174 A. TANAKADATE. 



whose convergence or divergence has nothing to do with the 

 *' sitz " of action.* The indeterminateness of the problem in 

 the general case, is fully considered in Article XXVIII of Sir 

 William Thomson's Keprint of Papers on Electrostatics and 

 Magnetism, of which the present is a particular case. 



The image must therefore be taken in literal sense, no 

 pretension whatever being made as to the physical reality of either 

 its strength or jDOsition, except that the variational anomalies can 

 be partly accounted for by numerical calculations performed on 

 certain number of constants and variables. We must also bear 

 in mind, that the electric current in the atmosphere is entirely 

 neglected in the calculation; for if the intensity of such current is 

 greater than 0.1 Amperes per square kilometer, the above result 

 will be materially aftected. 



The great depths of the images now found are just as might 

 be expected, for were they within a few kilometers from the 

 surface and of the sizes above given, an enormous number of 

 terms will be required in Gaussian expansion even for an ap- 

 proximate representation. The comparatively small depth of the 

 Asiatic image might account for the differences spoken of in 

 § 10 p. 37 above. 



The writer regrets not to have access to a valuable work of 

 Paul Passalskij, who, according to Leyst, seems to have treated 

 similar subject from harmonic analysis point of view. Section 12 

 is signed Aug. 7th. 1900 Mitake, and was read to the Physico 

 Mathematical Society of Tokyo on Sept. 29th. of that year. The 

 main features of the present section were onl}" qualitativly refer- 

 ed to and are now worked out for the report. 



* Gauss Gesammelt Werke Bd. Y p. 171. 



