380 Transactions of the Society. 



Sir Geo. Airy, who in 1835 published his results in the Cambridge 

 Philosophical Journal, vol. 5, p. 283, and subsequently renewed the 

 investigation in his Undulatory Theory of Optics, pp. 60-82, edition 

 of 1877. The immediate subject of his inquiry was the resolving 

 power of the telescope for fixed stars — the problem of point and anti- 

 point pure and simple. He did not advance to the consideration of 

 the way in which images could be built up of antipoints ; and although 

 the one follows, as we have seen, extremely simply from the other, it 

 may be that the limitations of Sir Geo. Airy's statement have been 

 mistaken for limits of his theory. Later, i.e. in 1896, Lord Rayleigh, 

 writing, as it would seem, independently of Sir Geo. Airy's work, 

 applied the same principles to the resolving power of the Microscope. 

 His paper appears in vol. 42 of the Philosophical Magazine, p. 167. 

 It has been objected to Lord Kayleigh's investigation, that he assumes 

 the full aperture of the objective to be occupied with rays from the 

 object on the stage, whereas it is said that in fact diffraction may cut 

 out certain parts of the cone of incident light, and leave the effective 

 aperture something less than the angular aperture of the lens. This 

 objection is somewhat beside the mark, because, a3 we have seen, it is 

 always quite easy to get rid of diffraction on the stage of the Micro- 

 scope by the expedient of critical illumination. Even were this other- 

 wise, the problem presented by a segmen tally illuminated objective 

 would have to be investigated by an extension of Lord Rayleigh's 

 method. It cannot possibly be solved by Professor Abbe's method, 

 which is vitiated by the fundamental and irremediable error that it 

 seeks in the object for the explanation of phenomena which originate 

 in the instrument. 



"While the work of Airy and of Eayleigh has left only gleanings 

 for other labourers in this field, the gleanings may themselves per- 

 chance prove valuable. I venture therefore to offer you the result 

 of my own attempt to contribute towards the labour of gathering up 

 such ears of corn as still remain ungarnered. In what follows I shall 

 not attempt to follow closely in the steps of the two investigators 

 just named, because their results are, from the point of view of the 

 ordinary reader, too abstractly mathematical — as a friend of mine puts 

 it — they are too much contaminated with differential calculus to please 

 a middle-aged taste. I shall take the liberty therefore of striking 

 out in a new direction, so far as the form of the explanation is con- 

 cerned, and shall hope to submit it to you in a shape better suited to 

 the exigencies of oral discussion. 



^ hen a train of wave-fronts — by which, of course, I mean a series of 

 wave-fronts advancing in orderly and rhythmic sequence — when a train 

 o! light wave-fronts is intercepted by an opaque screen, the segments 

 of the successive wave-fronts which escape past the edges of the screen 

 or through apertures in its expanse pass on and become a source of 

 light in the space behind the screen. But, as is well known, they do 

 not illuminate the whole rearward space. The luminiferous impulse 



