Form of Temperature Wave spreading by Conduction. 361 



actually spreads from a spark in an inflammable mixture. In 

 a full treatment of the problem, the effect of the pressure- 

 wave emanating from the spark, and the effects of convection, 

 radiation, conduction through the electrodes, and variable 

 conductivity of the medium must be taken into account. 

 Above all, the fact that during the process of ignition 

 chemical combination is proceeding causes the temperature 

 wave to be more elevated than it would be as a result of a 

 purely physical transmission of heat. The general effect of 

 the heat added to the system by chemical action would be 

 to intensify those differences that are shown to arise from 

 purely physical causes between one type of source of heat 

 and another. A temperature wave-form in which a con- 

 siderable volume of gas is raised by conduction of heat to 

 the temperature required for active combination to take 

 place, would be accompanied by a greater supply of "chemical 

 heat" than one in which the region of high temperature is 

 more restricted ; the chemical heat would therefore more 

 greatly enhance the effect of the source in the former than 

 in the latter instance. 



Our immediate purpose being to inquire what influence, 

 if any, the manner of supply of heat to the medium has upon 

 the wave-form, we will suppose that the total quantity of 

 heat (Q) supplied is constant. This quantity we will assume 

 to be supplied 10 the medium either at a point or throughout 

 a space symmetrically surrounding a point which is taken 

 as origin. Under these circumstances the temperature, 6, at 

 any point in the. medium at a distance, ?■, from the origin, 

 and at a time, t, after heating begins, can be deduced from 

 the well-known equation : 



, 2 d 2 , O7 d0 dO 



which expresses the fact that the excess of heat flowing into 

 any elementary concentric spherical shell through the inner 

 surface, over the heat flowing out to regions beyond, is equal 

 to the heat stored during the same time in the element. 

 The coefficient, k, is the thermometric conductivity of the 

 medium — that is to say, its thermal conductivity divided by 

 its thermal capacity, c, per unit volume. 



We will consider the supply of a constant quantity of 

 heat, Q, under four different conditions : 



(1) Instantaneously at the origin. 



(2) At the origin at a uniform rate during the time T. 



(3) Instantaneously over a spherical surface of radius a. 



(4) Instantaneously throughout a spherical volume of 



radius a. 



