Mr. Blackburn on the Modern Telegraphs. 365 



amined has proved to be linen. We owe, therefore, the satis- 

 factory establishment of the fact, that the Byssus of the an- 

 cients was flax, to the microscope of Mr. Bauer. 



XLIX. A Method of determining the Number of Signals 

 which can be made by the Modern Telegraphs* By Charles 

 Blackburn, Esq., B.A. 



To the Editors of the Philosophical Magazine and Journal. 



Gentlemen, 



TN the Number of the Philosophical Magazine for Octo- 

 ■*■ ber, you did me the favour to insert a method of find- 

 ing the number of signals which can be made by sema- 

 phores having one arm on a centre; I now send an investi- 

 gation for finding the signals when the semaphores have any 

 given number of arms on the same centre. 



Problem. — To find the number of signals which can be 

 made by a semaphore having any number 

 of centres; any given number of arms on 

 each centre; and each arm taking any 

 given number of positions. 



Let the figure represent a semaphore 

 having any number of centres, A, B, &c, 

 and any number of arms, AD, AE, &c, 

 on the same centre ; let also the number 

 of centres be denoted by c, the number 

 of arms by a, and the number of the po- 

 sitions of each arm as p. 



First, to find the number of signals 

 which can be made by using the arms on 

 one centre only. 



The number of positions in which each 

 arm can be placed may be considered as 

 distinct quantities capable of a certain 

 number of combinations. The number 

 of positions of each arm beings, the num- 

 ber of signals which can be made with 

 one arm only must = p. 



And since the number of combinations of p things, taken 



two and two together, is \ ~Z , the number of signals, using 



1 • 38 



two arms only, will be 



1.2 ' 



In like manner the number, 



