388 Mr. I. B. Cooke on the Use of a double Circuit in 



length of wire, of such section and conductibility as are best 

 fitted for a standard of resistance, and whose known resistance 

 may be represented by I, the units being linear inches, be in- 

 troduced between the electromotor and the double circuit, 

 and let the wires be again adjusted so as to deflect the needle 

 to 45°, noting the new length of secondary wire included = TO'. 

 The equation representing the force, which, previously to the 



introduction of the wire /, was F= ^j5 — y-, now becomes 

 F'= ^ 



R + ^+L" 

 and since 



F ~w" 

 therefore 



R + L _ w_ 



R + ^ + L'~w'' 



from which, substituting for L and L' their values and 



^ ?• + M 



,, „ and remarking that r + w=r' + t(;;', the value of R is de- 

 duced Iw 'W'vJ 

 liJ — vo r + iso 



Excepting in the case of very v^-eak forces, if the galvanometer 

 be sensitive, having a long helix of fine wire, both xv and w' 

 will be very small, while r + xo will be very large. Therefore 



Xnyw * 



the term — ; — will have no practical value: and unless the 



value of F be very small, R may be taken without sensible 



Iw 

 error = — , . 



w —w 



The resistance R of any electromotor which is constant in 

 its action being thus discovered, any other resistance may be 

 measured by the converse process. If it be introduced be- 

 tween the electromotor and the double circuit in the place of 

 the standard wire of the last paragraph, and the value of w' 

 be noted as before, the unknown resistance may be deduced 

 from the equation 



._ R . {w'—w) 'w'{w'—'iv) 

 ~~ xv r + xio ' 



The second term of the latter branch of the equation can only 

 be required when F is very small or I very large, and conse- 

 quently X)o'—xv considerable. 



