380 Reports on Special Researches 



POTENTIAL-GRADIENT. 



In former work on the ocean, the potential-gradient has almost invariably been meas- 

 ured by some method such as the following: A bamboo pole extends from the stern rail of 

 the ship and carries at its end a metal plate which is insulated and covered with some form of 

 radioactive material, usually ionium. Under these conditions, the air in the vicinity of 

 the plate is rendered conducting, and the plate itself takes up the potential of this air as 

 determined by the electrical field of the Earth modified by the presence of the ship, bamboo 

 pole, etc. An electroscope sei-ves to measure the difference of potential between the ship 

 and the disk, or collector as it is called, and this quantity is proportional to the potential- 

 gradient. In order to obtain absolute values, it is necessary to secure simultaneous ship 

 and shore observations, the latter being made over a flat surface by some apparatus which 

 does not itself distort the field, and which measures the true potential-gradient. 



The chief disadvantage associated with the use of a collector lies in the slowness of its 

 action, which necessitates very perfect insulation if accurate results are to be obtained. 

 Thus an ionium collector may require something of the order of two minutes to attain a 

 potential within 1 volt of its final steady potential. It will be obvious that since in the 

 final state there is a difference of potential of the order of 200 or 300 volts between the 

 collector and the earthed bamboo pole, the final potential of the collector can not have its 

 proper value unless the insulation is perfect. It will have a value somewhere between zero 

 and the proper value, and determined by the fact that the current of electricity flowing 

 from the collector to earth over the leaking insulation is equal to the current which is able 

 to flow from the air to the collector, due to the latter being at a potential below its proper 

 amount. A simple calculation will show that even the electrical dispersion from the wire 

 leading to the collector is sufficient to maintain the potential below its proper value by an 

 appreciable amount. Thus to consider an example, suppose V represents the amount by 

 which the collector differs from the potential which it would finally attain in the absence of 

 leakage due to dispersion or other causes. If c is the capacity of the insulated system, and 

 Vo the value of V when the collector is earthed, then in the absence of leakage, 



where A; is a constant. Hence 



"" dt "^ 



V=Voe-T (1) 



If, in the absence of leakage, the collector takes 1 minute to attain a potential within 

 V'o/100 of its final value, we find from (1), A;/c = 0.08. 



Thus, if, owing to the dispersion, the maximum potential differs by 57 from its proper 

 value, the quantity of electricity coming to the wire per second is k5V = 0.08c8V. If 57 

 were zero there would be no surface density of charge on that portion of the wire leading 

 to the collector, which was near the collector, but the surface density would not be zero on 

 portions of the wire remote from the collector. If C is the capacity of the wire and we write 

 C7o/2 as the total charge on the wire, we shall probably underestimate it. In this case, the 

 rate of supply of electricity to the wire by dispersion would be^ 47rC7oX+/2. Hence 



0.08f57 = 2jrC7oX+ 



Putting X+ = 10"■^ and observing that C/c would not be far from unity unless the electro- 

 scope had a considerable capacity, we find that, in the steady state, 8V forms about 1 per 

 cent of Vo. Thus if Vo were 200 volts there would, in the case cited, be an error of 2 volts. 

 It is true that this is not very much, but remembering that it is accounted for by the mere 

 dispersion from the wire, we see how seriously the results would be affected by faulty insu- 

 lation. 



'See W. F. G. Swann, Terr. Mag., vol. 19, pp. 81-84, 1914. 



