THE SMITHSONIAN INSTITUTION. 



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which joins the poles, and represent this by r, then the expression 

 becomes 



^ Xi i 



This is the fundamental equation of Ohm, from which all the rela- 

 tions of galvanic combinations can be derived. 



When currents of different forces or strengths are to be compared, 

 there must be, first of all, a common measure. Hitlicrto, to my 

 knowledge, there have been three different units proposed, each of 

 which we shall consider somewhat in detail. 



Pouillet proposed (Pog. Ann., xlii) as a unit of force of the galvanic 

 current that which a thermo-electric element of copper and bismuth 

 would produce, when so closed that the whole resistance is equal to a 

 copper wire of 20 metres long and 1 millimetre thick ; one soldering 

 being maintained at a temperature of 100°, the other at 0". 



Fig. 4. Jacobi (Pog. Ann., xlviii 26) compared the deflection of 



a Nerwander tangent-compass with the decomposition of 

 water produced simultaneously by the current ; thus re- 

 ducing the indications of the tangent-compass to the chem- 

 ical effect. For unit of force he assumed the current which 

 generates in one minute, one cubic centimetre of explosive 

 gas at the temperature of 0°, and height of the barometer 

 at 760 millimetres. 



Weber took for his unit the current which, circulating 

 at a distance around the unit of surface, produced the 

 same action as the unit of free magnetism. 



To explain what Weber means by the unit of free mag- 

 netism Ave must dilate somewhat. 



A magnetic bar s n placed north or south of a mag- 

 netic needle, and perpendicular to the magnetic meridian, as 

 represented in Fig. 4, will tend to deflect the needle from the 

 magnetic meridian, while the terrestrial magnetism tends to 

 draw it back. The magnitude of the deflection depends 

 upon the relation of the two forces ; the tangent of the 

 angle of deflection is the quotient of the force of the bar 

 divided by the 



/ 



j^ = tang V, 



(1) 



denoting by v the angle of deflection, by /the force with 

 which the bar attracts the needle from the magnetic me- 

 ridian, and by T the force with which the terrestrial mag- 

 netism tends to draw it back. 

 But the action of the bar upon the needle is proportional to the 

 third power of its distance from the needle, so long as this distance is 

 moderately great in comparison with the dimensions of the bar and 

 the needle. Denoting the distance by r, the product /r^ must be a con- 

 stant quantity, which we will denote by M. 



But this product//-^, or M, indicates the moment of revolution which 

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