458 REPORT— 1882. 



Now it can be shown that 



f 



r? i / ^ / ^\ 7 1 n + kanuanvy. 



A; i' su (u + v) — sn (u — v) } au=lo°; ( , — j 1 



J I ^ -' ^ ■' \ ^yi—kanuanvj 



= 2 {7i sn M sn v + ^ k^ sn ^u sn ^y + i k^ an ^u sn ^i> + &c.}, 



^1=^ , sn- (<J + ?;) + sn- (?« — y) — 2 sn ^u \ du clu = —log (1 — k- su -u sn -y) 

 ' ' 



= Z;' sn -u sn -y + ^ Z;^ sn ^u sn 'y + g- k'^ sn "w sn "a; + &c., 



80 that by equating the coefficients involving sn ^""ly and sn -"v we find that 

 A;'»-isn2«-'w 1 /,; sn «^ 1 I l 



Jn — 1 (2r! — 1)! ' 2n (^»)! I 1 



whence 



(//'- (2(1-1) /7-'»l-2 X 



_R^(2n-i) + 7j^(2n-n » + . . .i2 _^i__ U sn ?i 



aW" 2n— 1 "'* y 



(2«-l)! F« sn2''(« = f iZo^'O + J? »'0_^ . . . +_RC2>.)i!!Ii^;^2 g^ 2„_7vV-''.) 

 which are the equations written at the beginning of the paper. 



MOJ^DAr, AUGUST 28. 



The following Reports and Papers were read : — 



1. Fifteenth Report of the Committee on Under grotmcl Temperature, containing 

 a Synopsis of all previous Reports of this Committee. — See Reports, p. 72. 



'J. On the Orirjin of Hail. i?y/ Professor Theodore Schwedoff. 



The size and weight of hail is frequentlj^ such as to cause all the usual theories 

 as to the origin of hail in currents in the atmosphere to fail. The extreme lowness 

 of their temperature forbids the idea that they are newly frozen. The researches of 

 Abich, Secchi, Delcros, and others, leave no doubt that a hailstone is typically a 

 figure of revolution, a sphere, oblate spheroid, discoid or toroid, often having hol- 

 lowed poles and even annular. They are also frequently covered with large and 

 well-developed crystals of clear ice. From these facts, Professor Schwedoff argues 

 that thej' are of ultra-mundane or cosmical origin, and are in fact a species of 

 meteorite. The strongest apparent confirmation of this hypothesis is to be found 

 in the well-established fact of the existence of stony or pyritic nuclei in many 

 hailstones, which nuclei have been proved to contain iron, nickel, &c. 



3. Notes on Schivedoff's Tlieory of Hail. By Professor Silvanus P. 



Thompson. 



(1) In confirmation of Schwedoff 's views as to the typical form of hailstone 

 being a figure of revolution, examples were cited from the observations of Darwin, 

 Humboldt, Bnist, Blanford, Blanchet, CoUadon, Godefroy, and Loomis. The 

 conical or pyi'amidal forms recently described as typical, Ijy Professor Osborne 

 Reynolds, could only be regarded as fragments broken from a spherical or spheroidal 

 fiirm of radial structure. 



(2) As to Schwedoff's theory of a meteoric origin, this could, if accepted at all, 

 only be accepted for certain cases of hail-falls. Becquerel had long ago divided 

 hailstorms into 'ordinary' and 'extraordinary'; the latter being independent of 

 local circumstances. If Schwedofl''s theory were true, there should be regular 

 hailstone days and hailstone periods. Some evidence appeared to be forthcoming 



