WHITE: PRECISION OF THERMOSTATS 431 



surface. The interior portions of bulb fluid are largely inert, 

 but the detrimental effect of bulb wall expansion, if that is 

 present, increases with the volume of the bulb. 



There are, however, two further considerations not treated 

 hitherto. One is the fact that the effective or integrated tem- 

 perature of the bulb fluid is zero only one-eighth of a period before 

 the maximum temperature is reached at the surface . Hence if the 

 bath lags only 3 seconds behind the heater, the bulb, no matter 

 how sensitive it is, cannot possibly function normally and regu- 

 larly for a constancy of 0.001° Avith a rate, V, of 0.01° per 

 minute, and similarly for other lags. 



A second consideration is the damping and delay of the wave 

 as it goes through the bulb wall,^ which still further cuts down 

 the efficiency, more with mercury than with gasoline, and much 

 more with glass than metal for the bulb wall. 



If the rate, V, is made smaller, which can be done by dimin- 

 ishing the room-temperature fluctuations, then the period for 

 any given precision becomes longer, and the effect of all lags, 

 in the heater, in stirring, and in the bulb, may become very 

 much less. Thus, if the bath is put in a large packing box, or 

 in a space inclosed by curtains, and the air temperature in this 

 space is controlled by another simple regulator, V can often be 

 made over fifty times as small. This means that a precision 

 of o. 001 ° can be reached with the heat going on or off only once 

 in ID minutes or so. The lag effect, which is LV, is now far 

 smaller than before even with the lag somewhat larger, hence 

 large and, therefore, sensitive bulbs can be employed, and a pre- 

 cision beyond 0.001° can be thought of. Another advantage 

 peculiar to this method is the diminution of differences between 

 one part of the bath and another. Inclosure, however, is often 

 inconvenient. 



This cascade thermostat is one means of securing high 

 precision. A second, giving practically no short-period tem- 

 perature oscillations at all, is the Gouy, or oscillating-wire, 



3 The mathematical problem presented by this additional complication has 

 been seldom, if ever, treated in the literature. Prof. L. B. Tuckerman has worked 

 out for me a number of solutions for different cases, an account of which will belong 

 in a more complete publication. 



