190 BARUS— ADJUSTMENT FOR PLANE GRATING [April 24, 



for a negative needle. In addition to this however there is a 

 voltaic difference, aluminum-brass, at AC when radium is in place 

 and the medium therefore highly ionized. The latter potentials are 

 usually negligible. These are the chief electromotive forces, the 

 first very high (150 volts) and in a weakly ionized medium; the 

 other low (.2 volt) but in an intensely ionized medium: thus they 

 may produce equal currents. Other voltages such as the room 

 potential may be operative, but their effect is secondary. If the 

 capacities C, C", are successively removed the electrometer current 

 increases proportionately, showing its origin to be directed from the 

 needle toward the insulated or non-earthed pair of quadrants. 



If the condenser metals are reversed (see Fig. i), the voltaic 

 couple is reversed. This makes it possible to obtain both the voltaic 

 contact potential and the ionization in the condenser C, from a pair 

 of commutated measurements. 



2. Theory. — Let F„ be the potential at the electrometer, Vc the 

 voltaic potential difference of the two metals of the condenser, V the 

 potential of the insulated conductor BB, measured by the electrom- 

 eter. Let n be the hypothetical ionization in the electrometer, A^ the 

 (radium) ionization in the condenser (length /, radii R^, R2). Let 

 C be the total capacity of the systems CBBE. Then 



where A is a constant, n and v the normal velocities of the positive 

 and negative ions, e the charge of the electron. The needle is posi- 

 tively charged. This may be written 



V=:=V^ — KiV—Vc), 



where for A'' = o, i^ = o, or 



V=V, = A(Vn — V)n, 



i. e., the current in the electrometer, observed in the absence of 

 radium, from needle to quadrants. This is directly measurable with 

 accuracy. It is nearly proportional to Vn since V is much within 

 I per cent, of F„. 



The integral of this equation is, t being the time, 



V={Va/K){i—KVc/Va){i—e-'"). 



