CHAPTER III. 



PRELIMINARY SURVEY OF THE APERTURES OF CORONAS, IN RELATION TO THE 

 NUMBER OF NUCLEI AND THEIR SIZES. 



i . Introductory. Throughout my earlier work with coronas, I have relied 

 chiefly upon the color sequences, and have taken the data for numbers and sizes 

 of cloud particles (a fixed degree of supersaturation presupposed) from the 

 tables given elsewhere. 1 When apertures were measured this was done chiefly 

 for the identification of the series to which the corona belongs. There is no 

 doubt, however, that an expression for the diameters of particles in terms of the 

 aperture of the coronas would be a great and immediate convenience, par- 

 ticularly as facility in using the color sequences is apt to be lost, unless one is at 

 work with them continually. Apart from this, the colors represent steps of 

 progress, while the apertures should be continuously, even if irregularly, variable. 

 The purpose is then to find under what conditions the discrepancies of aperture 

 may be reduced to a minimum. 



If the supersaturation is constant throughout, the diameters of cloud 

 particles and their distance apart will in general be proportional quantities. 

 Let m be the grammes of water precipitated, n the number of particles per 

 cubic centimeter, D = n ~ I/3 their distance apart, d the diameter of each, 5 the 

 aperture of the corona. If, therefore, for normal coronas d = a/s, where a is a 

 constant found by purely optical experiments, 



n= (6w/7ra 3 ) 5 3 = (6m/7T)/d i = i/L> 3 , and d = D(n/6mY /i . 



But it is doubtful if these equations are true even for normal coronas; 

 they must certainly be a very crude approximation for coronas of the higher 

 orders, where d and D are possibly both implicated in producing coronal effects. 

 If one builds up a system of glass plates each sprinkled with lycopodium par- 

 ticles, the diffraction pattern, which is finely multi-annular for a single plate, 

 is a mere blur for 10 plates placed within a linear foot, for instance, without 

 changing the aperture appreciably. If the source of light and the eye are both 

 distant, the coronas gradually lose sharpness and soon cease to be measurable 

 as the number of plates increases. This indicates that greater uniformity of 

 distribution and equality of diameter must be met with in case of cloud par- 

 ticles, but it leaves the question open whether the distance apart of particles is 

 not from the outset a consideration. 



l Am. Journ. o/ Science (4), xm, p. 81, 1902; Phil. Mag. (6), iv, p. 26, 1902; cf. 

 Structure of the Nucleus, Smithsonian Contributions, 1903, Chapter III. 



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