AND THE OTHER PLANETS OF THE SOLAR SYSTEM. 633 



sufficiently rare near the outer surface, the number of particles of the shell with which 

 the thermometer will be in contact when placed there, will be smaller than at lower 

 points within the shell, and consequently, their maximum effect in depressing the ther- 

 mometer may be at some point within the shell, and not at its outer boundary. But 

 whatever may be the point at which the instrument may indicate its lowest temperature, 

 it will rise continually as it proceeds from that point till it reaches the interior surface 

 of the shell, or external surface of the nucleus. 



6. It has been already remarked that the excess of x, above t 2) and also that of r t 

 above t must be such as to admit of the transmission of a certain quantity of heat from 

 the inner to the outer surface of the shell in a given time, that heat being derived from 

 the center of the shell in the hypothetical case of Art. 4, and by radiation from the 

 external envelope and through the shell, in the present case. The difference, then, 

 between t x and t will depend in the present case on the following circumstances: 



(1) The quantity of heat (//j) which radiates from the external envelope, and 

 for which the shell {A) is perfectly diathermanous, and which is entirely absorbed and 

 given out again by the internal nucleus. 



(2) The conductivity of the matter of the shell, through which the heat given 

 out by the nucleus is here supposed to pass entirely by conduction. 



(3) The emissive power of the outer surface of the shell. 



(4) The thickness of the shell. 



The fourth condition is manifestly independent of the three preceding ones, and it 

 follows that if the thickness of the shell be sufficiently great, the excess of t, above t 

 may be increased to any amount, and may thus become greater than t v although this 

 latter temperature is derived directly from the radiant heat (H^ from which the heat 

 of the nucleus, or t 1( is derived. But this heat produces the temperature t x in the bulb 

 of a thermometer from which the heat radiates again freely into surrounding space, whereas 

 the temperature T, is produced by beat radiating on the nucleus, from which, instead of 

 again radiating freely, it can only pass away by the slower process of conduction, and conse- 

 quently accumulates till t x sufficiently exceeds t Q to enable the heat to pass as rapidly 

 through the shell by conduction as it first passes through it to the nucleus by radiation. 



7- The general analogy between the case now considered and that of a planet, as a 

 nucleus enveloped by its atmosphere, forming a spherical shell around it, is obvious; but 

 to make the analogy complete with the case of the Earth, or that of any planet sufficiently 

 near the Sun, we must consider the thermal condition of such planet independently of the 

 heat received from a particular focus like the Sun, leaving the influence of that luminary 

 for separate consideration. The heat received by the remoter planets from solar radiation 

 must be too small to render such separate consideration essential. For the greater 

 distinctness we may here limit ourselves to the case of the Earth, considering it independently 

 of solar radiation. 



81—2 



