SCIENCE AND PRACTICE. 333 



whence, by integration 



r 



2 r TT 2 r 2 TT 



7" 



But <rpp is the resistance of a tube, whose length is equal 



to its radius. The resistance to the current spreading 

 at the ends, therefore, in the case under consideration, 

 amounts to the addition of its radius to its length, by which 

 the corrected resistance, "W, becomes 



*T) 



65. The absolute Units. Professor Weber first proposed, 

 defined, and determined units of resistance and electro-motive 

 force referred to units of mass, space, and time ; and Pro- 

 fessors Thomson and Helmholz have since determined similar 

 units, with reference further to work performed, on strictly 

 mechanical principles. 



The so-called absolute units hold the same relation to the 

 arbitrary ones which the expression of mechanical effect in 

 foot-pounds does to the same expressed in horse-power. In 

 the latter case, we refer the capability of an engine to the 

 average capabilities of so many strong horses ; in the former 

 we refer to an unit of work, based on fixed standards in 

 other words, to the number of pounds which the engine could 

 lift one foot high from the ground, in one second of time. 



In determining the absolute units of electrical force and 

 resistance, it is only necessary to follow the natural relations 

 between the various electrical magnitudes and the relations 

 between these and the common units of time, mass, and space. 

 Each of these magnitudes is capable of direct experimental 

 comparison with others of the same nature, while their 

 dependence upon each other is expressed by mathematical 

 formulae, the truth of which has been proved by experimental 

 research. 



These magnitudes are, (1) intensity or mechanical effect, 

 (2) quantity, (3) electro-motive force, and (4) resistance. 



