422 TENTH ANNUAL REPORT OF 



but as the second power of the distan«5e. If they were inversely as 

 the first power of the distance, the deflecting force in the position Fig. 

 5 would be the same as in the position Fig. 4. 



(See page 323.) A magnet whose moment of rotation is a unit may 

 be represented by amagnet having two poles at theunitof distance apart, 

 each of which would attract or repel an equal pole, at the distance of 

 a unit, with a force of a unit. Weber ' s unit of measure for the galvanic 

 current may then be represented as that current, which, circulating 

 in the circumference of a circle around a magnetic pole at the centre 

 n of a unit of force, would have the differential of its action upon that 

 pole expressed by the length a b of an infinitely short element of the 

 current when the distance n a is a, unit ; or, freely expressed, the cur- 

 rent of which a unit of length, at the distance of a unit, would act 

 upon a unit pole with the force of a unit. Starting from this point 

 of view, the equations of the text will be easily understood. 



Let a current of a unit quantity circulate around a circle in_ the 

 plane of the magnetic meridian whose radius =: r. _ In this circle 

 draw any two parallel chords, c f and d e, at an infinitely small dis- 

 tance apart, and in the direction of the terrestrial magnetic force. 

 Draw also d g perpendicular to c/, and intersecting it in g. Let the 

 terrestrial magnetic force be a unit. Then the force with which the 

 element c d of the current is urged in the direction perpendicular to 

 the plane of the circle is expressed by the perpendicular distance d g 

 of the chords ; that is, the same as the force with which it would be 

 acted upon by a unit magnetic pole placed at the distance of a unit in 

 the direction of the chords. The element e/is urged with an equal 

 force in the opposite direction. The moment of rotation impressed by 

 these two forces will, therefore, he d g X d e=: area c d ef. Conse- 

 quently, the moment of rotation of the whole circular current is ex- 

 pressed by the area of the circle. And if the current be of the quan- 

 tity g, the moment of rotation will be 



G =: area x gz=z7z r^ g. 



Now, in the tangent compass the deflecting force of the circle, or 

 ring, may be represented by the force with which the circle would act 

 upon a single unit pole at its centre n. The element of this force for 

 an infinitely short part, a h, of the circumference, when the current 



is of the quantity^, is ^g^ and the whole force is, therefore, — ^ y 



and T tan. to is the value of this force as given by the tangent com- 



10. 



pass, or 27Tg _ ,p ^^^_ 



r 



(Seepage 362.) It will readily be seen that a + ^ is always greater 



than 2, except when a =: 1, by substituting for a, successively, the 

 values 2, 3, 4, &c., or ^, \, ^, &c. 



