112 REPORTS ON THE STATE OF SCIENCE. 



and a balance is obtained by shunting R', when, if R,' represents the 

 shunted value of R', 



R,7(P + R,)=(S + B)/(Q + R). 



Combining this with the previous equation, we have 



R/=P[(S + B) (Q + S + r + B)/(Q + r)2]. 



The value of r is obtained with considerable accuracy by moving the 

 galvanometer lead at e to c^ and balancing. In an analogous manner the 

 value of B may be obtained ; the correction due to B is usually less than 

 1 part in 10,000,000. The ratio of S to Q may be eliminated from the 

 last equation by interchanging Q and S in the bridge and repeating the 

 operations indicated above. If Q and S are not very different from their 

 nominal values, then 



R,' + R,/=P[4-6(r- B)/Q], 



where Rj' represents the second shunted value of R'. 



With a galvanometer resistance of 2 ohms, with P=R=1, and 

 Q=S = 1000, the sensitiveness of the arrangement is proportional to 

 0-35 tA. With P=R=2, and Q=S=1000, this is increased to 0-47 iA, 

 the values for % being the same in the two cases. If a greater current 

 value than 0-03 ampere is permissible, then Q=S may be made equal to 

 100 ohms, and the increase in sensitiveness is approximately propor- 

 tional to the increase in the current. 



The following observations were made on May 30, 1906, the mercury 

 standard, Y, being used, and two coils in series (C.l) evaluated : — 



1st observation, P=Y=l-00027o "^*'- ohms Q=1000"18 approx. 



8 = 1000-19 

 X=40-l 

 X' =30900 



Shunt on R'=31500. r=0-033. B=000007 



2nd observation, Q and S interchanged 



Shunt on R'= 16400. 

 Hence 



X =40-1 

 X'=28400 



R , ' + R/ = 1 -000270 [4 - 6(0-0000329)1 

 =4-0008825 

 .-. 2R'=4-0008825 + 2(1/31500 + 1/16400) 

 .-. Cl=R'=2-000534 int. ohms. <=17°-21C. 



Comparing the various methods as practically employed, the sensiti- 

 vities are proportional to 



0-025 i A for the Kelvin double bridge. 



0-098 i \ „ Kohlrausch differential galvanometer. 



0-35 i A „ Wheatstone bridge. 



0-35 i A „ Potentiometer. 



The maximum permissible values of % are the same for the first three 

 methods. For the potentiometer a smaller current must be used. 

 Possibly the arrangement considered for the differential galvanometer 

 might be modified so as to make the method more sensitive. 



