134 Mr. A. R. McLeod on the Lags of 



It can be shown that, neglecting grid conductance, 

 persistent oscillations are produced when M, the mutual 

 inductance, is given by the equation 



aM + ^ + RC(1 + b R') = (8) 



II: we take into account the grid conductance we must 

 substitute for R the effective resistance value ah (see (4)). 

 Thus (8) becomes 



hM 2 

 aM-f -~ + (CR + L* 1 )(1 + &R') = 0. . . (9) 



Sum 



mary. 



The effects of grid currents in a three-electrode vacuum 

 tube are discussed, treating the conductance of ihe grid 

 circuit inside the tube as a high-resistance leak across the 

 condenser of the oscillatory circuit connected to the grid and 

 filament. The effect of this leak in amplifying and oscillation 

 circuits is investigated quantitatively. 



X. On the Lags of Thermometers with Spherical and 

 Cylindrical Bulbs in a Medium whose Temperature is 

 changing at a Constant Bate. By A. R. McLeod, M.A., 

 1851 Exhibition Science Research Scholar of the University 

 of Toronto, and Wollaston Scholar of Gonville and Cuius 

 College, Cambridge *. 



Summary. 



^^HE lag of a thermometer, situated in a medium whose 

 -L temperature is changing, is of practical interest in 

 the case of ascending aeroplanes and balloons. The medium 

 in this case is the atmosphere ; but application might also 

 be made to the case where the variable temperature of any 

 other medium, say a liquid, is to be determined by the 

 thermometer as a function of the time. In the following 

 paper we suppose the temperature of the medium to change 

 uniformly. Expressions are given for the stead}' values of 

 the lags for spherical and cylindrical bulbs, when the 

 surface conductivity is finite; and for the lags at any 

 instant when the surface conductivity is infinite. 



The lag of the mean temperature of the bulb behind that 



* Communicated by Dr. G. F. C. Searle, F.R.S. 



