786 
Proceedings of Boyal Society of Edinburgh. [sess. 
and it easily results from (10) that we obtain a set of thirty 
formulae, from which selecting, 
2Say{Soc8Si8ycS/3f8 = V - tfvf - /Art) + W ; 
2Sa 7 8Sa C {Sj88fS f3ye = Y 2 (^ - $y\ - - W ; 
we have, see (7) 
Say^SaSe Y 2 (^i - &v\ - /*J) + W 
SayeSa^S 2/^Y 2 ; 
SaySSa^ __ Y 2 (/^ - ^ - /iM) - W 
SayeSa£S 2/^Y 2 ; 
we have thus an expression for SaycSa£S, and by permuting we 
can form, in like manner, expressions for 
SaycS PCy- and SafSS/?£y , 
and so obtain S 2 aye. In fact we have, 
[{' V 2 (/*I^ - f4A) + W}SyeYS£ + t4vtY*(Sy£VSe + SySVW]Say€Saf8 
= -2^Y 2 F 2 . 
It will be observed how Quaternion methods enable us to express 
simply forms which, without this powerful analysis, would present 
formidable complexities. 
Report on Atmospheric Circulation, based on the Observa- 
tions made on Board H.M.S. “Challenger” 1873-76. 
By Alexander Buchan, LL.D. 
(Part I. read April 16, 1888 ; Part II. read May 6, 1889.)* 
(Abstract.) 
In these papers the meteorological observations taken during the 
voyage of the “ Challenger ” are discussed ; and, from data collected 
from all parts of the world, fifty-two maps have been prepared, 
showing for each month of the year the distribution of temperature 
and pressure over the globe and the prevailing winds. Part I. 
* These papers were submitted by permission of the Lords Commissioners of 
Her Majesty’s Treasury. For the Report itself see “Report of the Scientific 
Results of the Voyage of H.M.S. ‘Challenger,’” Physics and Chemistry , 
vol. ii. part vi. 
