EFFECT OF LAST ICE AGE 715 



Trap, density 2.90 Conductivity 0031 



2 . 82 . 0036 



Amygdaloid 2.67 .0035 



2.71 .0034 



Conglomerate 2 . 55 . 0047 



2.64 ■ .0052 



The dilfusivity is tlie conductivity divided hy the density X the spe- 

 cific heat capacity per unit weight. This hitter is not far from .2, Init 

 has not been determined. With due regard to the fact tliat the forma- 

 tion is mainly trap and but very little amygdaloid, and still less con- 

 glomerate, I have taken .006 as a fair value for the diffusivity in c. r/. s. 

 units = 203 in terms of feet and years. 



This value is much that Avhich Lord Kelvin found for damp Calton 

 Hill trap, and .0064 in c. g. s. units is quoted as an average for certain 

 crustal rocks by Ingersoll and Zobel. It is only about half the value, 

 400, so' often used. It is clear that it would Ira wrong to assume an in- 

 flection of the curve at 4,000 feet, so tliat there must have been a marked 

 amelioration of the climate since 19,600 years ago. On tlie other hand, 

 if the heat wave had only gone 2,000 feet, the change Avould have started 

 only 5,000 years ago. It has plainly gone farther. It looks as thougli 

 there had been an era of milder climate betAveen the present and the Ice 

 Age, with a mean annual temperature perhaps as much as GO degrees 

 Fahrenheit. 



Mathematical Discussion 



For shallow depths relative to the curvature of the eartli tlie latter 

 may be neglected, and the case may be considered one of the flow of heat 

 in an infinite body with the temperature at different depths at the begin- 

 ning given, and also the variation of temperature from time to time at 

 the surface. This problem has been treated by many authors beside 

 myself.^* 



Among those more readily accessible than my old text-book, Eie- 

 mann's "Differential gleichungen," the works of W. E. Byerly^-^ and 

 Ingersoll and Zobel,^^ the article by Byerly in Merriman's Course in 

 Higher Mathematics may be mentioned, as well as an article by Dr. T. 

 Tamura in the Monthly Weather Review for July, 1903. 



It is the case stated in problem 3, on page 88 of Byerh's work, easily 

 solved by combining the solutions of sections 50 and 51. 



"In vol. vi, the aunual report for lOOo, and i)u))lic-ation of Ihe now series of tlie 

 publications of the Geological Survey of Michigan. Lansing, Michigan. 



'^^ "Fourier's series and spherical harmonics," articles 49-54. Ginn. 



^** An introduction to the mathematical theory of lieat conduction with engiueeriny 

 and geological applications, Ginn, 191.3. 



