362 M. C. Cheneveau on tlie Magnetic Balance 



We thus have 



K m D±W 



K'"ro' D' + D" l ; 



Whence K_D^ W _ 



K'~D' + D"*m ^ 



This formula is not corrected for the effect due to the 

 magnetization of the air ; the exact formula may be obtained 

 as follows : 



Let k' and k" be the susceptibilities of the substance taken 

 as standard, assumed to be paramagnetic, and of the air 

 respectively. Let A' be the density of the comparison body, 

 and A a constant of the apparatus. In reality the exact 

 expression for the force when one deals with the standard 

 body is 



/' = («'-«")^A=(K'-^)» l 'A, . . (13) 



since , 



K =A'- 



When a measurement is made with a paramagnetic body 

 of susceptibility re and density A the true value of the force 

 in this case is 



/=(«-«") | l A=(K-0»A. . . . (14) 

 Dividing (14) by (13) we have 



or 







K 



«" 





./• 







A 



m 



./' 





K' 



k" 



'm' 

















A' 











K- 



k" 



./' 



m 







A 



/' 



m 





K'- 



k" 



A' 



(15) 



f m' 

 If we put r—'jr, — : this is the approximate ratio of the 

 / m 



coefficients of specific magnetization K and K' previously 

 determined by the aid of formula (12) ,*. 



* We have in fact, from what has been proved above, 

 //=KwA = B(D±D"), 

 /7=KVA = B(D'+D") ; 

 A and B as well as I being- constants ; whence 



/ - Ji??L - D -+ p " /W _ K _ B+D" m[ 



f K'm' " I)'±D" ' f'm ~ K' ~ \V ±\)" ' m ' 



