SUMMARY OF THE EXPERIMENTS. 549 



If the ratio is equal to , for instance, we may operate 



R + 7" 100 



on a resistance R 100 times greater than with a direct contact 



The error in this calculation' of M arises especially from the 

 estimation of the mean radius of the coil. The radius a' of the 

 disc may be ascertained with far greater exactitude. In his first ex- 

 periments Lorenz had given to a 1 a value too near a; as the intensity 

 of the field increases very rapidly near contact with the coil, the 

 least error in the radius introduces a considerable error in the co- 

 efficient M. In his latter experiments he placed the disc in what 

 is practically the uniform field of a long coil. This consisted of a 

 single layer of wire comprising 472 turns wound on a brass cylinder 

 loocm. in length and 33 cm. in diameter. The calculation was 

 made by a formula analogous to that of 771. 



Lord Rayleigh used two coils which are sensibly identical, placed 

 either in contact or at a distance 2X = 0\/2. With this latter arrange- 

 ment, the relative error of M is almost independent of the error made 

 in the valuation of the mean radius, and depends more particularly 

 on the distance 2X, a quantity far more easy to measure. For 

 if each of the coils contains n turns, and we take the approximate 

 value 



M = 47T 2 - -, 

 U B 



we deduce from it 



_ da da' du 



2 h 2 - 3 



M a a u 



Taking equations u 2 = a* + x 2 into account, we get 



da x* dx 



now, the first term of the second member vanishes for the condition 

 2u 2 = $a 2 , or 2X 2 = a 2 . 



1127. SUMMARY OF THE EXPERIMENTS. In the following table 

 we shall collate the numbers furnished by various methods for the 

 length of the column of mercury at zero, a square millimetre in 

 cross section, which represents the value of the ohm, or a resistance 

 of io 9 absolute units (C.G.S.). 



In certain cases the conductor, the absolute resistance of which is 

 determined, has been compared with a copy of Siemens' unit, either 

 with a column of mercury of known dimensions ; in other cases the 

 comparison has been made with a copy of the British Association 



