PEIRCE. — TIME OF CONTACT ON A TELEGRAPH KEY. 



97 



are open, the charge in coulombs in the originally empty condenser, 

 t seconds after the key, 7", is closed, is 



and Q. 

 so that t — 



U + V 



_ evk 

 " ~ u + v 



k (uv + tir -{• V r) 



u + v 



'A<I^) 



The values of the natural logarithms which enter into this equation 

 for several values of the ratio of Q^ to Q^ are as follows : 



For the long scale distances actually used, the throw of the galva- 

 nometer caused by a discharge of electricity through its coil was, as 

 measured on the scale of the instrument, sensibly proportional, up to a 

 reading of say 25 centimeters, to the quantity of the discharge. The 

 galvanometer and the resistances ti and v were usually so adjusted 

 that a complete load (Q^) of the condenser, when sent through the 

 coil, caused a throw of exactly 20 centimeters. After k, u, v, and r 

 had been fixed, the coefficient of the logarithm remained constant ; if, 

 for example, its mean was 0.05, a throw of 50 millimeters would be 

 caused by closing the key for about 0.0144 seconds. 



In order to make sure that the apparatus had been properly set up, 

 I made use of a body falling from rest through a measured space to 

 close the gap T for a short interval of calculable length. A heavy 

 weight sliding on a stout vertical brass rod carried with it an insulated 

 frame which held securely a printer's lead, which formed one terminal 

 of the gap T. Projecting about a millimeter from a hole in the vertical 

 rod, near the lower end, was a piece of sharpened drill rod which formed 



VOL. XLU. 7 



