to be employed in testing with Wheatstonc's Diagram. 367 

 Instead of equation (1) we may put 



*-&+&**» w 



which is identical with the other if 



(ac-bd) 2 



7 = 



{a + b){c + d)\(a + b)(c + d)+f(a + b + c + d)\ 



But as it is evident that the law (1) is of no practical interest 

 unless balance is almost established, we have always ac— bd very 

 near zero ; consequently y, which is proportional to the square 

 of ab — cd, must approximate still nearer to zero; and /, the 

 resistance in the battery branch, being already as small as pos- 

 sible, we may in this case, without sensible error, put 



/r=0; 



hence we have approximately 



ab cd 



9=VTb + J+d- (1) 



But as (ac—bd) 2 is infinitely small, we may write 



9- a + b+c+d W 



This equation gives us the following simple law for Wheat- 

 stone's diagram when near a balance : — 



To raise the magnetic moment of the galvanometer to its maxi- 

 mum, its resistance must be equal to the parallel resistance of the 

 two double branches which are opposite to the galvanometer*. 



And according to this, we can always calculate the proper 

 resistance of the galvanometer, viz. the diameter of wire to be 

 used when the space to be filled is given. 



The above law gives us, for every other resistance to be mea- 

 sured, another resistance of the galvanometer; but as the galva- 

 nometer can only have a very limited number of definite resist- 

 ances, the law we have given must apply to those values to be 

 measured for which the other conditions are the most unfavour- 

 able ; and it is evident this will be the case for all large resist- 



* I will mention here that this law is only correct when the sectional 

 area of the insulating covering is always in the same proportion to q, the 

 sectional area of the wire. But as the thickness of the insulating co- 

 vering is generally the same for thick as for thin wires, this condition is 

 never fulfilled in practice, especially with small galvanometers used in 

 measuring large resistances. 



