THE STRUCTURE OF THE NUCLEUS. 



75 



the number being found by experiment for normal coronas. Hence, r.(l6 + 6.dr = (2) 

 where ;• ■= s/2. Again, if the angle cp increases counter-clockwise by dcp, 



rdcp cos q) -f- dr sin qi = dli. (3) 



Let dd = adli (4) so that the diameter of the water particles is supposed to 



decrease {a being negative) uniformly upward. Other laws of distribution would 



merely complicate the problem without conducing to the present purposes, seeing 



that the observed facts will be sufEciently interpreted by equation (4). Combin- 



ing (i), (3), (2), 



r. cos (pd<p + sin cpdr — — {6 /a) (d/'/r) = — .00072 d/-/ar^, by equation (1). (5) 

 Put A = .00072/a and integrate (5) whence sin tp = C/r + A/r^. To determine 

 C equation (1) is available, since for ,p = 0, ?• = r^. Therefore 



8in9,= -(47l/s)(lAo-l/s). 

 To construct these coronas, distorted in consequence of the linear distribution 

 of size of particles, it will generally be more convenient to express s in terms of tp, 

 so that finally, 



s =3 - (2A/So sin <p) (1 - \/A + s% sin ,p/rl) = 



-(d^/asmcp){l-Vl-\-2A/sQ sin <p/So). (6) 



lY^. 2 



Fig. I. — Diagram. 



yio, 2.— Campanulate Coronas Due to Distributions of 

 Nuclei, Graded in the Ratio of 3 = </5/<///. =0005, .00010, 

 .00035, .00050, AND .00100. Corresponding Curves Have the 

 same Number above and iselow the Horizon. 



9. With this equation the following table has been computed {a is for con- 

 venience entered positively). To have an average case at the datum level, put 

 6 = 001™^ as the diameter of particles. The values of s are given for 9 values of <p 

 and for 6 values of a; viz., a = .00005, .0001, .00035, .0005, .001, or for a/s^ = 

 .05, .1,.35,.5, 1.0, as decrements of diameter'per linear centimeter of level above h^. 



