INTENSITY OF THE EARTH'S MAGNETIC FORCE. 261 



the total intensity might be found directly, without the inter- 

 vention of its horizontal component. In the Paper in which it 

 was explained,* it was shown that the ordinary dip-circle may be 

 employed in' both parts of the observation. Subsequent consider- 

 ations, however, derived from the probable errors of observation, 

 led me to propose that the dip-circle should be employed only in 

 one part of this process, and that the observation should be com- 

 pleted by the known methods. 



The present communication is intended to show in what 

 manner this complication may be avoided, and the original 

 proposal carried out. It is of great importance to the scientific 

 traveller that the instruments which he has to carry should be 

 reduced, as far as possible, in number and in weight, and that 

 their adjustments should be few and simple ; and it is believed 

 that these objects are attainable by the method explained in this 

 Paper. Before entering into details, it will be convenient to revert 

 to the theoretical principles on which the method is founded. 



If X and Y denote the horizontal and vertical components of 

 the Earth's magnetic force, m the magnetic moment of the needle 

 acted on, and a the azimuth of the plane in which it moves, 

 measured from the magnetic meridian, the effective forces exerted 

 upon it are 



mXcosa, mY; 



and their moment to turn the needle is 



m ( Y cos ?/ - X cos a sin >j), 



jj denoting the actual inclination of the needle to the horizon. 

 This moment is opposed by that of the added weight, or by Wr, 

 W being the weight, and r the radius of the pulley by which it 

 acts ;f and the equation of equilibrium is therefore 



m ( Y cos ri - X cos a sin >j) = irr. 

 When the needle is removed, in the second part of the process, 



* froecedinffs of the Royal Iruh Academy, January 24, 1848. 



t It is here supposed that the weight is attached to a fine thread pasiii 

 light pulley, whose centre is on the axis of the cylindrical axle of the needle, in 

 manner proposed by Mr. Fox. If the weight he attached to the s< 

 needle, at a fixed point, its moment is icr COST;. 



