July 25, 1913] 



SCIENCE 



131 



of electricity for the generation of heat has 

 come the need for greater accuracy in cal- 

 culating the rate of heat flow through insula- 

 tion, the temperature distribution in bodies 

 after aiiy time interval, etc. In 1811 Fourier 

 developed the mathematical theory of the con- 

 duction of heat, but until lately the practical 

 applications have been few. The " Mathe- 

 matical Theory of Heat Conduction," by L. E. 

 Ingersoll and O. J. Zobel, although primarily 

 a text-book, is a step towards making Fourier's 

 methods available to the engineer. 



After a historical sketch in the first chapter, 

 the authors derive the Fourier conduction 

 equation from the fundamental laws of the 

 flow of heat. This equation is solved first, 

 for bodies in which the temperature distribu- 

 tion has become steady. These bodies are the 

 thin plate, the long thin rod, the infinitely 

 long thin rectangular plate, etc. The general 

 cases in which the temperature is not steady 

 are then attacked. Equations are developed, 

 giving the temperature as a function of the 

 variables time and distance, the temperature 

 distribution at zero time being known. These 

 general solutions require Fourier's series and 

 integrals, which are developed, and extended 

 to the limits + oo and — oo . Solutions are 

 given for such specific shapes as the infinite 

 solid, the semi-infinite solid, the slab, the thin 

 rod, the sphere, etc. Also solutions are given 

 for the cases where there is either an instanta- 

 neous or a permanent source of heat in the in- 

 terior of the body. ISTo attempt is made to 

 prove that any of the solutions are unique, as 

 this rightfully belongs to larger treatises. 



Throughout the work the authors give many 

 numerical applications, such as calculating the 

 flow of heat through furnace walls ; the rate of 

 cooling of a setting concrete wall in cold 

 weather; the heating effect of thermit weld- 

 ing; the rate of cooling of steel in tempering; 

 the rate of cooling of the earth, taking into 

 account the effect of radioactivity; the rate at 

 which heat penetrates a fire-proof wall, etc. 



In deriving the fundamental equations the 

 authors assume, in common with previous 

 writers, that thermal resistivity does not vary 



with temperature. The error due to this as- 

 sumption is usually unimportant for metals, 

 but the so-called insulating materials often 

 show large temperature coefiicients. It is 

 necessary to consider this in many cases if 

 we are to secure accurate resiilts. In dealing 

 with problems involving heat losses from a 

 surface exposed to the air, the authors follow 

 the custom of assuming the rate of energy loss 

 to be proportional to the temperature of the 

 surface. It is well know that this is not true, 

 and there is sufiicient data available in the lit- 

 erature to allow a much closer approximation 

 than can be secured with the above assump- 

 tions. 



One of the most important applications of 

 the theory of heat conduction is to problems 

 in which there are permanent sources of heat, 

 as in dealing with electric furnaces. The 

 authors solve a few problems of this kind, but 

 they do not give them nearly enough atten- 

 tion. 



Considerably more values of thermal con- 

 ductivity constants have been published than 

 are given in the appendix. The statement 

 that " in the constants for poorer conductors 

 the disagreement between diiierent observers 

 is frequently 50 per cent, or more " is correct. 

 But there need be no such disagreement if 

 the conditions of the measurements are given. 



The book is quite the most satisfactory yet 

 published, as a text for the study of heat con- 

 duction, and it should be widely used in engi- 

 neering schools. As a reference book for the 

 practising engineer it leaves much to be de- 

 sired, although the material included in it is 

 made more easily available than heretofore. It 

 is a long step towards the development of an 

 engineering knowledge of the transmission of 

 heat. 



C. P. Eandolph 



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