On Tempcrature'Coefficients for Insulating Envelopes. 21 iS 



the resistances for the same difFerences of temperature but 

 corresponding to different periods of contact. 



From these fticts, electrification phenomena are capahk^ of 

 receiving a mathematical rendering which must prove of im- 

 mense use to telegraph-engineers. 



If the temperature-coefhcient were constant for all and every 

 period of contact, we should obviously obtain a series of curves 

 with ordinates increasing in a constant ratio, which w^ould 

 mean that the ratio of the resistances for successive periods of 

 contact did not diminish as we reach the higher temperatures. 

 Now, as the temperature-coefficients for increased duration of 

 contact diminish, the curves more nearly approach each other 

 as the temperatures increase, which agrees with the fact that 

 electrification-ratios are reduced less and less as the resistance 

 itself diminishes. 



A very curious result arises from this treatment of the sub- 

 ject, which I have not yet had sufficient time to examine, 

 but may be mentioned here, as probably it may assist us to 

 explain something of the nature of electrification. 



To determine approximately the electrification-ratio, and 

 consequently the resistance at any required temperature and 

 for any period of contact. Calculate first the temperature- 

 coefficient for the required temperature, which is simply the 

 expansion of the ratio for 1° Fahr. to the power correspond- 

 ing to the degrees of difference. Using this as the factor, 

 extract the root of the ratio for any tw^o given periods of con- 

 tact ; this will give very nearly the electrification -ratio corre- 

 sponding to the same periods of contact at the required tem- 

 perature. 



It thus appears that electrification, w-hich is an inseparable 

 property of all insulators, follows some law of variation in 

 which the temperature-coefficient of the insulator itself is a 

 function. 



I hope to have the pleasure of communicating at a future 

 time the mathematical development of the application of loga- 

 rithmic functions to electrification and thermal changes in 

 insulating media. 



4 Lansdowne Terrace, 

 Stratford, Essex. 



Phil Mag. S. 5. Vol. 4. No. 25. Oct. 1877. 



