302 M. F. Kohlrausch on the Absolute Value of the 



III. The Absolute Measurement of Resistance by the method 

 of Recoil (Zuriickwerfungsmethode). 



The process described at page 296, as the " second ** method 

 of determining the absolute resistance of a circuit consisting of 

 an earth-inductor and a galvanometer with narrow coils, depends 

 on the connexion between the coefficient of sensitiveness of the 

 galvanometer and the ratio of damping of the vibrating needle. 

 I intercalate here a demonstration of this principle, as the ex- 

 pression given by Weber * requires a trifling correction. 



The coefficient of sensitiveness q is the deflecting moment 

 which a current of unit strength exerts on the galvanometer- 

 needle, when the latter is parallel to the windings of the coil. 

 Then, according to the general laws of induction, the electro- 

 motive force which the needle induces in the coil when moving 



dsc 

 with the angular velocity j— in the neighbourhood of the par- 



dec 

 allel position is — q -7-. If w is the resistance of the galvano- 

 az 



meter, including the path which forms the connexion between 

 the ends of the conducting wire (in the case before us, there- 

 fore, w is the resistance of the galvanometer + that of the 

 inductor), the moving needle induces a current of strength 



o dx 

 — -fJ and thereby in its turn experiences a deflecting moment 



qi £<£ 



= — - n, which tends to damp its motion. 



w dt r 



Besides this galvanic damping, other resistances to motion 

 may exist (such as resistance of the air, &c.) which may be repre- 

 sented by— C -rr. 



Now let the position of equilibrium of the needle be parallel 

 to the windings of the coil ; and let the vibrations be so small 

 that, if x denote the angle of deflection at any instant, the de- 

 flecting moment due to the earth's magnetism and to the 

 elasticity of the suspending fibre may be represented by — Dx. 

 If, lastly, K stands for the moment of inertia of the needle, its 

 motion will be determined by the equation 



d*x L I /q\ \dxB 



K\w + C )dt + K i 



This is the equation, so often discussed f, of the motion 



* Abhandl. d. Gotting. Gesellsch. d. Wissench. vol. x. p. 25 (1862). 



t Gauss, Resultate des magn. Vereins, 1837, p. 74; 1839, p. 55. W. 

 Weber, Abh. der konigl. Sachs. Ges. der Wiss., 1846, vol. i. p. 345. Du 

 Bois-Reymond, Monatsber. der Berl. Akademie, 1869, p. 807. 



