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 



ff= 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") = fc 

 and eliminating k t we obtain 



Log. />/ = -C, log. ()j 



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. 



PMNTKD BY WILLIAM CLOWES AM) SONS, STAMFORD BTKEET 

 AND CHARISG CUOS8. 



