272 K. YAMAliAAVA 



tlicn 



tan ßi = -j- 



\'>y this lacdiotl, a's :iiid ß's can he luimd willi an accuracy v\[un\ to 

 lliat of the experiment. 



The determination of" the amplitude a^ of any term of tlic series 

 wonld enable us to calculate the value of the conductivity. If we 

 were to determine all the a's, the value of K calculated from each 

 Avould be same, provided that the exi)eriment had been performed, 

 so as to satisfy all the theoretical conditions. But, from necessary 

 imperfections of experiment, the ^'alues would almost certainly all 

 differ from one another. Inasmuch, however, as the first term is by 

 far the most important, we may safely assume that the value of A' 

 calculated from it cannot be far from the truth. 



In the same way, different /3's will give different values of 7v ; 

 but for the i-eason just given the one obtained from ß^ will probably 

 be a better \-d\nc than that dcducible from any of the other ß's. In the 

 following calculation, the values were obtained from ai and ß^ oidy. 



The value of ß^ cnabK'S us to calculate 7^i , and 7)^ is related to 

 the other (juantities by 



-S. = 

 Hence 



, ro n £""'' •'•" -sm (7^- f',' A')- g'-' ^ sin (L>, + ;-,' X ) 



tan Jü i= V = pf^ T-Y 



£-'■'•' ^ cos{l>,- ;^' A- ) - £ "'■' ^ cos (D, + 1^' A' ) 



or £-",iXs)«(7>j— ;^i' A') = £'V ''^' si« (Z^ + F;' A' ) 



putting /'j' A' = Si 



we find sin {D,- 5.) -= £2«/ sin (7>,+ S,) 



hu, ir^ + ^f' "^ ] tan S^ 



or 



And when .V. is large, 



tan I>i= ± tan (nn ± S^) 



