THE 



LONDON and EDINBURGH 



PHILOSOPHICAL MAGAZINE 



AND 



JOURNAL OF SCIENCE. 



[THIRD SERIES.] 



OCTOBER 1834. 



XXXV. A Method of determining the Number of Signals 

 which can be made by the Modern Telegraphs. By Charles 

 Blackburn, Esq., A.B. 



To the Editors of the Philosophical Magazine and Journal. 



Gentlemen, 

 A LTHOUGH the French telegraph or semaphore has 

 ■"■ been in use for a considerable period, I am not aware 

 that any general rule for determining the number of signals 

 that can be made by these instruments has been given to the 

 public. The following investigation, therefore, may not be 

 unacceptable to such of your readers as are interested in that 

 mode of communication. Its object is to furnish a rule for 

 determining the number of distinct signals which can be made 

 by any semaphore, whatever be the number of arms or indi- 

 cators, or whatever be the number of positions of each arm. 



In the Cyclopaedia of Rees, the number of signals which 

 the semaphores of the line of communication between Paris 

 and Landau were capable of making, is stated to be 823,54-3, 

 which is no less than 1,274,608 fewer than the real number, 

 an error not arising from the press, but from the principle of 

 computation. The following method, besides giving the true 

 number of signals, has the advantage of being reducible to an 

 expression of remarkable simplicity. 



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

 made by any semaphore having any given number of arms, 

 and each arm taking any given number of positions. 



Third Series. Vol. 5. No. 28. Oct. 1834. 2 I 



