1823.] Pi'°f- Barlow on Magnetic Attractions. 459 



natural horizontal direction of the needle. The latter, therefore 

 (which, for simplicity sake, we shall at present consider as inde- 

 finitely short with regard to the distance), will, at either of those 

 points, be acted upon by two rectangular forces ; viz. the gal- 

 vanic force in an east and west direction, and which we may 

 denote by f, and the natural magnetic or directive force m ; 

 consequently, according to the principle of forces, the resultant 

 will be expressed by */ (f~ + ?>i") and the angle which it makes 

 with the natural direction of the needle, being called A, we 

 shall have 



tan. A = - (1) 



Hence the magnetic force being constant, the tangent of the 

 needle's deviation at the north or south, will be a correct measure 

 of the galvanic power." 



" We have thus a principle by means of which we may verify 

 a part at least of our theory by experiments. For example ; 

 since by the supposition every particle of the galvanic vertical 

 wire acts inversely as the square of its distance from a given 

 point, we ought to find a determined relation between the tan- 

 gent of deviation and the length of the wire; or the length of the 

 wire remaining constant, between the tangent of deviation and 

 the distance, provided always that the intensity of the battery 

 remain constant." 



" The apparatus already explained furnishes us with the oppor- 

 tunity of making both these comparisons. For by means of the 

 sliding horizontal rods, the vertical conducting part of the wire 

 may be shortened in an instant ; and, in the second case, it is 

 only necessary to slide up the compass to different distances, 

 which may likewise be done so quickly, that it will not be neces- 

 sary even to have recourse to the standard compass." 



" It is fortunate also that the calculation here alluded to is of 

 the simplest kind. For denoting the length of the wire by 2 /, 

 and the distance of the compass by d; assuming also x as any 

 variable length, the corresponding elementary action at this 



distance will be -=— — „> and the sum of these actions will be 



«■ + X 3 



r x i x 



I = - arc. tan. -, 



./ d* + x* d d ' 



which vanishes when x vanishes ; and which, therefore, when 

 x = /, and the two lengths are included, becomes - arc. tan.-, 



consequently if we denote the deviation, as we have done above 

 by A, we ought to find this force vary inversely as tan. A, or 



cot. A \- arc. tan. -t = a constant quantity. 



" The following are a few out of numerous experiments of 

 this kind which Fhave made, and which have been all found 

 equally satisfactory. 



