632 Mr W. HOPKINS, ON THE EXTERNAL TEMPERATURE OF THE EARTH, 



Under these circumstances a thermometer placed beyond the sensible influence of the body 

 (A) would indicate a temperature t„, but would rise as it approached the outer surface of A, 

 in consequence of radiation from that surface, supposing t 2 sensibly greater than ^ . At that 

 surface the instrument would indicate the temperature t 2 ; and if t denote the temperature at 

 any point within the shell, t would be the temperature indicated at that point, and would 

 continually increase in approaching the lower surface of the shell, when it would become t { . 



5. Let us now proceed a step further in our hypothetical case. Instead of supposing the 

 interior of the shell (A) to be hollow, conceive it filled with homogeneous matter. Also 

 suppose the envelope to send forth heat uniformly of the kind H x as previously supposed 

 (Art. 3) in addition to the heat H , the heat H x having the property of permeating the matter 

 of the shell (A) by radiation, and consequently without communicating any heat to the con- 

 stituent particles of the shell. Suppose all the heat of this kind which falls upon, and thus 

 passes through the shell, to be absorbed by the interior nucleus of the shell. The quantity 

 thus absorbed by the nucleus in a given time, when the temperature has become steady 

 throughout the nucleus and shell, must necessarily pass out of it in the same time; and if we 

 assume the heat thus emitted from the nucleus to have lost its power of radiating back through 

 the shell, it will return through it by conduction; and since the heat H lt when incident from 

 without, passes through A without affecting in any degree the thermal state of its particles, it 

 will not affect the conduction of the heat (H,) back from B through the shell into the sur- 

 rounding space, and therefore t„ t 2 , and t may be considered precisely the same in this case 

 as in the case of the previous Article. 



But here it must be carefully remarked that r is the temperature of the constituent 

 particles of the body, at any proposed point, but not that which would be indicated by a 

 thermometer of which the bulb should be placed at that point. Let us again consider what 

 would be the indications of a thermometer in different positions. If placed beyond the 

 influence of A it would give the temperature t + t l , (derived from the radiating heat H and 

 H\) as that of the general surrounding space. The temperature (t 2 ) of the outer surface of 

 the shell (A) would be the same as in the previous case, and under ordinary conditions would 

 not much exceed t ; we may therefore suppose t + t } to exceed r 2 as much as we please. If 

 we suppose this excess to be considerable, the thermometer will be depressed below t + £, as 

 it approaches A by radiation from the surface of A, and this effect will increase till the 

 instrument reaches that surface, the indicated temperature being always intermediate to t 2 and 

 <„ + <!■ If the instrument be then placed within the shell {A) at a point where the temperature 

 of its constituent particles = t, the instrument will still be equally affected by the radiating 

 heat //, , and the temperature indicated will be between t x + t and r ; i.e. it will be higher 

 than at the exterior surface, and will manifestly continue to rise till the instrument reaches the 

 interior surface of the shell. » 



I have here supposed the^ensity of the shell uniform, in which case the greatest 

 depression of the thermometer would take place when it came in contact with the coldest 

 particles, i. e. at the external surface of the shell, as above represented. If, however, 

 the density of the shell decrease in ascending from the interior surface till it becomes 



