of Terrestrial Magnetism, 353 



fore, as a first approximation, put Y equal to the product of 

 two quantities, one depending on the latitude, the other on 

 the time only. This seems true approximately, but only 

 approximately. Writing, therefore, 



Ysinw=U -7-; 

 at 



where U is a function of w, and T a function of the time, we 

 get 



au 



where no constant is added, as we only consider periodic 



terms. 



The result I wish to draw from this equation, which can 



easily be tested, is this : — If our assumptions are all justified, 



X will be a maximum or a minimum as far as the time is 



concerned, whenever T is a maximum or a minimum ; that is 



dT 

 to say, whenever — , and therefore also Y, vanishes. In other 



words, the northerly component of horizontal force ought to 

 be a maximum and a minimum, whenever the westerly com- 

 ponent vanishes. 



At Greenwich, X has a maximum at 7 o'clock in the even- 

 ing and a minimum at noon ; while Y vanishes a little after 

 7 o'clock, and between 12 and 1 in the afternoon. 



At Bombay the declination-needle seems to pass its mean 

 position on the average a little after 10 in the morning and 

 about 10 in the evening. The horizontal force has its maxi- 

 mum a little after 11 in the morning, and the minimum at 

 a quarter past 9 o'clock in the evening. Considering that, 

 owing to the southerly position of Bombay, the type in the 

 declination-range differs considerably from that in our own 

 latitude, the agreement is satisfactory, and so far tends to 

 disprove the existence of vertical currents through the earth's 

 surface. 



The observations taken at Lisbon and Hobarton show an 

 equally good agreement, those at St. Helena and the Cape of 

 Good Hope less so ; but in these two latter places the observa- 

 tions taken at different months show a considerable difference 

 of behaviour. 



We may now attempt another step, and try to gain an idea, 

 however imperfect, as to the direction and intensity of the 

 currents which may produce the diurnal variation. The 

 variation in westerly force increases with the latitude, and we 



Phil. Mag. S. 5. Vol. 21. No. 131 April 1886. 2 C 



