222 



this latter effect however being very small. Such dampinj;: as did occur 

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

 would have occui'red if there had been no danipiiiu', which is given by 



04) 



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 metlaod was Ivuown to lacli precision, and indeed became unusable 

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

 laboratory experiment' of this period 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 possible only with a needle of large 

 magnetic leakage, and with special adjustments of the coils. 



With the introduction of the suspended coil type of galvanometer and 

 its rapid displacement of earlier 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 increased air friction as 

 compared with that acting on the small polished bell-shaped steel needles, 

 and second because of the very greatly increased electro-ma'^netic reac- 

 tions due to induced currents circulating within the coil Itself. 



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

 ations which r(H|uhv careful attention, innsnnich as the methods applicable 

 to the older type will usually lead to incorrect results if ap])lied to the sus- 

 pended coil type. Particularly is this true in calibrating the galvanometer. 

 With the older type concoi'dant 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 appropriate coiTectious 

 being applied. But with the suspended coil galvanometer, where the elec- 

 tromagnetic damping is large freipiently indeed causing the motion to lose 

 its oscillatory character entirely and become ai)eri(xlic, it is impracticable 

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

 then clear that the dam])iiig. and licncc I lie discnKhnice between the ob- 

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

 of the resistance in the external lin iiit. which function is not easy to de 

 terra ine. 



Kolilranscli, I.<'ln-I)ii(li (Icr I'rak, I'liysik. !Mli cd., p. ;>01t 



