48 Wm. A. Norton on the Variations 



the earth would have attained to a " movable equilibrium' 5 of 

 temperature. Pouillet has calculated that this would be the case 

 at the temperature of - 89° C. Taking the fundamental princi- 

 ple that one layer gains what the next below it loses, we can de- 

 rive a very simple formula, connecting the loss of heat at the 

 surface of the earth in a given time with the losses of tempera- 

 ture of the different layers during the same interval of time. 

 Let L = absolute loss of heat at the earth's surface, in a given 

 time, by nocturnal radiation; /, /', /", &c, denote the losses of 

 temperature of the first, second, third, &c. layers in the same 

 time ; a t a', a", &c, the quantity of heat received by the suc- 

 cessive layers from the layer next below. Then L = l + a, 

 a — l'+a'i a' = Z"-j-a", &c, and hence 



L^Z+^ + ^ + ^+fcc (4.) 



The losses of temperature, /, /', Z", &c, of the different layers 

 decrease with the depth, and for a night of twelve hours become 

 zero at the depth of about eighteen inches. After sunrise, when 

 the temperature at the surface is rising, the losses of temperature 

 will still continue with the layers below the surface until the heat 

 propagated downward reaches them in succession, and the cool- 

 ing will gradually extend below 18 in., but these variations of 

 temperature are not attended with any absolute loss of heat. It 

 appears from observation that the law of decrease of the annual 

 variations of temperature at different depths is that of a geometrical 

 progression for depths which increase in an arithmetical progres- 

 sion. The same law probably holds good for the entire diurnal 

 variations. The losses during the night simply probably decrease 

 more rapidly, for, while the entire fall of temperature at and near 

 the surface is about the same as for the night, lower down it is 

 greater, and for a number of inches below 18 in. takes place dur- 

 ing the day. 



It is to be observed that formula (4) is equally applicable if we 

 suppose L to represent the absolute loss of heat from the com- 

 bined action of all the causes which affect the temperature of the 

 surface. The same relation also obtains between the gain of 

 heat during the day and the increments of temperature at differ- 

 ent depths. 



Since the loss of heat, L, by nocturnal radiation from the 

 earth's surface is the same at all temperatures, for any given in- 

 terval of time, it follows that whatever may be the variations of 

 /, /', Z", &c. during the night, the actual loss of heat from the 

 whole stratum which undergoes a daily variation of temperature, 

 occasioned by nocturnal radiation, is uniform at all temperatures. 

 Accordingly any variations of I that may arise from the flow of 

 heat towards the surface cannot be the cause of the observed 

 variations of the horizontal magnetic intensity during the night. 



