342 PROCEEDINGS OF THE AMERICAN ACADEMY. 



by a gas engine at 1,700 revolutions per minute, corresponding to a rim 

 speed of over 50 meters per second. 



Under these circumstances, no light was admitted to the eye until 

 ToU(j ^^ ^ second after the current had been cut off. And the line of 

 vision was again interrupted xij'uij of a second before the arc was again 

 made. In later experiments, the aperture was stopped down to jt/qo 

 second in time ; but the maximum time for which the arc was visible 

 was rrPoo ^^ * second. 



At this point the question naturally arises as to whether the self-induc- 

 tion of the circuit can prolong the purely electrical effects, whatever they 

 may be, through an interval of time as great as X(/jj^ of a second. 



The form of the cii-cuit is practically that of two parallel copper 

 wires, each 180 cm. long and separated by a distance of 30 cm. If the 

 current be not oscillatory [?] we may fairly assume that its time constant 

 will lie somewhere between that of a circle of wire (having the same 

 diameter as the wire actually used and enclosing the same area as the 

 circuit actually used) and a 180 cm. section of two parallel wires 30 cm. 

 apart and open at both ends. 



Computing the time-constants for these two cases, we have* for the 

 parallel wires, 



L = 2fji loge — 4- i (/(^i + Ma) ; 



'Z = self-induction of unit length. 

 jx = permeability of medium between wires. 

 [Ml =■ permeability of one wire, 

 where { ix<i^= permeability of other wire, 

 a, = radius of one wire. 



(72 = radius of other wire. 



Here 

 Hence, 



, h ■= shortest distance between the axes of the wires, 

 yu, = /xi = /Ao = 1) «i = «2 = 0.1 cm., and i = 30 cm. 



L = A loge 300 + 1 = (4 X 2.477 x 2.30) -f 1 = 23. 



Inductance of circuit 180 cm. long = 23 X 180 == 4140. C. G. S. 



Resistance of 360 cm. of this wire = 0.02 ohms approx. = 2 x 10'' C. G. S. 



rr- . . 4140 ^ 1 



... Time-constant = ^ooooOOO < ItOOO '^'- 



* Gray, Absolute Measurements, Vol. II. Pt. I. p. 293. 



