APPENDIX. 151 



Let us next Inquire to what extent the directive intensity 

 of the compass ought to be reduced in consequence of the 

 increase of the dip, and whether this decrease is sufficient 

 to account for the powerless state of the needles during the 

 passage of the vessel across Hudson's Bay. 



The theory of magnetism, to which we have already al- 

 luded, (See Barloiv's Essays on Magnetic Attraction, Art. 

 206, second edition,) leads to this result, that the intensity 

 of direction of a horizontal needle, is always proportionate 

 to the co-sine of the magnetic latitude of the place, or to 

 the sine of its distance from the magnetic pole ; or, as re- 

 ferred to the dip, the horizontal intensity varies inversely, 

 as ^ (3 + sec.^^), ^ being the dip. That is, the intensity 

 at Seahorse Point was to the same at Green Hythe, as 

 V (3 + sec:''70) : V (^ + sec.^ 86° 32'), that is, as 1 to S 

 nearly. 



It is impossible to investigate this law of the decreasing 

 magnetic intensity of the horizontal needle, without em- 

 ploying abstnise mathematical processes, Avhich might em- 

 barrass the general reader ; but a simple view may be 

 taken of the subject, whicli will assist him in comprehend- 

 ing that a very considerable reduction must take place as 

 the dip increases. For example, let ns (Fig. 2,) represent 

 a horizontal needle in London. It will be perceived that 

 the force which draws it into its magnetic direction is 

 exerted in the line of the dip, viz., in the line P/i, forming 

 an angle of 70° with the horizon ; and, therefore, by the 

 most siniple laws of mechanics, it follows that this force 

 being resolved into the two forces NP, N?z, the latter is the 

 only part of the force which is effective in giving it direc- 

 tion : that is, the horizontal intensity is to the direct intensity 

 in the line of the dip, as N/i to P??, or as co-sine 70° to ra- 

 dius. In the same way, in the second part of the figure, 



