368 Mr. Blackburn on the Modern Telegraphs. 



The signals using one centre at a time = cA 



using two centres 



c . c— 1 



using three centres = — - — - — - — . A i \ 



&c. &c. &c. 



using c centres = 



Corollary 2.— In any semaphore which has as many arms 

 upon each centre as each arm has positions, the formula for 

 the number of signals will be 2 ac — 1. 



For in this case, since 



a. a — I a. a — 1 . a— 2 - Q 



a ~p, A = a + 1<2 + j . 2 . 3 + > &c *' to a 



terms = 2 a — 1. Hence by substituting for A in the formula 

 (A+l) c — 1 we have(2°) c — 1 = 2 oc — 1. 



Example.— Let «=p = 6, c=2; then 2 ac — l = 2 12 — 1 

 = 4095, which is the number of signals which could be pro- 

 duced by the Admiralty semaphore, if it had six arms upon 

 each centre instead of one. 



Example 2. — To find the number of signals which might be 

 made with a pocket watch, supposing twelve instead of two 

 fingers on the same centre. 



Here a = 12, c = 1, therefore 2 ac - 1 = 2 12 -1 = 4095, 

 as in the preceding example. 



All the signals requisite for the purposes of communication 

 may be exhibited by machines of great simplicity. A tele- 

 graph like that in the an- 



Nkl ±kL 



nexed sketch is capable of 

 producing sixteen thousand — ^~- 

 three hundred and eighty- 

 three distinct signals; and 

 since these admit of a sy- 

 stematic arrangement, by which the signal for every word, 

 and the word to every signal, may immediately be found, it 

 seems desirable that lines of telegraphs should be established 

 between the metropolis and the more important towns. Com- 

 munications of any nature might then be conveyed verbatim 

 with the utmost facility, and with a rapidity approaching even 

 to the velocity of light. 



