July i6, 1891] 



NATURE 



253 



the thickened edge, which bounds the still unbroken por- 

 tion. The speed, then, at which the edge will go depends 

 upon the thickness of the film. Duprd took a rather 

 extreme case, and calculated a velocity of 32 metres per 

 second. Here, with a greater thickness, our velocity was, 

 perhaps, 16 yards a second, agreeing fairly well with 

 Dupr^'s theory. 



I now pass on to another subject with which I have 

 lately been engaged— namely, the connection between 

 aperture and the definition of optical images. It has long 

 been known to astronomers and to those who study 

 optics that the definition of an optical instrument is pro- 

 portional to the aperture employed ; but I do not think 

 that the theory is as widely appreciated as it should be. 

 I do not know whether, in the presence of my colleague, 

 I may venture to say that I fear the spectroscopists are 



lenses may be. In accordance with the historical deve- 

 lopment of the science of optics, the student is told that 

 the lens collects the rays from one point to a focus at 

 another ; but when he has made further advance in the 

 science he finds that this is not so. The truth is that we 

 are in the habit of regarding this subject in a distorted 

 manner. The difficulty is, not to explain why optical 

 images are imperfect, no matter how good the lens em- 

 ployed, but rather how it is that they manage to be as 

 good as they are. In reality the optical image of even a 

 mathematical point has a considerable extension ; light 

 coming from one point cannot be concentrated into 

 another point by any arrangement. There must be 

 diffusion, and the reason is not hard to see in a general 

 way. Consider what happens at the mathematical focus, 

 where, if anywhere, the light should all be concentrated. 

 At that point all the rays coming from the original radiant 



A, B, Electrodes of Wimshurst machine. 



c, D, Terminals of interior coatings of Leyden jars. 



E, F, Balls on insulating supports between which the discharge is taken. 



G, Attracted disk of electrometer. 



H, Knife edge. i, Scale pan. 



J, Stops limiting movement of beam. 



K, Sparking bills in connection with exterior coatings of jars. [These 

 exterior coatings are to be joined by an imperfect conductor, such as a 

 table.] 



L, Lantern condenser. m, Soap film. 



N, Photographic camera. o. Daniell cell. 



p, Key. Q, Electro-magnets. R, Balls. 



among the worst sinners in this respect They constantly 

 speak of the dispersion of their instruments as if that by 

 itself could give any idea of the power employed. You 

 may have a spectroscope of any degree of dispersion, and 

 yet of resolving power insufficient to separate even the 

 D lines. What is the reason of this ? Why is it that we 

 cannot get as high a definition as we please with a limited 

 aperture? Some people say that the reason why large 

 telescopes are necessary is, because it is only by their 

 means that we can get enough light. That may be in 

 some cases a sufficient reason, but that it is inadequate 

 in others will be apparent, if we consider the case of the j 

 sun. Here we do not want more light, but rather are 

 anxious to get rid of a light already excessive. The prin- 

 cipal raison d'etre of large telescopes is, that without a { 

 large aperture definition is bad, however perfect the | 



NO. I 133, VOL. 44] 



point arrive in the same phase. The different paths of 

 the rays are all rendered optically equal, the greater 

 actual distance that some of them have to travel being 

 compensated for in the case of those which come through 

 the centre by an optical retardation due to the substitu- 

 tion of glass for air ; so that all the rays arrive at the 

 same time.^ If we take a point not quite at the mathe- 

 matical focus but near it, it is obvious that there must be 

 a good deal of light there also. The only reason for any 

 diminution at the second point lies in the discrepancies 

 of phase which now occur ; and these can only enter by 

 degrees. Once grant that the image of a mathematical 

 point is a diffused patch of light, and it follows that there 

 must be a limit to definition. The images of the com- 



' On this principle we may readily calculate the foc.^1 lengths of lenses 

 withDut use of the law of sines (see Phil, -^fag., December 1879). 



