all know7i Suhstanceft to the Magnetic Influence^ ^c. \\\ 



method of measuring the thickness of solid substances, a suffi- 

 cient approximation, we find, may be readily obtained by expe- 

 riment, for the position of the foci of attraction in any regularly 

 magnetized bars whatever. 



Hence the law of the directive power of bar-magnets, at any 

 distance, however remote, may be considered, I apprehend, as 

 satisfactorily determined ; 



2»-i-l ' x^,x + \*' 

 as before stated, representing the resultant action of all the 

 forces in the magnet, at any distance, in measures of its focal 

 length, or in fractional parts of such measures, on a compass 

 situated in the line of the longer axis of the magnet, and bear- 

 ing east or west from each other. And hence the directive force 

 of all magnets, of proportional intensity of power, must be in 

 the direct ratio of their focal lengths ; so that if a bar of 1 foot 

 focal length will produce a given sensible action on a compass 

 (suppose of 5'), at the distance of 12 feet, — then a bar of 2 feet 

 focal length, proportionally strong, will produce the same de- 

 viation at 24 feet, a bar of 3 feet focal length at 36 feet, or one 

 of 6 feet interval between the foci of attraction, will produce a 

 similar sensible deviation at the distance of 72 feet. 



3. The foregoing investigations enable us satisfactorily to de- 

 termine The extent to which this method of ascertaining distances 

 may he carried. 



As the directive power of different magnets, similar as to 

 proportions and quality, is very nearly in the relation of their 

 lengths § 1. (2) 6; and as the accuracy of different well-con- 

 structed compasses, as to their capability of indicating very mi- 

 nute quantities of magnetic influence, may be considered to be 

 in the relation of the lengths of their needles, — it is evident that 

 there can be no assignable limit to the application of the method 

 of ascertaining distances now proposed. For, by increasing the 

 length or number of the magnets, and improving the quality or 

 increasing the dimensions of the compass-needles, still further 

 and more extensive applications of the principle wiU be ob- 

 tained. 



