AND WATER ON THE EARTH. 321 



perature gradient at i° C. per 33 m. the temperature under the land 



at the same level as the sea bottom would be 16° 4- — — = 140°. 



33 

 Trabert^ carried Faye's idea a step farther. He assumes a land 



surface temperature of 10° C, a temperature gradient of 3° per 

 100 meters, and a mean ocean depth of 4300 meters, with a bottom 

 temperature of 0° ; and thus gets a difference of 140°. He then 

 calculates what would be the difference of average temperature of 

 two cones, extending to the earth's center, one under the land and 

 one under the sea, sufificient to account for a difference in length of 

 5000 meters, which he gets roughly by adding the mean height of 

 the land to the mean depth of the ocean. He finds the relation 

 oi^r^ 5000 m., where a = .00001 is the coefficient of expansion of 

 the rock, R the radius of the earth, and T the average dift'erence of 

 temperature of the two cones. This gives ^^78°, which, in view 

 of the difference of temperature of the sea bottom and the same 

 level under the land, he considers a very reasonable figure ; and 

 therefore thinks the ocean basins are entirely due to low tempera- 

 ture of the underlying rock. 



But it is quite impossible for the two cones to differ by anything 

 like 78° in mean temperature. Both Faye and Trabert were m.isled 

 by comparing the temperatures at the sea bottom level. This dif- 

 ference has no bearing whatever on the difference in the mean tem- 

 peratures of the two cones. To illustrate : Suppose we have two 

 cones of exactly the same size, and with a similar distribution of 

 temperature ; for simplicity, suppose the temperature is diminishing 

 continuously from the apex to the base. Now let one of these cones 

 expand uniformly, each of its elements keeping its temperature. 

 Its mean temperature will not have changed at all ; it will still be the 

 same as that of the other cone ; but at the same distance from the 

 apex it will have a higher temperature than the other cone. It is 

 easy to imagine a distribution of temperature which would yield a 

 great difference between the two cones at the level of the base of the 

 unchanged one ; though the mean temperatures of the two cones 



9 " Eine mogliche Ursache der Vertiefung der Meere," Sit:;. Kais. Ak. 

 Wiss. Wien, Math. Nat. Kl, 191 1, Bd. 120, Abt. 2 A, 175-180. 



