494 SUBJIAPJNE CABLE LAYING AND EEPAIEING. 



The correcting factor arrived at in these investigations is 

 by a consideration of the time of charge and the approximate 

 insulation and capacity of the cable. The true capacity is pro- 

 portioual to the instantaneous charge, as in a condenser or a 

 short length of a naut or two of cable ; but when a long sub- 

 merged cable is being tested, a certain time must be allowed for 

 the charge to attain its full value at the distant end. Let K 

 stand for the ratio of the full charge to the instantaneous 

 charge, and we have, by Siemens' law of the fall of charge, 



br 

 or, converting to the common log, 



logK= * 



^ 2-B026 Fr 



where F is the capacity of the cable in microfarad?, r the insu- 

 lation resistance in megohms at the 5th minute, and t the time 

 of charge in seconds. Assuming the ratio of the apparent to 

 the true capacity to be the same as the ratio between the final 

 and Instantaneous charges at the distant end, we have 



m -^ Apparent capacity 

 irue capacity = — ^-i- — — i- \ 



The value of the ratio K having been found from the above 

 expression by inserting approximate values for F and r, and 

 putting t the time of charge in seconds, the true capacity is 

 found by dividing the apparent capacity by this number. 



The authors balanced condensers of approximately 20 and 

 80 microfarads against each other, one of them having a leak 

 artificially applied varying from |^ to 3 megohms. The results 

 show that the apparent capacity increased considerably as the 

 insulation resistance was reduced, but that the application of 

 the correction gave the true capacity to within one-half of 1 per 

 cent. The periods of charge were varied from 2 to 15 seconds. 

 The following example of a Gott test on 1,500 miles of cable- 

 will show how the leakage correction is applied : — 



Approximate capacity of cable 500 microfarads 



Insulation of cable at 5th minute 0'92 mep:olim 



Capacity of condenser 60 microfarads 



Insulation of condenser 25 megohms 



Megohms per microfarad : — 



Cable approximately 500 X 0-92= 460 

 Condenser 60x26 ^1,500 



