702 PROCEEDINGS OF THE AMERICAN ACADEMY. 



tions occurring during the initial unsteady state can be easily grasped 

 and followed to the final steady state. ^ It will be readily seen by the 

 aid of these formulas that the final steady state is approached by suc- 

 cessive sudden jumps, and not by a uniform continuous advance. The 

 unsteady state is a state of leaps and bounds ; but these, although not 

 necessarily or generally of successively diminishing magnitude, dimin- 

 ish in a definitely irregular way, and finally disappear. From a phys- 

 ical point of view, the process is very beautiful, and from a practical 

 engineering standpoint, it is not without importance. 



We may first derive the formulas for voltage and current in the 

 circuit of Figure 1 in the usual way, starting with the differential 

 equations of the circuit, and then lead to these already known for- 

 mulas in the new way. 



At any instant t, and at any distance a; centimeters from A along 



the Hue in Figure 1 , we have ^ 



— e' = zi abvolts per cm. (2) 



and — i' = ye absamperes per cm. (3) 



where e = the instantaneous e. m. f , -abvolts 



de ,, T ^ /. abvolts 



e' = -r- the space gradient oi e 



ax t- o gjjj 



i = the instantaneous current, absamperes 



di ,, V .^ r . absamperes 

 z' = -J- the space gradient ot ^ 



absohms 



r = conductor linear resistance, 

 I = conductor linear inductance, 

 g = dielectric linear conductance, 

 c = dielectric linear capacity 



cm. 

 abhenrys 



cm. 

 abmhos 



cm. 

 abfarads 



cm. 



, d absohms ,.. 



dt cm. 



d abmhos ,^. 



^=time.rate of change -^ 



dt second 



1 Compare, however, " Alternating Currents," by Bedell and Crehorc, 1893, 

 pp. 201-207. 



2 "Electromagnetic Theory," by Oliver Heaviside, 1, 450 (180o). 



