576 Transactions of the Society. 



light from this slit being focussed by a condenser upon those 

 particles which are to be made visible. The size of the slit can be 

 precisely controlled, and, with a knowledge of its width and of the 

 condensing system employed, the exact thickness of the layer of 

 illuminated particles can be regulated to a nicety. It will be found 

 convenient to adjust the thickness of this illuminated layer to 

 about 1 or 3 /i, so that it may correspond with the depth of focus 

 of the objective. 



We will now examine the limit of the smallest size of particles 

 which it is possible to render visible by this method. The follow- 

 ing considerations will help us to solve this question, at least 

 approximately. It is known that radiation from a surface de- 

 pends on three main factors — first, on the specific intensity of 

 radiation ; secondly, on the area of the radiating surface ; thirdly,, 

 on the solid angle at which the radiation is emitted from the sur- 

 face. This amount of energy can be expressed in terms of candle- 

 power, and the limit of sensitiveness of the human eye for light is 

 also known. From these two quantities, namely, the limit of least 

 sensitiveness of the eye, and the limit of the greatest radiation 

 which can be obtained by diffraction from the particles, we are in 

 a position to determine the limit for the smallest dimensions which 

 can be made directly visible. Within the scope of practical ex- 

 periments this limit approximately works out at forty square 

 millionths of a millimetre, which therefore corresponds to a circle 

 of a radius of about tqooooo mm -* It is of particular interest 

 to note that the result of these practical observations appears to 

 approach very nearly to the theoretical limit of visibility of the 

 minutest particles. 



Now, it may be taken for granted that with no artificial illu- 

 mination, however intense, will it be possible to discern with the 

 human eye dimensions so small as those attributed to medium 

 sized molecules (about • 6 /x /x). Even if we were to succeed in 

 making the molecules self-luminous by any conceivable process, 

 the specific intensity of the luminosity would have to considerably 

 exceed the power of the sun's rays, a feat decidedly improbable. 



Permit me here* to mention that I particularly wish to guard 

 against any over-estimation of the capabilities of the methods ex- 

 hibited to-night. In particular I would wish to repeat that the 

 procedure in question does not give any optical solution of the 

 true shape and size of the small particles. Whatever their form 

 may be you will always obtain a small diffraction disc as the 

 image. Only when an ultra-microscopic particle is so much en- 

 larged that one of its dimensions exceeds half a wave-length (in 

 other words when it in part passes out of what may be called 



* H. Siedentopf unci R. Zsigniondy, ' Uber Sichtbarmachung und Groseen- 

 bestimmuns ultramikroskopischer Teilchen niit besonderer Anwendung auf Gold- 

 rubinglaser.' Ann. d. Physik, x. (190;>) pp. 1-39. Diam. = -008 /*. 



