SKILL IN TARGET-SHOOTING. 507 



pressed numerically by such a multiple of this integral, so taken, as 

 to give I for its value when r is infinite : which gives 



H= I E(-kr*) ; and therefore M= E (-kr*). 



Now, when r a, the radius of that circle within which just half 

 the total number of arrows strike ; the probabilities of hitting and 

 missing that circle are equal : so that H and M are in that case 

 each = . We have, consequently, 



(~A^.fc 



nd eliminating k, we obtain 



Log.M=~-, log. (*)} 



or, 



i* 



"- (*)* 



COLLINGWOOD, June 8, 1866. 



NOTANDUM. 



The experiment suggested in 9 of Lecture XIII. has been made 

 by Herr G. QUINCKE, with complete success. A full account of it 

 will be found in Poggendorff's Annalen, voL cxxviii. pp. 177, et seq. 



PRINTED BY T. BRETTELL AND CO., RUPERT STREET, LONDON, W. 



