ON OHM S LAW. 



61 



force in volts between D and F, i. e. the ^ , E of the formula above ; s do- 

 Jo +p 

 notes the radius iu centimetres of the line wire ; the other letters have the 

 same meanings as before) : — 



The formula by which the limit to 7t is calculated is 



_ A.r;rV 

 ~ 7/RP^E^ ' 



where Av is the diifercncc between -f + and -f- — balances (see above). In 

 the four experiments discussed, the arrangement was abundantly sufficient 

 to indicate a difference of a millimetre, so that A.v is 



<10^ohm; 



757rV 



:7i< 



10^1^ (PE)^ 



Assuming, then, that the heating- and cooling-effect discussed above may be 

 neglected, the result of the experiments is that 7i is certainly less than 



10'-' 



In other words, if we have a conductor whose section is a square centimetre, 

 and whose resistance for infinitely small currents is an ohm, its resistance 

 (provided the temperature is kept the same) is not^ diminished by so much as 



the Y~Ji P^rt when a current of a farad per second passes through it= 



With regard to the heating- and cooliug-eifect, it must evidently be very 

 small, since it takes place, if at all, in something like the y^ part of a seconcl. 

 It is of course possible that these alternations were at that particular rate for 

 which the two effects would balance each other ; but when we consider that 

 the temperatures of the thin wire were very different in the different ex- 

 periments (notably so in (3) and (4) with the iron wire, where the current 

 passing was in one case more than double that in the other), and that the 

 heating- and cooling-effect must depend on the temperature of the wire, while 

 the other is independent of that as well as of the rate of alternation, the pro- 

 bability that any such balancing of the two effects existed at all is reduced to 

 almost nothing. We may therefore look on this experiment as a verification 

 of Ohm's law to the degree of accuracy indicated above. 



Appendix. 



While thinking how to repeat Dr. Schuster's experiments as nearly as was 

 possible without the command of a sine-inductor, the writer of the Ileport 



