PEIRCE. — BALLISTIC GALVANOMETERS OF LONG PERIOD. 2S9 



mounted for use by Mr. John Coulson, who has helped me in all the 

 work. 



When the coil of a d'Arsonval galvanometer is disturbed from its 

 position of equilibrium and is then allowed to swing under the action of 

 a righting moment proportional to the angular deviation from its orig- 

 inal place, the damping effects of the resistance of the air and of the 

 induced currents in the frame and the coil, as they move between the 

 poles of the permanent magnet of the instrument, may usually be ac- 

 counted for, with an accuracy sufficient for most practical purposes, on 

 the assumption that the motion of the suspended system is hindered 

 at every instant by a force-couple of moment proportional to the angu- 

 lar velocity. Gauss and Weber showed that this hypothesis served to 

 explain very well the motion of the magnets which they used in their 

 measurements at Gottingen, and they put the mathematical theory of 

 motion resisted in this way into the form in which it appears in most 

 treatises on Physics 5 at the present day. When, however, a system 

 swings under strong air damping, the motion sometimes 6 departs pretty 

 widely from the Gaussian law at the beginning, at least, and it is not 

 always safe to apply Gauss's equations to a ballistic galvanometer 

 which has air damping as well as electromagnetic damping until one 

 has found out whether the ratio of successive amplitudes is fairly con- 

 stant during the whole motion, as Gauss's hypothesis demands. Even 

 in the case of one of Gauss's own magnets, the logarithmic decrement 

 of the amplitudes increased on a certain occasion from 1168 X 10 -6 to 



6 Gauss, Resultate des Magnetischen Vereins, 1837 ; W. Weber, Resultate des 

 Magnetischen Vereins, 183G, 1838; Maassbestimmungen, 2 ; Math-phys. Abhand- 

 lungen der K. Sachs. Gesellsehaft, 1852 ; I)u Bois-Reymond, Monatsberichte der 

 Berl. Acad., 1869, 1870; Chwolson, Bulletin de St. Petersbourg, 1881 ; Dorn, Ann. 

 der Physik, 17 (1882) ; 35 (1888) ; Maxwell, Treatise on Electricity and Magnet- 

 ism, 2; G. Wiedemann, Lehre von der Elektricitat, 3; Deprez et d'Arsonval, 

 Comptes Rendus, 94 (1882) ; Riecke, Abhandlungen der K. Gesellsehaft der Wis- 

 senschaften zu Gottingen, 30; Rachniewsky, Lumiere Elect., 17 (1885) ; see 

 also Lumiere Elect., 29 (1888) ; 33 (1889) ; 45 (1892) ; Ledeboer, Comptes Rendus 

 102 (1886); Ayrton, Mather and Sumpner, Philosophical Magazine, 30 (1890); 

 42 (1896); 46 (1898); Classen, Electrotechnische Zeitschrift, 16 (1895); Sack, 

 Electrotechnische Zeitschrift, 17 (1896) ; Des Coudres, Zeitschrift fur Electro- 

 chemie, 3 (1897) ; Barus, Phys. Rev., 7 (1898) ; Salomon, Philosophical Magazine, 

 49 (1900); Robertson, Electrician, 46, 901-904; 47, 17-20 (1901); G. Kum- 

 mell, Zeitschrift fiir Electrochemie, 7 (1901); Diesselhorst, Ann. der Physik, 9 

 (1902) ; Jaeger, Instrumentenkunde, 1903; Stewart, Phys. Rev., 16 (1903); White, 

 Phys. Rev., 19 (1904); 22(1906); 23 (1906) ; Shedd, Phys. Rev., 19 (1904) ; Smith, 

 Phys. Rev., 22 (1906) ; A. Zeleny, Phys. Rev., 23 (1900) ; Wenner, Phys! Rev., 22 

 (1900) ; 25 (1907). 



6 Peirce, These Proceedings, 44 (1908). 



vol. xliv. — 19 



