138 Transactions of the [Sa.! Zrc^!xm. 



aberration by the distance between the glasses ; bnt the effects 

 appear altogether inconsistent, if not contradictory. Thus, as 

 regards coma, two of Fraiinhofer's glasses which, if used singly, 

 gave slight outward coma, gave when combined and near together 

 a great deal of coma rather outward, but when separated by 1 • 2 

 inch an almost entire absence of coma, and what there was rather 

 inwards. But, farther down, three glasses which each gave out- 

 ward coma when single, are seen to present in combination an 

 inward coma when close, and an outward coma when separated. 

 With respect to spherical aberration we seem for a while to meet 

 with something hke a law. We find that two glasses which, if 

 used alone, are free from spherical error, when combined and close 

 have that error over-corrected, but this over-correction is removed 

 by separating the glasses. And the same thing occurs with several 

 other combinations. But looking down the table we come to a 

 case where the excess of spherical correction caused by a com- 

 bination of three glasses placed close, cannot be removed by sepa- 

 rating them, and then follows a combination of three, in which 

 " the excess of spherical correction is increased by separating for 

 the short distance we can go." And, again, a httle lower occurs 

 a combination, also of three, in which " the excess of spherical cor- 

 rection is diminished but not conquered" by separation of the 

 glasses. 



Yet out of this apparent confusion he 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 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 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 

 further 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 



