304 Dr. E. H. Barton on the Attenuation of Electric 



And this factor, for half an ohm resistance, would diminish 

 the electrometer-throw by 0*5 per cent. This again is almost 

 negligible, being within the limits of the errors of determi- 

 nation of the ratios of the electrometer-throws. 



Let us, however, in spite of the smallness of these effects 

 on the electrometer-throw due to imperfect absorption or 

 reflexion, inquire as to whether they are additive or compen- 

 satory. We at once see that they are additive, and that any 

 departure from perfect absorption or perfect reflexion would 

 result in a lessening of the observed ratio r of the electrometer- 

 throws. Hence the true value of r which would be obtained 

 under ideal conditions may be expected to exceed the actual 

 one, if they differ at all. 



In order to follow this possibility to its consequence, let us 

 take each experimental value of r, plus its probable error, and 

 from these data determine the corresponding value of <r. 

 These probable errors, it will be noticed, exceed those which 

 might be attributed to imperfection in the absorbing and 

 reflecting arrangements, so entirely cover any errors which 

 may be due to those sources. To still further test the conse- 

 quences of extreme suppositions, values of the attenuation 

 have been calculated for a value of one ratio r x plus its pro- 

 bable error, and the other r 2 minus its probable error, and 

 vice versa. The results are scheduled in Table III. 



It is thus seen that none of the suppositions considered 

 bring the experimental value of the attenuation down to the 

 theoretical value, though the slight difference made in the 

 most probable case (second line of Table III.) is in the right 

 direction, and lessens the value by nearly 6 per cent., whereas 

 a reduction of 50 per cent, is required for agreement. 



Turning now to the question of the validity of the expres- 

 sion for the effective resistance in the case under discussion : 

 we have to notice (1) that this formula was developed for a 

 wire whose return* was at a distance, and (2) that it is for 

 " periodic currents following the harmonic law "f. 



Whereas in the actual experimental case we have 



(1) The two wires comparatively near together (diameter 

 1*5 millim., distance of centres apart 8 centim.); and 



(2) The wave-train is a rapidly damped one (see fig. 2). 

 To me it appears probable that each of these considerations 



if introduced into the theory would lead to a modification of 

 the expression for the attenuation which would bring its value 

 nearer the experimental one. Whether or not they would 

 be competent to entirely bridge the discrepancy I do not 

 pretend to say. 



* Phil. Mag. May 1886, p. 390. t Ibid. p. 387. 



