A CONTINUOUS RECORD OF ATMOSPHERIC NUCLEATION. 67 



as will be more ftiUy explained below. Here S is an appropriate subsidence con- 

 stant depending on the mean time of observation or on the time within which 

 nuclei are suspended in the fog particles. Conformably with this view « or 5 

 depends essentially on the height of the vessel in which the condensation is pro- 

 duced, being larger, ccet. par., in shallow vessels, seeing that v/h is larger. (§ 25) . 



12. The optic constant. — The proportionality of diameter with the inverse 

 aperture may be assumed for normal coronas. The occurrence of periodicity in 

 the higher coronas, even if merely a question of color were involved, would 

 modify these simple conditions for these cases. It is well known that for a 

 single particle, the masterly work of Lommel ' has given a complete treatment 

 of the diffractions in terms of Bessel functions. 



In meteorological work for a particle of diameter d and for uniformly nor- 

 mal coronas, the equation srn.q)=i.22X/d is usually assumed, if the angular 

 radius of the corona is q> and the wave length in question A. Since in my goni- 

 ometer 2 smqj = s/R, where i? = 3o cm., ti5 = o = 73. 2A. 'Hence, for the succes- 

 sive spectrum colors, the following values obtain for the constant a: 



In view of the theoretical uncertainty of these values in the case of the 

 distribution of particles met with in the above experiments, I have usually 

 relied on the results of direct comparisons with the corona of lycopodium spores 

 where ^,= .0032 cm. Placed in the position of the near plate of the coronal 

 chamber, the corresponding aperture for lycopodium spores was 53=1.05 cm., 

 at the far plate, 50=1.03. Hence a = d^s^= .oo2,A for measurements to the 

 outer edge of the first ring. Tliis corresponds to the preceding value for blue, 

 though these apertures were measured through ruby glass. In the above 

 tables, where merely relative results w^ere in question, a = .003 2, a datum of 

 earlier measurements, was inserted. Reduction was deemed needless. For 

 the case of measurements to the inner edge of the first ring or to the edge of the 

 white disc, 5,, = . 7 to .8, the demarcation being more vague. Assuming the 

 latter, a = .0026 for such measurements. Still more troublesome is the measure- 

 ment of a when the condensation chamber is remote (250 cm.) from the goni- 

 ometer and near (85 cm.) the source. The datum was a = .ooi25 from 5„ = .39. 



13. The optic constant. Diameters from subsidence. — This is an independ- 

 ent method of standardizing s. In my earlier w^ork the condensation chamber 

 was not cloth-lined, and the subsidence data quite untrustworthy, showing 

 rapid retardation of abnormally high initial values due to evaporation. In the 

 present cloth-lined receiver kept wet on all sides, stibsidence data are reasonably 

 satisfactory. The coronas, however, change character during subsidence, and 

 in case of the initial opalescent coronas (Series II above) all coronas vanish into 

 a mere fog before subsidence is even appreciable. Finally, the upper plane 

 ■ Lommel, Abhandl. der kdn. Bayerischen Akad. der Wissensch., xv, 1886. 



