210 



. = ni + „=)(„+f-^), 



in which u is the cotangent o^ p. 



The analogy between the formulaa given in this paper and 

 those usually employed in discussing the motion of a point 

 on a plane is very striking. The former too become identical 

 with the latter when the portion of the sphere on which the 

 trajectory is described becomes infinitely small in comparison 

 with the radius. 



The Rev. H. Lloyd V. P. read the following paper " on a 

 New Magnetical Instrument, for the Measurement of the In- 

 clination, and its Changes." 



In order to know all that relates to the earth's magnetic 

 force, at a given place, observation must furnish the values of 

 three elements. Those which naturally present themselves 

 for immediate determination are, the intensity of the force 

 itself, and the two angles (the declination and inclination) 

 which determine its direction. We may substitute for these, 

 however, any other system of elements which are connected 

 with them by known relations. Thus, we have hitherto pre- 

 ferred to observe the declination, and the two components 

 (horizontal and vertical) of the intensity ; and, in general, 

 the main considerations which should guide us in our choice 

 are, the exactness of the observed results, and the facility of 

 their determination. 



In this point of view, the declination and the horizontal 

 component of the intensity leave us nothing to desire, their 

 determination being now reduced to a degree of precision, 

 hardly (if at all) inferior to that of astronomical measure- 

 ments. The same thing, however, cannot be said respecting 

 the third element, as hitherto observed. In the Dublin 

 Magnetical Observatory, and in the Observatories since es- 

 tablished by oi'der of the Government and of the East India 

 Company upon the same plan, the third element chosen for 



