632 Prof. A. Battelli and Mr. L. Maori on 



rv 



(c) Value of Resistance and Self-induction. 



35. The calorimetric methods used by us afford, in our 

 opinion, the most satisfactory comparison between the re- 

 sistances offered by two different circuits to oscillatory 

 discharges. We therefore, having by Lord Rayleigh's 

 formula calculated the resistance of some rectilinear con- 

 ductors, with which we have compared the resistances of our 

 spirals (§ 24 and following), may claim to have succeeded in 

 finding in absolute measure those same resistances with the 

 degree of approximation the calorimetric measurements will 

 allow of. 



It might be objected that in fact Lord Rayleigh's formula 

 rigorously applies to perfectly harmonic currents only, and 

 that the effects the damping will produce on the resistance 

 should be taken into account ; but one easily understands 

 from Barton's * f ormulge that the correction on account of 

 the damping would in our case be less than 1 per cent. 

 Now Barton *, from a calculation recorded in Maxwell's 

 Treatise, recently found (as did Lord Rayleigh) the expression 

 for the resistance and self-induction of a current for damped 

 harmonic currents as well as for those obtained by a con- 

 denser-discharge. In Barton's theory the damping of the 

 currents is measured by a certain number k, which, using 

 the notation adopted by us, is given by the equation : 



R _T 



2L2tt' 



and thus in our case is without any doubt always inferior 

 to 0*02. Now, denoting by R" and R / the values of the 

 resistances of the same circuit, as calculated by Barton's and 

 Rayleigh's formulae respectively, their ratio is given by 



a quantity absolutely to be neglected as being inferior to the 

 mean approximation the calorimetric measurements were 

 made with. 



Moreover, Cardani's f direct experiments made with con- 

 denser- discharges prove experimentally that within the limits 

 of error of those measurements the resistance of a rectilinear 

 wire may for those discharges be regarded as having really 

 the value assigned to it by Lord Rayleigh's formula. 



* Phil. Mag. [5] xlvii. p. 483 (1899). 

 f N. Cim. [4] vii. p. 229 (1898). 



