EMPIRICAL FORMULAE. 395 



in which F represents the strength of the field, and q a constant 

 given by the equation 



Green assumes that the coefficient of magnetisation /, is constant 

 throughout the whole extent of the body ; in this case the linear 

 density is proportional to the perpendicular component of the 

 magnetic force at every point of the surface. Maxwell gives the 

 following table of the corresponding values of q and of k: 



k q k q 



oo 0.00 11.80 0.07 



336.4 0.01 9.13 0.08 



62.02 0.02 7.52 0.09 



48.41 0.03 6.32 0.10 



29.47 0.04 0.143 1.00 



20.18 0.05 0.0002 10.00 



14.79 0.06 0.0000 oo 



For negative values of k, q becomes imaginary ; the formula does 

 not seem then to apply to diamagnetic bodies. 



Green's formula seems to represent very exactly the distribution 

 of temporary magnetism in soft iron as well as that of permanent 

 magnetism in cylindrical bars. Green showed that the value of the 

 moment which is deduced for a needle of this form, 



'\ 



(5) 



agrees remarkably with determinations made by Coulomb with 

 needles which only differed in length. The agreement ceases, how- 

 ever, to be very close when the length of the needle is less than 

 twenty-five times the diameter. 



The expression for the area of the curve corresponding to Green's 

 formula is, for each half of the bar, 



it represents the total value of the flow of lateral force. For a very 



