Galvanometer when used with the Thermopile. 419 



The phenomenon appears to be due to the inertia of the 

 galvanometer needle, and to the fact that a considerable time 

 elapses after the pile has been exposed to a source of heat, 

 before a constant temperature is reached. On account of its 

 inertia the needle is unable to follow immediately the rapidly 

 increasing current that flows when the face of the pile is first 

 exposed. In a short time, however, the continued action of 

 the deflecting force imparts sufficient velocity to carry it not 

 merely to the position which corresponds to the current then 

 flowing, but to a considerable distance beyond this point. The 

 result is that the motion of the needle is stopped, and a retro- 

 grade movement begins, which continues until tHe pile has 

 been heated sufficiently to cause another throw forward. This 

 behavior is then repeated until the temperature of the pile has 

 become constant, or until the oscillatory motion of the needle 

 has been destroyed by damping. If it be assumed that the 

 heating of the pile takes place in accordance with Newton's 

 Law of Cooling, and that the electromotive force of the pile, 

 throughout the small range of temperatures with which we 

 have to deal, is proportional to the difference in temperature 

 between the junctions, the equation of motion of the needle 

 may be derived as follows : 



Let T be the final difference in temperature between the 

 two faces of the pile, and T the difference at any time t. Then 

 the current in the galvanometer is given by the equation : 



E PT PT , 



k being the radiation constant of the surface of the pile, and P 

 the electromotive force developed by a difference in temper- 

 ature of one degree between the two junctions. 



The couple due to the action of this current upon the 

 needle, and tending to deflect it, is K im I cos d, d being the 

 deflection, and K a constant depending on the form and di- 

 mensions of the galvanometer. Since 6 is always small, cos 6 

 will never differ appreciably from unity. If, therefore, we 



K m I P 



substitute for i its value as given in (1) and replace — ^ by 



Q, the expression for the deflecting couple is reduced to 

 QT (1 — £~ M ). The only other forces that act upon the 

 needle are the return force of the earth's field, which for small 

 deflections is equal to N0, and the retarding effect of damping. 

 The latter force being proportional to the velocity of the 



7/3 



needle, may be represented by L -=-. These three forces may 



oi t 



now be equated to the product of the moment of inertia of the 



