222 



this latter effect however being very small. Such damping as did occur 

 was corrected for by the use of that convenient fiction, the throw which 

 would liave occurred if there had been no damping, wliich is given by 



=*('+t) 



where <p is the observed throw and ^ is the logarithmic decrement of Gauss, 

 which is the natural logarithm of the ratio of successive amplitudes. 



This method was known to lack precision, and indeed became unusable 

 when the logarithmic decrement reached a value of 0.4 or 0.5. A common 

 laboratory experiment' of this perifnl was one designed to determine the 

 resistance of a galvanometer or of an unknown coil in terms of the loga- 

 rithmic decrements taken successively on open circuit, circuit closed through 

 the galvanometer only, and circuit closed including the resistance to be 

 measured. Satisfactory results were iK>.ssible only with a needle of large 

 magnetic leakage, and with special adjustments of the coils. 



With the intrmluction of the suspended coil type of galvanometer and 

 It.s rapid displacement of eiirlier types, it claimed attention also as a val- 

 uable and accurate ballistic instrument. However the normal damping is 

 much greater in this case, first because of the increastnl air friction as 

 compared with that acting on the small polished bell-shape<l steel needles, 

 and second because of the very greatly increased electro-magnetic reac- 

 tions due to induced currents circulating within the coil itself. 



In passing from the older to the newer type there are certain consider- 

 iitions which nM|uire careful attention, inasnnich as the methods applicable 

 to the older tj'pe will usually lead to incorrect results if applied to the sus- 

 pended coil tyi>e. Particularly is this true in calibrating the galvanometer. 

 With the older type concordant results were obtained either with a stand- 

 ard cell and condenser, or with a mutual inductance, the logarithmic de- 

 crement being calculated in either case, and the ai)i)roi)riate corrections 

 being ai)i)lied. But with the suspended coil galvanometer, where the elec- 

 tromagnetic damping is large frecjuently indeed causing the motion to lose 

 its oscillatory character entirely and become aperunlic, it is impracticable 

 to calculate or use the logarithmic decrement in the regular way. It is 

 then clear that the damping, and hence the discordance between the ob- 

 served and fictitious throws will not only be large, but will be a function 

 of the resistance in the external circuit, which function is not easy to de 

 terraine. 



' Kohlrausch. Lphrbuch dor Prnk, Pliysik. 9th Pfl.. p. 399. 



