148 Transactions of the Society. 



Test-objects. — The various test-objects included in the bequest 

 are mostly for use with the telescope, and were evidently con- 

 structed for the purpose of Lister's experiments on limits of resolu- 

 tion, conducted with telescopic objectives. From his experiments 

 he deduced that the limit of resolution was about 4*33 seconds of 

 arc for an aperture of 1 in., and, consequently, that an aperture of 

 2 in. meant a resolving-power of 2*17, and so on. ♦ But as 

 Lister, so far as it can be gathered, never published this statement, 

 it makes the fact all the more remarkable that his estimation is 

 almost identical with that arrived at by the illustrious Dawes, 

 nearly half a century later. This astronomer came to the conclu- 

 sion — which was in a measure arrived at by observational and 

 perhaps arbitrary methods — that a 1-in. aperture would or should 

 separate double stars 4*55 seconds apart. The extraordinary 

 closeness of these two sets of figures cannot be said to be anything 

 else than startling. Lister, however, distinctly states in his me- 

 moranda that the object of the experiments was to obtain data pre- 

 liminary to ascertaining the limits of resolution in the microscopical 

 objective. This investigation Lister carried out with consummate 

 care and skill by a series of characteristically ingenious experiments, 

 by whicli he came to the astounding conclusion that resolving- 

 power was proportional, not to the angle of the objective — as, indeed, 

 it was believed to be up to the time of Abbe — but to the " chord of 

 the angle," which is the same as saying to the sine of half the angle. 

 In other words, this is the ]N"umerical Aperture which was enun- 

 ciated by Abbe some forty years later. Putting it another way. 

 Lister said he considered the limit of resolution for what we now 

 call N.A. 1*0 was in the region of 95,249 lines to the inch, whilst 

 Abbe (using light 47,500 waves to the inch) made it 95,000 — an 

 approximation to Lister's statement that is simply extraordinary. 

 As previously explained. Abbe could not have heard of Lister's 

 figures for the reason that his papers — to the best of our knowledge 

 at the moment — were never published, and only came to light for 

 the first time last summer. 



The first ])iece of apparatus to be noticed in this connexion 

 appears to be an anticipation of Abbe's test-plate, only designed for 

 the telescope instead of for the Microscope. It consists of several 

 tubes of glass filled with mercury, laid side by side, with a small 

 interval between, on a piece of black material — the idea being, 

 of course, to provide objects with as great a contrast as possible. 



Another piece of apparatus was evidently designed for the 

 formation of artificial points of light by reflections from the bulbs 

 of mercurial thermometers illuminated by candles shielded by 

 screens. But in making this arrangement of thermometer-bulbs 

 he evidently appreciated the necessity of testing oblique pencils, 

 as shown by a simple contrivance for throwing out one of the bulbs 

 towards the edge of the field. It seems pretty certain he had in his 



