254 SUMMARY OF CURRENT RESEARCHES RELATING TO 



molecular shocks acting irregularly against the particles. J. Perrin 

 now describes experiments which he believes prove that molecular 

 movement is indeed the real and only cause of Brownian motion. He 

 obtained an emulsion of gamboge, and found it full of microscopic 

 particles exhibiting active Brownian movement. By centrifuging this 

 emulsion he obtained a finer emulsion, from which, although unchanged 

 to outer appearance, the microscopic particles had disappeared, leaving 

 ultra-microscopic spherical particles (or granules) in their place. He 

 studied the distribution of these particles at various levels, and, as the 

 result of averaging several thousands of readings, he found that if the 

 concentration of particles at a certain level be represented by 100, it is 

 represented at levels 25, 50, 75, and 100 microns lower by numbers 

 closely approximating to 119, 142, 169, 201, which are in geometrical 

 progression. This leads to the conclusion that the distribution of 

 equilibrium of these particles in the gamboge emulsion, and probably 

 in every other colloidal solution, resembles those of a gas in equilibrium 

 under the influence of its own weight. But in this case reduction to 

 half-density, which in the atmosphere requires an elevation of six 

 kilometres, here requires one-tenth of a millimetre. By further ex- 

 periments, involving minute measurements, he showed that the osmotic 

 pressure exerted by these particles corresponds, within the limits of 

 experimental errors, to the laws of gaseous pressure. Thus the spherical 

 particles in suspension act as visible molecules of a perfect gas. The 

 mean kinetic energy of a granule of a colloid is thus equal to that of a 

 molecule. 



E. E. Fournier d'Albe,* in summarising the present state of know- 

 ledge on this subject, remarks that if particles one-tenth of a micron 

 in size could be observed, the conditions would be favourable for 

 observing Brownian motions in gases themselves. 



Aberration of Sloped Lenses, and their Adaptation to Telescopes of 

 Unequal Magnifying Power in Perpendicular Directions.! — Lord 

 Rayleigh, in treating the above subject, divides his paper into two parts, 

 which are, to a large extent, independent. The first part deals with 

 mathematical aspects of the question, while the second discusses the 

 advantage which often attends a magnification unequal in different 

 directions, and describes the methods available for obtaining it. Among 

 these methods is that of the sloped object-lens. Such sloping introduces 

 in general unsymmetrical aberration, and the intention of the first part is 

 largely to show how this may be minimised so as to become unimportant. 



It is a common experience in optical work to find the illumination defi- 

 cient, when an otherwise desirable magnification is introduced. Sometimes 

 there is no remedy except to augment the intensity of the original source 

 of light, if this be possible. But in other cases the defect may largely 

 depend upon the manner in which the magnification is effected. With 

 the usual arrangements magnifying takes place equally in the two 

 perpendicular directions, though perhaps it may be required in only one 



* English Mechanic, No. 2285 (1909) p. 529. 



t Proc. Roy. Soc, lxxxi. No. A 544 (July 1908) pp. 26-40. 



