1873.] Dr. R. S. Ball's Researches in Dynamics. 



385 



position of another distinct variation having two maxima and two 

 minima in the twenty-four hours like the barometer variation ; and he 

 supports his views by a reference to the variation of the east components 

 of the wind in the months of July and August, when the land- and sea- 

 breezes have almost disappeared. This is found to exhibit a decided 

 double period. The north components of the land- and sea-breezes are 

 then approximately eliminated from the north components of the whole 

 variation, and the variation which then remains exhibits a very decided 

 double period in this direction also. These variations with double periods 

 are regarded as indicative of the existence of a double diurnal variation 

 in the general movements of the atmosphere. Upon this hypothesis 

 typical diurnal variations of the wind are deduced for north and south 

 low latitudes — that for north latitudes exhibiting a double diurnal right- 

 handed rotation, and that for south latitudes a double diurnal left- 

 handed rotation ; and from these the diurnal variation of the barometer is 

 deduced. 



The movements of the wind-vane at Bombay are then analyzed ; and 

 the writer concludes that the greater part of the excess of " direct " over 

 " retrograde " rotation of the vane at Bombay is due to the diurnal varia- 

 tion of the wind. 



Extracts are given from observations made at St. Helena, Toronto, 

 and Falmouth, showing the character of the diurnal wind-variations at 

 those places, and their greater or less agreement with the deduced 

 typical curves. The writer maintains that these variations afford inde- 

 pendently a possible, if not a probable, explanation of that movement 

 of the air which Dove had called the " Law of Gyration and, in conclu- 

 sion, he points to the extent of their applicability in deducing weather 

 probabilities, and to the method of discussing storms. 



A postscript is added, giving the mean diurnal variation of the wind 

 at Sandwick Manse, Orkney, and pointing out its general conformity 

 with the results deduced from the Bombay wind-observations. 



VII. " Researches in the Dynamics of a Rigid Body by the aid of 

 the Theory of Screws." By Robert Stawell Ball, LL.D. 

 Communicated by Professor Cayley. Received May 29, 

 1873. 



(Abstract.) 



This paper contains some developments of a theory sketched in the 

 Transactions of the Royal Irish Academy, vol. xxv. p. 157. 



Part I. discusses the quantity of energy necessary to give a body a 

 twist about one screw while acted upon by a wrench about another screw. 

 The expression virtual coefficient is denned, and application is made of the 

 reciprocal character of the virtual coefficient to solve the problem of 

 resolving a wrench along six given screws. 



