VARIATIONS OF THE MAGNETIC NEEDLE. 285 



15. The connexion of the diurnal changes of the horizontal 

 needle with earth-currents being assumed, we may reason from 

 the former to the latter, and infer the laws which govern the 

 diurnal changes of the earth-currents from the known laws of the 

 related phenomena. 



We have already seen that the intensity of the current in the 

 magnetic meridian (flowing northward) = ai\ ; and that of the 

 current perpendicular to the magnetic meridian (flowing east- 

 ward] = - . Hence, if p denote the intensity of the resultant 

 current, and the angle which it makes with the magnetic 

 meridian, measured to the east of north 



in which r\ = Xty sin 1', and = $X, X being the horizontal 

 component of the earth's magnetic force, and ip the magnetic 

 declination*. The azimuth of the direction of the current, 

 measured from the true meridian in the same direction, is 



Substituting in these formulas the mean values of cty and 

 $X at Dublin, for summer, winter, and for the entire year, we 

 obtain the daily changes of p and o>, given in the following Table. 

 The values of Si/ and $X were observed at Dublin during the four 

 years 1840-43, twelve times in the day, namely, at the alternate 

 hours. The values corresponding to the intermediate hours are 

 obtained from them by the usual formulas of interpolation. 



* The preceding combination of the daily changes of the declination and horizontal 

 intensity, as well as the graphical representation of the results, seems to have been first 

 employed by Professor Hansteen, to represent the laws of the disturbing force, to which 

 these changes are due. The only difference between the two representations is, that 

 the azimuth of the disturbing force at any hour is 90 greater than that of the earth- 

 current. Hence, if the diagrams of Plate II. be turned 90 forward in azimuth, th. y 

 represent the daily changes of the horizontal disturbing force. 



