INTERCHANGE OF HEAT VON BEZOLD 407 



Assume that we have at different depths perfectly similar accu- 

 rate thermometers, whose scale degrees have exactly the same 

 length, and that these are placed horizontally, imbedded in the 

 ground so that all the zero points lie vertically one above the other, 

 then the curVe connecting the ends of all the mercurial columns 

 is the tautochrone for any given moment of time. See fig. 57. 



Since the phase of the oscillations going on daily and annually 

 in each layer changes from one stratum to the next, therefore the 

 curves A t B 1 and A 2 B 2 intersect each other at special depths and 

 generally speaking an infinite number of times; but since these 

 curves steadily approach each other as the depth increases and 

 almost coincide at very moderate depths, therefore we shall not 

 often need to consider more than two such intersections. 



Of course, in the computation of the 

 total heat received and expended, the 

 areas on each side of such intersecting 

 points must be given opposite signs, as 

 is shown by the signs inscribed in fig. 



57- 



But the consideration of these curves 

 becomes especially valuable in that 

 they allow us to recognize at once when 

 the quantity of heat contained in the 



ground below any given horizontal plane attains a maximum or 

 minimum. 



Of course this is only the case when no heat passes through the 

 plane in question neither in one direction nor the other, i. e., when 

 the temperature gradient in this plane is zero or 



<*? = (, 



dh 



Therefore at this place the tangent to the curve representing the 

 temperature is a vertical line. 



If, therefore, we know only the daily mean temperatures for 

 the upper layers of the earth we can then directly find the two days 

 of the year on which the heat contained in the ground attains a 

 maximum or a minimum by seeking for those days on which the 

 above-mentioned condition is fulfilled, i.e., when the temperature 

 curve is perpendicular to the earth's surface. 



If then we also know for these days the distribution of tempera- 

 ture in the strata below, then the area between the tautochrones 



