158 A. TANAKADATE. 



Location of 3Iagnetic Image from Vertical Variations of the 

 Observed 3Iagnetic Elements. 



The simplest case now discussed can be applied to sources 

 of finite extent if its distribution of magnetism is centrobaric, or 

 to cases where it can be represented by finite number of images 

 by mere addition of the rectangular components above given. 

 Any other distribution whose potential is known in finite form 

 can also be treated in similar manner. 



If the potential is expanded in harmonic series, no matter 

 how fiir that expansion be carried, its application to the varia- 

 tion of the force in neighbourhood of the source will be utterly 

 untenable, unless the distribution be such as can be exactly 

 represented by finite number of terms. The presence of minute 

 ripples in the imitation of known curves by 80 harmonics work- 

 ed out with Michelson's analyser shows us to what danger we 

 are exposed in similar cases.* 



As we recede from the source, however, the higher har- 

 monics tend to vanish in the well known way, approaching more 

 and more nearly to be centrobaric as the distance of the source 

 becomes great compared with its extent. If the distribution is 

 not extravagantly irregular, a few number of images properly 

 disposed will give a fairly good approximation at tolerable dis- 

 tances from it. A pair of positive and negative images of equal 

 strength will give the effect of a simple magnet. When its 

 length is short (1) and (3) may be differentiated with respect 

 to its axis and the strength of pole m replaced by the magnetic 

 moment. 



* rJiil. Mag. Vol. XLV, Fil\li Scries PI. XII to XVII. 



