120 Best Arrangement of Wheatstone's Bridge. 



telegraph lines, the battery resistance is usually very small 



in comparison with that of the line; hence -r^~? will be very 



little different from/. When this is the case, formula (9) be- 

 comes 



c=^f(d + e). 



If also the galvanometer resistance is small compared with the 

 resistance to be measured, then these equations are sufficient for 

 the determination of b and c, 



b— Vd~e> 



As a numerical example of these formula?, suppose /=100 

 ohms, e=1000 ohms, and d is known to be about 1,000,000 

 ohms. Then by (10), 



a= ^100,000=316 ohms. 

 By (9), 



V! 



6 y 1 O 2 



(10 6 + 10 3 ) = 10004 ohms, 



10 6 + 10 2 



b = — =31608 ohms. 

 c 



These values of a, b, and c will be the best. The more conve- 

 nient arrangement, 



a=300, c= 10,000, 



6 = 30,000, d= 1,000,000, 



would be very nearly the best. 



It appears to me that the formulae (9), (10), and (11), or 

 those following, will be found of considerable practical value. If 

 the same battery and galvanometer be always used, the side a of 

 the bridge will be a constant resistance, and a Table of the near- 

 est convenient values of b and c could be easily calculated for dif- 

 ferent values of d. Formula (3), which is Schwendler's, can 

 evidently have only a very limited application, as, for instance to 

 the construction of galvanometers for particular purposes. For- 

 mula (4) could be sometimes used; but it is a troublesome thing 

 to make combinations of cells for " quantity " or " intensity/' 

 besides spoiling them if they are not all precisely similar. 



In conclusion, if, to measure a certain resistance, the best 

 resistances for the galvanometer, battery, and the three sides a- 

 b, and c were required, then we should have to make a = b = c 

 z=d=e=f, which can be proved by combining equations (3), 

 (4), (6), and (10). This, however, is more curious than useful. 



