140 Lord Rayleigh and Dr. A. Schuster. [May 5, 



We may, in fact, treat both R and L as unknown quantities, and 

 employ the methods of least squares to find out the most probable 

 values. We use for this purpose the approximate values already found, 

 and find the most probable corrections to them. Neglecting the small 

 corrections for torsion, magnetic moment, and level, and writing 

 P=2R/GKw, we find for the quadratic which determines R — 



P 2 -Pcot0 + U=O, 

 where U as before is written for ^— (^- — 1\ 



We find approximately by differentiation, remembering that 

 dPIP=dR/R, 



K * J R \P P 3 / P 3 



We may consider cZR/R and dJJ to be the unknown quantities to be 

 determined. The coefficients with which they are multiplied are known 

 with sufficient accuracy. c£tan0 is found for each observation by put- 

 ting dJJ=0 and dH equal to the difference between the value of R cal- 

 culated by means of that observation, and the value of R provisionally 

 adopted. The usual methods to form the normal equations were 

 employed. We find in this way — 



R=10 9 x (4-5433 + 0-0019) 

 L = 10 7 x (4*5130 + -0110) 



It is satisfactory to note that the final value of R derived with the 

 aid of the theory of probability is practically identical with the mean 

 value directly calculated from our experiments with 4* 51 x 10 7 as 

 coefficient of self-induction. A remarkable agreement is shown 

 between the value of this coefficient of self-induction best fitting our 



experiments 4"5130 X 10 7 



and the value calculated from the dimensions of 



the coil 4-5145 xlO 7 



The large probable error, however, shows that the agreement is 

 partly accidental. 



To give an idea of the accuracy with which R has been determined 

 by means of our experiments independently of constant errors, it may 

 be mentioned that the probability of our value being wrong by one in 

 a thousand is only one in ten, while the experiments made by the 

 British Association give an even chance for the same deviation. 



It only remains to determine the resistance of the German silver 

 standard in ohms at a temperature of 11°"5 C. 



We had at our disposal the original standards prepared by the 

 Committee of the British Association. These are very nearly equal 



