633 



MICROSCOPE. 



MICROSCOPE. 



631 



focus. To cement together also the two surfaces of the glass dimin- 

 ishes by very nearly half the loss of light from reflexion, which is con- 

 siderable at the numerous surfaces of a combination. I have thought 

 the clearness of the field and brightness of the picture evidently 

 increased by doing this; it prevents any dewiness or vegetation from 

 forming on the inner surfaces ; and I see no disadvantage to ' be 

 anticipated from it if they are of identical curves, and pressed closely 

 together, and the cementing medium permanently homogeneous. 



" These two conditions then, that the flint lens shall be plano- 

 concave, and that it shall be joined by some cement to the convex, 

 seem desirable to be taken as a basis for the microscopic object-glass, 

 provided they can be reconciled with the destruction of the spherical 

 and chromatic aberrations of a large pencil. 



" Now in every such glass that has been tried by me which has had 

 ita correcting lens of either Swiss or English glass, with a double 

 convex of plate, and has been made achromatic by the form given to 

 the outer curve of the convex, the proportion has been such between 

 the refractive and dispersive powers of ita lenses, that its figure has 

 been correct for rays issuing from some point in its axis not far from 

 its principal focus on its plane side, and either tending to a conjugate 

 focus within the tube of a microscope, or emerging nearly parallel. 

 "Let AB (Jig. 13) be supposed such an object-glass, and let it be 

 t'i" 13 G II rou o n 'y considered as a plano-convex lens, with a 

 curve ABC running through it, at which the 

 spherical and chromatic errors are corrected which 

 | / are generated at the two outer surfaces ; and let 



the glass be thus free from aberration for rays 

 F D E o issuing from the radiant point F, H K being 

 a perpendicular to the convex surface, and I D to 

 the plane one. Under these circumstances, the 

 angle of emergence OKH much exceeds that of 

 incidence r D I, being probably nearly three times 

 as great. 



" If the radiant is now made to approach the 

 glass, so that the course of the ray F D E o shall 

 be more divergent from the axis, as the angles of 

 incidence and emergence become more nearly 

 equal to each other, the spherical aberration pro- 

 duced by the two will be found to bear a less 

 proportion to the opposing error of the single 

 correcting curve A c B ; for such a focua therefore 

 the rays will be over-correcled. 



" But if F still approaches the glass, the angle 

 of incidence continues to increase with the in- 

 creasing divergence of the ray, till it will exceed 

 that of emergence, which has in the meanwhile 

 been diminishing, and at length the spherical 

 error produced by them will recover its original 

 proportion to the opposite error of the curve of 

 correction. When F has reached this point p"(at 

 which the angle of incidence does not exceed 

 that of emergence so much as it had at first come short of it), the rays 

 again pass the glass free from spherical aberration. 



" If F be carried from hence towards the glass, or outwards from its 

 original place, the angle of incidence in the former case, or of emer- 

 gence in the latter, becomes disproportionately effective, and either 

 way the aberration exceeds the correction. 



" These facts have been established by careful experiment : they 

 accord with every appearance in such combinations of the plano- 

 convex glasses as have come under my notice, and may, I believe, be 

 extended to this rulo, that in general an achromatic object-glass, of 

 which the inner surfaces are in contact, or nearly so, will have on one 

 side of it two foci in its axis, for the rays proceeding from which it 

 will be truly corrected at a moderate aperture ; that for the space 

 between these two points its spherical aberration will be over-corrected, 

 and beyond them either way under-corrected. 



" The longer aplanatic focus may be found, when one of the plano- 

 convex object-glasses is placed in a microscope, by shortening the tube, 

 if the glass shows over-correction; if under-correction, by lengthening 

 \V, or by bringing the rays together, should they be parallel or diver- 

 gent, by a very small good telescope. The shorter focus is got at by 

 sliding the glass before another of sufficient length and large aperture 

 that is finely corrected, and bringing it forwards till it gives the re- 

 flexion of a bright point from a globule of quicksilver, sharp and free 

 from mist, when the distance can be taken between the glass and the 

 object. 



" The longer focus is the place at which to ascertain the utmost 

 aperture that may be given to the glass, and where, in the absence of 

 ,;il error, its exact state of correction as to colour is seen most 

 distinctly. 



" The correction of the chromatic aberration, like that of the sphe- 

 rical, tends to excess in the marginal rays ; so that if a glass which is 

 achromatic, with a moderate aperture, has its cell opened wider, the 

 circle of rays thus added to the pencil will be rather over-corrected as 

 to colour. 



" The same tendency to over-correction is produced, if, without 

 Tarying the aperture, the divergence of the, incident rays is much 

 augmented, as in an object-glass placed in front of another; but gene. 



r ally in this position a part only of its aperture comes into use ; so 

 th;it the two properties mentioned neutralise each other, and its 

 chromatic state remains unaltered. If for example the outstanding 

 colours were observed at the longer focus to be green and claret, 

 which show that the nearest practicable approach is made to the union 

 of the spectrum, they usually continue nearly the same for the whole 

 space between the foci, and for some distance beyond them either way. 



" The places of these two foci and their proportions to each other 

 depend on a variety of circumstances. In several object-glasses that I have 

 had made for trial, plano-convex, with their inner surfaces cemented, 

 their diameters the radius of the flint lens, and their colour pretty 

 well corrected, those composed of dense flint and light plate have had 

 the rays from the longer focus emerging nearly parallel ; and this 

 focus has been not quite three times the distance of the shorter 

 from the glass : with English flint the rays have had more con- 

 vergence, and the shorter focus has borne a rather less proportion to 

 the longer. 



" If the surfaces are not cemented, a striking effect is produced by 

 minute differences in their curves. It may give some idea of this, 

 that in a glass of which nearly the whole disc was covered with colour 

 from contact of t'ne lenses, the addition of a film of varnish, so thin 

 that this colour was not destroyed by it, caused a sensible change in 

 the spherical correction. 



" I have found that whatever extended the longer aplanatic focus, 

 and increased the convergence of its rays, diminished the relative length 

 of the shorter. Thus by turning to the concave lens the flatter instead 

 of the deeper side of a convex lens, whose radii were to each other as 

 31 to 35, the pencil of the longer aplanatic focus, from being greatly 

 divergent, was brought to converge at a very small distance behind the 

 glass ; and the length of the shorter focus, which had been one-half 

 that of the longer, became but one-sixth of it. 



" The direction of the aplanatic pencils appears to be scarcely affected 

 by the differences in the thickness of glasses, if their state as to colour 

 is the same. 



" One other property of the double object-glass remains to be men- 

 tioned, which is, that when the longer aplanatic focus is used, the 

 marginal rays of a pencil not coincident with the axis of the glass are 

 distorted, so that a coma is thrown outwards ; while the contrary effect 

 of a coma directed towards the centre of the field is produced by the 

 rays from the shorter focus. These peculiarities of the coma seem 

 inseparable attendants on the two foci, and are as conspicuous in the 

 achromatic meniscus as in the plano-convex object-glass. 



" Of several purposes to which the particulars just given seem 

 applicable, I must at present confine myself to the most obvious one. 

 They furnish the means of destroying with the utmost ease both 

 aberrations in a large focal pencil, and of thus surmounting what has 

 hitherto been the chief obstacle to the perfection of the microscope. 

 And when it is considered that the curves of its diminutive object- 

 glasses have required to be at least as exactly proportioned as those of 

 a large telescope to give the image of a bright point 

 equally sharp and colourless, and that any change 

 made to correct one aberration was liable to disturb 

 the other, some idea may be formed of what the 

 amount of that obstacle must have been. It will 

 however be evident that if any object-glass is but 

 made achromatic, with its lenses truly worked and 

 cemented, so that their axes coincide, it may with 

 certainty be connected with another possessing the 

 same requisites and of suitable focus, so that the 

 combination shall be free from spherical error also 

 in the centre of its field. For this the rays have 

 only to be received by the front glass B (Jig. 14) 

 from its shorter aplanatic focus F", and transmitted 

 in the direction of the longer correct pencil F A of 

 the other glass A. It is desirable that the latter 

 pencil should neither converge to a very short focus 

 nor be more than very slightly if at all divergent ; 

 and a little attention at first to the kind of glass 

 used will keep it within this range, the denser flint 

 being suited to the glasses of shorter focus and larger 

 angle of aperture. 



" The adjustment of the microscope is then 

 perfected, if necessary, by slightly varying the dis- 

 tance between the object-glasses; and after that is 

 done, the length of the tube which carries the 

 eye-pieces may be altered greatly without disturbing 

 the correction, opposite errors which balance each other being produced 

 by the change. 



" If the two glasses which in the diagram are drawn at some distance 

 apart are brought nearer together (if the place of A for instance is 

 carried to the dotted figure), the rays transmitted by B in the direction 

 of the longer aplanatic pencil of A will plainly be derived from some 

 point 7. more distant than F", and lying between the aplanatic foci of 

 B ; therefore (according to what has been stated) this glass, and con- 

 sequently the combination, will then be spherically over-corrected. If 

 on the other hand the distance between A and B is increased, the 

 opposite effects are of course produced. 



" In combining several glasses together it is often convenient to 



fie. 14. 



