of Iron and German Silver' 493 



and tlie suspension : — 



dv^ KW dd K ^ KW 



It is only for small angles (f> that the integration of this equation 

 can be effected in a definitive form. Presupposing small angles, 

 it is transformed into 



from which by integration we obtain 



^~wTm ^ KW « [/'(0)12 Tm 



WIC ^ K 



«'-''^"'-"{<»'-V?-i(«J^)'}- 



C and C here denote two integration constants. From this we 

 perceive that the motion of the needle is composed of two mo- 

 tions superposed the one upon the other — first, of that which the 

 needle would have if no thermo-current were present, and then 

 of that which it would have if the periodic part were omitted. 



If now we construct a galvanometer with great deadening 

 force, so that the needle approximates to the aperiodic state, as 

 was done in the present case, and make the time of an oscillation 

 t of the needle and the resistance external to the galvanometer 



small, then the log-arithmic decrement X=4 "-^ ^^ -, /will have 



WK, 



a great value, and the periodic part in the motion of the needle 

 will after the lapse of a very short time be vanishingly small. 

 Consequently, if at the commencement of each period we let a 

 certain time elapse before we begin the observation of the deflec- 

 tions <h corresponding to the different times Q — which, besides, 

 is necessary in order that we may employ the simplified expres- 

 sions of D2|a and Dg^a+b equations (6), — the periodic part may 

 be omitted, and we obtain for <^ simply an expression of the form 



where P' and Q' are constants. If these observations are made 

 with mirror and scale, it is more convenient to introduce the 

 arcs of double the angles of deflection instead of the deflections 

 (^ themselves. Let r be the distance of the mirror from the 

 scale, s the arc corresponding to the angle ^, then 5 = 2r(/), and 

 we have 



5=P + Qe-p^ (13) 



