354 Mr. A. Schuster on the Diurnal Period 



shall not go far wrong in taking it as a first approximation 

 proportional to the sine of the latitude. I write therefore, 

 with an arbitrary unit of force, 



Y = cos u cos (t + X), 



where t is reckoned in arc from 2 o'clock Greenwich time. 



It is well known that in the expression for Y there is an 

 important term having a double period each day ; but it is 

 not my intention to enter into any details at present, and we 

 may see what we get with the above expression. 



Applying the equation 



d Y sin u __ d'X. 

 du d\ 



we obtain 



X= cos 2u sin (t + \). 



The important point here is the factor cos 2w, which changes 

 sign at a latitude of 45°. If our equation is approximately 

 right the northerly force ought to be a maximum in the 

 morning, a minimum in the afternoon in the equatorial 

 regions, where cos 2u is negative ; while in the latitudes 

 above 45° the minimum ought to take place in the morning. 

 This is exactly what happens, with the exception that the 

 change seems to take place in latitudes smaller than 45°. At 

 Bombay the maximum of horizontal force takes place at 

 11 o'clock a.m. At Greenwich the minimum takes place a 

 little after that time. At Lisbon (w = 51°) the minimum lies, 

 as at Greenwich, in the morning, but the range is considerably 

 reduced*. 



It is surprising that the above equation represents so well 

 the general type of character of the horizontal-force variation, 

 both in the northern and southern hemispheres. Consider- 

 able importance is to be attached to the fact that the maxima 

 and minima of horizontal force agree in sign with the observed 

 phenomena, for, as regards magnitude, all these variations 

 might equally well be due to currents crossing the surface of 

 the earth ; but the sign of X would have to be reversed, so that 

 the minima and maxima would be inverted. This is another 

 argument in favour of the supposition that no appreciable 

 part of the diurnal variation is due to currents crossing the 

 surface of the earth. 



* I find, since writing the above, that in the winter months Lisbon 

 agrees in phase with Bombay j so that it is very likely near the line at 

 which the change takes place. 



