536 The Rev. Dr. Llotd on the Determination of 



I was induced to consider the means of supplying this defect some years 

 ago, upon the occasion of the Arctic Expeditions of 1845 and 1848 ; and I 

 then suggested another process, by which the total intensity might be found 

 directly, without the intervention of its horizontal component. In the paper in 

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

 ployed in the two parts of the observation, — the product of the Earth's magnetic 

 force into the moment of free magnetism of the needle being determined, by 

 observing the position of equilibrium of the dipping-needle loaded with a 

 small weight, and the ratio of the same quantities being found (as in Gauss's 

 method) by removing the needle, and employing it to deflect another substi- 

 tuted in its place. Subsequent considerations, however, derived from the pro- 

 bable 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 

 completed by the known methods. 



The present communication is intended to show in what manner this com- 

 plication 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 simple theoretical principles on which it 

 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 azi- 

 muth of the plane in which it moves, measured from the magnetic meridian, 

 the effective forces exerted upon it are — 



MX cos a, MY; 



and their moment to turn the needle is — 



il/( Fcos tj — X cos a sin tj), 



7] 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 



* Proceedings of the Bojal Irish Academy, January 24, 1848. 



