C. Barus — Coronas with Mercury Light. 81 



successive value n' zJr Jn f z — s 3 z+1 /s\ in their relation to y — -771 

 the exhaustion applied. • The table shows that for very large 

 coronas n / z+1 /n / z >y, whereas for very small coronas n f z+ Jn' z <iy. 

 For the intermediate coronas (g 5 ), i. e., from the seventh to the 

 tenth exhaustion among twenty, the ratio is nearly equal to y. 

 Ratios smaller than y may be reasonably interpreted as due to 

 subsidence and the constant Sis actually of the order of values 

 to be computed from the viscosity of the medium and the size 

 of the vessels and fog particles. Within this range (coronas 

 smaller than g 9 ) the optic and the presumptive nucleation may 

 in fact be brought into agreement. 



In case of the large coronas, however, subsidence is virtually 

 absent and the occurrence of n r z+1 /n z > y calls for some appar- 

 ent production of nuclei at each exhaustion, which is altogether 

 improbable. Therefore, fig. 2 and 3, compare n' and n, whence 

 n-n' shows the number of nuclei not registered by condensation. 



For, no matter whether condensation on a given group of 

 nuclei occurs or not, no matter how many nuclei have failed of 

 catching a charge of water, the identical removal of nuclei by 

 partial exhaustion must take place. Such removal is indepen- 

 dent of condensation, and would occur in a dry atmosphere 

 under similar treatment. Consequently y cannot be too large. 

 It may be too small not only from subsidence, but from time 

 losses (decay), or as the result of the purification of air due to 

 turbulent motion across a solid or liquid surface. Consequently 

 n may be regarded as an inferior limit of the nucleation with 

 a probably close approximation to the true value. A comparison 

 of n and n-n' would, in such a case, show the percentage of 

 nuclei of irregular size which have failed of capture, .the 

 number being n-n'. 



At the same time it must always be recalled, that no ade- 

 quate theory of coronas exists and that therefore the meaning 

 of n' is obscure. We must in any case place a part if not all 

 the discrepancy between n and n' within the province of such 

 a theory as is evidenced by the dependence of aperture on the 

 position of the eye. The need is particularly manifest for the 

 large coronas, in which there is accentuated superposition of 

 interference and diffraction. Small coronas may be tested by 

 coincident results obtained from subsidence and the agreement 

 is then well within the errors of observation. 



Brown University, 



Providence, R. I. 



Am. Jour. Sci. — Fourth Series, Vol. XXVII, No. 157. — January, 1909. 



