Dr. Hare's Correction in his Strictures on Dove. 145 



xTi(\+ A -. rrV • • (19-) 



\ ■mxio-{-nmt + o<pj-\-p'\ik/ 



[;», «, 0, J) integers from oo to — oo , omitting m = 0, w = 0, 

 = 0, p = 0]. 



It seems as if some supposition of this kind would remove a 

 difficulty started by Jacobi (Crelle, t. ix.) with respect to the 

 multiple periodicity of these functions. Of course this must 

 remain a mere suggestion until the theory of quaternions is 

 very much more developed than it is at present; in particular 

 the theory of quaternion exponentials would have to be deve- 

 loped, for even in a product, such as (18.), there is a certain 

 singular exponential factor running through the theory, as 

 appears from some formulee in Jacobi's Fund. Nova (relative 

 to his functions 0, H), the occurrence of which may be ac- 

 counted for, a])riori,as I have succeeded in doing in a paper 

 to be published shortly in the Cambridge Mathematical 

 Journal. 



I remain, Gentlemen, 



Your obedient Servant, 



Cambridge, December 4, 1844. A. Cayley. 



XIV. Correction of an Error in the authm's " Strictures on 

 Professor Dove's Essay on the Law of Storms." By 

 Robert Hare, M.D., Professor of Chemistry in the Uni- 

 versity of Pennsylvania. 



To the Editors of the Philosophical Magazine and Journal. 

 Gentlemen, 



I BEG leave to correct an error, committed in my Strictures 

 on Dove's Law of Storms, Phil. Mag. S. 3. vol. xxv. 

 p. 100, in assuming that the contents of the zones in a circular 

 area between equidistant concentric parallel lines are to each 

 other as the squares of their mean distances from the common 

 centre; instead of assuming them to be simply as those di- 

 stances. Of course the velocity of the air in the zone nearest 

 the upward columnar current, in a tornado or hurricane, will 

 not be to the velocity of any greater zone inversely as the 

 squares of the mean distances from the axis of the column, 

 but simply in the inverse ratio of those distances. 



Hence, supposing the centripetal velocity at a mile from the 

 centre, or say five thousand feet to be one hundred miles per 

 hour, at twenty miles, it would be five miles per hour, or 

 merely a breeze. By this amendment of the calculation my 

 argument is strengthened, so far as it was an object of it to 

 prove that in an extensive hurricane the central area protected 



