232 SEE— TEMPERATURE, SECULAR COOLING [April 20, 



the exact path of the temperature curve where it passes through the 

 layers just beneath the crust. The only condition one can be sure 

 of is that it shall be everywhere continuous and have no change of 

 flexure. It is outwardly concave near the surface, and it must re- 

 main so till we reach the arch of the ellipse. In the diagram for 

 the earth's temperature we have drawn this curve according to what 

 seemed to be its most probable course. 



It is interesting to observe what the efifect of this change of tem- 

 perature near the surface is on the analysis of Lord Kelvin. We 

 have 



dx \/irKt 



e 4k<. 



And it appears that if the temperature increases more rapidly as we 

 go downward, V would be larger for given depth, and the gradient 

 near the surface would be steeper. The same efifect could be pro- 

 duced by shortening the time t without changing, the value of V . 

 We have adopted this course as the most probable in the treatment 

 of the question given above. 

 Also since 



(@ - @^);/^ 



ZEl ' 



2 I e~- dz 



V would be changed by changing the limits of the integral, or by 

 modifying the value of 0. But the integral depends only on x and t, 

 and when these do not change appreciably it is most natural to depart 

 from Fourier's solution by change of 0. 



IV. On the Theory of Earthquakes Held by the Ancients. 

 § 17. On the Inaccessibility of the Views of the Greeks. 



Since Science is the outgrowth of successive revolutions of 

 thought in the course of centuries, it is unfortunate that the views 

 of the Greeks and Romans on many questions are not always accessi- 

 ble to modern readers. It is chiefly by a survey of human thought 

 over long periods that one is enabled to form a clear conception of 

 what has been done in a given subject. Too few students of science 



