SECTIONAL TRANSACTIONS,.—A. 299 
other two. Many facts regarding it have been established, of which a summary is 
given in the paper, and the controlling factor appears to be the pressure distribution 
rather than the sea temperature ; but the causes of the pressure variation are mostly 
still unknown. Hildebrandsson’s theory that the conditions are controlled by the 
quantity of ice seems to present considerable difficulties. 
12. Prof. A. E. Kennetty.—Some New Properties of Hyperbolic Func- 
tions and Integral Series of Numbers, with Applications to Electrical 
Engineering. 
13. Prof. H. Barreman. — A Certain System of Partial Differential 
Equations. 
If A and pare constants the equations 
ol Gr 0g yop On _ Om 
Oz Oy Oz Ox Oy Oz 
Om _ Op _ Or, yog_ Ol On 
Oy Oz Ox Oy Oz Ox 
On _ Og _ Op, Or _ Om _ ob 
Oz Ox Cy Oz Ox oy 
imply that each of the six quantities 1, m,n, p,q, 7 is a solution of the partial 
differential equation 
av ov, OV, OV 
0x8 * Oy? ' O28 eh reac a 
oO 
A set of solutions may be expressed by means of definite integrals of a well- 
known type. 
Monday, August 31. 
14. Joint Discussion with Section C (see page 314) on Variation in 
Gravitational Force and Direction and its Relation to Geological 
History. 
15. Report of Seismology Committee (see page 216). 
16. Mr. J. H. Suaxpy.—The Diffusion of Suspended Particles and 
Avogadro's Number. 
As a suspension settles under gravity a certain number of its particles reach the 
vertical walls of the containing vessel as a result of their Brownian movements ; they 
can be made to adhere to it and can thus be counted. Their number increases with 
depth, since the time during which a given level of the wall is in contact with fluid 
containing particles is limited by the rate of fall of the upper boundary of the settling 
cloud. The adherent population thus gives a measure of the diffusion and provides 
its own time-record if the rate of settling is known. From the theory of diffusion, due 
to Smoluchowski, Avogadro’s Number can be determined. In the present work the 
eee used were the minute natural spheres of Staphylococcus. Avogadro’s 
umber was found to be 5.9x 10. 
17. Prof. J. G. Gray.—Some new Gyroscopic Tops (with demonstrations). 
