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, 



E (-ka?) = |, 

 and eliminating /, we obtain 



Log. M = ~< log. 



or, 



COLLINGWOOD, June 8, 1866. 



THE END. 



Ballanlyne, Roberts, &> Comfany, Printers, Edinburgh, 



