118 



REPORTS ON THE STATE OF SCIENCE. 



connecting P to R and Q to S have to be evaluated by changing the 

 position of the battery leads. 



(e) Potentiometer. — With very small resistances, if great sensitiveness 

 is required, two currents of large value have to be maintained in a steady 

 state. As the probable error is proportional to the variation in the 

 current strengths this necessitates great care. In practice the sensitive- 

 ness may be made greater than that of any other method. If P=00001, 

 R=0'001, Q=0-001, S=0'01 (see fig. 3), and if we suppose the resistance 

 of the other portions of the circuits to be comparatively great, then, with 



Fig. 10. 



y^/^y* 



G=l ohm, the sensitiveness for one position of balance is proportional to 

 001 i A v/P, and for the second position of balance 0031 i\ \/R. If 

 Q=l, S = 10, the sensitivities corresponding are proportional to 0'005 

 i A v/P and 0-0029 i A x/R. 



(f) Kelvin Double Bridge^ (fig. 11). — For measurements of pre- 

 cision this method is used at the National Physical Laboratory. Balance 

 is first obtained by shunting R or S, when 



,_QE' 



ftd 



S' ^a + /3 + tf 



(s'-i)' 



R' and S' representing the shunted values of R + L and S-f L' + L". To 

 obtain the value of L the battery lead at P'L is disconnected and joined 

 to L-R and the bridge again balanced. L' + L" is similarly evaluated (see 

 example which follows). For d, a and ft are disconnected and the galva- 

 nometer circuit completed by connecting to the junction of Q and d and 

 balancing. The ratio of a to fl must be known with considerable accuracy 

 if d is comparatively great. a consists of a resistance coil plus a 

 potential load of P, and /3 of another coil phis a potential lead of Q ; 

 hence the ratio must be determined with a and /? in position in the 

 bridge. The bridge is first balanced in the ordinary way by shunting 

 R or S. The connector which joins P to Q through the arm d is then 

 removed and balance restored by shunting a or /3. The original arrange- 



' W. Thomson, Phil. Mag., 1862, 24, 149. 

 Diesselhorst, Zeitichr. Instrument enli., 190.3, 33. 



See also Jaeger, St. Lindeck, and 



