TKANSACTIONS OF SECTION A. 627 



5. Investigations on the Electrical State of the Upper Atmosphere. 

 By W. Makower, Margaret White, and E. Marsden. 



The iuvestigations made during July and August 1908 is chiefly concerned 

 with the measurement of the electrical currents flowing from a kite down the wire 

 by which it is attached to the winding machine. In the first experiments diflerent 

 lengths of wire were let out with the kite, detached from the winding machine, 

 and the free end of the wire attached to an ebonite insulator fixed to the ground. 

 The kite was then connected to earth through a sensitive dead-beat galvano- 

 meter and the current measured. In these experiments the currents at considerable 

 heights were so large that it was found necessary to reduce the sensitiveness of 

 the galvanometer by shunting. The plan was therefore adopted in later experi- 

 ments of using as a shunt a portion of the kite wire when attached to the drum 

 of the winding machine, which was earthed, and thus making use of the usual 

 daily flights taking place at the Glossop observatory. The mean currents obtained 

 are given in the accompanying table : — 



Height of Kite Current in 



above Ground Amperes 



2,000 feet 5x10"^ 



■4,000 13x10-* 



0,000 „ 23x10-* 



The current at any fixed height varied considerably from day to day. There 

 seemed, however, to be a fairly close connection between the current and wind 

 velocity, the currents being great when the wind was high. A few experiments 

 have been made on the potential of the air at different heights, but no very 

 reliable results have yet been obtained, on account of the difliculty of satisfactorily 

 insulating for the high potentials to be measured. 



TUESBAY, SEPTEMBER 8. 

 Department of Mathematics. 



The following Papers were read :— 



1. Applications of Quaternions to Pi'ohlems in Pliysical Optics. 

 By Professor A. W. Conway. 



o 



On a Generalisation of the Question in Probabilities known as '■ Le 

 Scrutin de Ballotage.' By Major P. A. MacMahon, F.B.S. 



3. On Conformal Transformations of a Space of Four Dimensions and 

 their Application to Geometrical Optics. By H. Bateman. 



The study of the conformal transformations of a space of four dimensions is 

 simplified by the introduction of the six homogeneous coordinates 



l = x+iy m-z + iw n = x'' + if + z- + w^ 



\ = x—iy yL = z-iw v=—\ 



ponnected by the identical relation 



Ik + mfi + wv = 0. 



ss3 



