gray: linear expansivity t 251 



gradient — dT/dN and a thermal conductivity k in the surround- 

 ing substance, will be directly proportional to both dT/dN and 

 k. Encasing the region in a poor conductor of heat will reduce 

 the latter, and making the layer thick will reduce the former; 

 but this procedure will never eliminate completely either of these 

 factors. However, dT/dN and, consequently, dQ/dt can be made 

 to vanish by supplying heat around the surface in such a way as 

 to compensate exactly for the loss at every place. But the 

 accurate regulation of such a supply presents difficulties which 

 augment rapidly as T departs from the surrounding temperature, 

 because the increased heat flow involved is subject to greater 

 irregularities of surface distribution and to greater fluctuations 

 with time. Conductivity parallel to the boundary, or the much 

 more efficient action of a circulating fluid, will promote a uniform 

 distribution of both the losses and the supply. The usual prac- 

 tice of abundant thermal insulation outside the source of heat 

 will reduce variations in the former but not in the latter. But 

 the effect that variations in either will produce upon the tempera- 

 ture of the region to be controlled can be materially lessened by 

 the introduction of an insulating layer between the region and the 

 source; since the mere separation of the two will reduce the al- 



d (dT\ 

 ready small dT/dN and also its rate of change -7 ( -ttt ) at the 



surface of the former, while the reduction in k will still further 

 lessen dQ/dt and d 2 Q/dt 2 . Whatever variations continue to exist 

 near the region can be still further reduced by applying a small, 

 properly regulated supply of heat around the surface, but best 

 separated from it by an insulating layer for the reasons just 

 given. 



Neglect of certain of the conditions discussed above is quite 

 justifiable where simplicity of construction and operation is more 

 essential than refinement of temperature control. However, 

 proper design of the temperature bath and its accessories can 

 go a long way towards realizing the ideal conditions without 

 introducing troublesome complications. 



Attention is first directed to a simple device in which the principles 

 just enunciated have been successfully employed to reduce the long- 



