’ The light then proceeding through each glass, as if from one of its aplanatic foci, is brought correctly to a focus by the combination. Supposing two glasses to have been so arranged, if the front glass is carried nearer to the back one, light proceeding from the shorter aplanatic focus of the front glass will reach the back glass as if from a point nearer than its longer aplanatic focus, that is to say from a point between the foci, and therefore the spherical error will be over-corrected. On the other hand, separation of the glasses beyond their original interval produces under-correction. Thus, by merely varying the distance between two such lenses, the correction of the spherical error may be either increased or diminished at pleasure according to a definite rule, and slight defects in the glasses