1889.] The Diurnal Variation of Terrestrial Magnetism. 485 



same year as the calculated ones, the result is strikingly in favour of 

 the outside force. The results for Greenwich argue in the same 

 direction. As regards St. Petersburg, the results for 1870 neither 

 agree with one nor with the other hypothesis, and it has already been 

 mentioned that the observations for 1870 are doubtful, but the results 

 for 1878 agree well with the hypothesis of an outside disturbing force. 



Table III gives the comparison for amplitude. It is seen that the 

 observed amplitudes are throughout smaller than the calculated ones. 

 If curves are drawn representing the results of Tables I, II, III, it is 

 clearly seen how well the calculated vertical forces agree with the 

 observed ones as regards phase, if we assume the cause of the varia- 

 tion to be outside. 



If we then take it as proved that the primary cause of this varia- 

 tion conies to us from outside the earth's surface, we are led TO 

 consider that a varying magnetic potential must cause induced 

 currents within the earth, if that body is a sufficiently good con- 

 ductor. These induced currents might be the cause of the apparent 

 reduction in amplitude. As my colleague, Professor Lamb, has given 

 considerable attention to the problem of currents in a conducting 

 sphere, I consulted him, and he gave me the formulae by means of 

 which the induced currents can be calculated. His investigation is 

 given in an appendix to the paper. The result is very interesting. 

 If the earth is treated as a conducting sphere, the observed reduction 

 in amplitude is accounted for, but that reduction should be accom- 

 panied by a change of phase which is not given by observation. We 

 can reconcile all facts if we assume, as suggested by Professor Lamb, 

 the average conductivity of the outer layers of the earth to be very 

 small, so that the reduction in amplitude is chiefly due to currents 

 induced in the inner layers. If the conductivity inside is sufficiently 

 large, a considerable reduction in amplitude would not be accom- 

 panied by a sensible change of phase. We have arrived, therefore, 

 at the following result : 



The vertical forces of the diurnal variation can ~be accounted, for if we 

 assume an outside cause of the variation, which induces currents in the 

 earth y and if the earths conductivity is greater in the lower strata than 

 near the surface. 



Professor Balfour Stewart's suggestion that convection currents in 

 the atmosphere moving across the lines of the earth's magnetic forces 

 are the causes of the daily variation, gains much in probability by 

 this investigation. If the daily variation of the barometer is accom- 

 panied by a horizontal current in the atmosphere similar to the 

 tangential motion in waves propagated in shallow canals, and if the 

 conductivity of the air is sufficiently good, the effects on our magnetic 

 needles would be very similar to those actually observed. The 

 difficulty as to the conductivity of the air is partly met by the author's 



