306 ME. W. DUDDELL ON THE EESISTANCE AND 



only contains the current raised to the powers and 1, and the coefficients of these 

 terms are considered as constant specific properties of the conducting apparatus under 

 the given conditions. It is, however, quite conceivahle that conductors might exist 

 for which the equation might contain other powers of the current, and in this case 

 their coefficients would be equally justly considered as specific properties of the 

 conductor for which at present no names exist. Is the arc such a conductor ? 



On the assumption that when the conditions are maintained constant the P.D. can 

 be represented by an equation of the form V = E + PA, for all values of the current, 

 then the power spent or furnished by the apparatus VA = EA + KA 2 , that is, it 

 consists of two parts the one depending on A 2 , and therefore irreversible, so that the 

 sign of the power does not change with change of sign of the current, and the other 

 depending on the first power of the current, and therefore a reversible phenomenon, 

 so that if the apparatus absorbs energy when the current flows in one direction, it 

 will give back energy when the current flows in the opposite direction. 



This idea of distinguishing E.M.F.'s from resistances, according to whether the 

 dissipation or absorption of energy is a reversible or irreversible phenomenon, is by 

 no means new, as it underlies the views expressed by Professor FITZGERALD* and 

 GRAY! in the letters they contributed to the 'Electrician' in the discussion of 

 Messrs. FRITH and RODGERS' paper,! and has also been suggested by Professor 

 S. P. THOMPSON. It seems to afford a satisfactory basis for a definition of resistance 

 and E.M.F., which will be adopted in this communication. 



Definition.. 



Suppose any apparatus under any given set of conditions, through which a certain 

 current is flowing, and that it is required to determine its resistance and E.M.F. 

 under these particular conditions and for this particular current. The energy 

 transferred electrically between the source and the apparatus can be divided into two 

 parts : the one an irreversible part, so that if the direction of the current be conceived 

 reversed the direction of the transfer of energy remains unchanged, and the other a 

 reversible part. If it be found that the irreversible transfer of energy is proportional 

 to the square of the current, and the reversible to the first power of the current, 

 when in some way or other perfect constancy is maintained in all the conditions of 

 the apparatus, such as the size, shape, nature, temperature, temperature gradients, 

 relative movements, &c., of the different parts of the apparatus which are existing 

 with the particular current and under the given set of conditions, then the irreversible 

 rate of transfer of energy divided by the square of the current will be defined as the 

 resistance, and the reversible rate of transfer of energy divided by the first power of 



* 'The Electrician,' 1896, vol. 37, pp. 386, 489. 

 t 'The Electrician,' 1896, vol. 37, p. 452. 

 \ 'Proc. Phys. Soc.,' 1896, vol. 14, p. 307. 



