508 A. VaugJian — Problem of a Cooling Earth. 



formed, tliat is to say, if we suppose the heat to be uniformly con- 

 ducted through, the mass, and not to flow mainly along the separation 

 surfaces (as is the case in the flow of electricity through a solid 

 cylinder), we shall have the conditions which are assumed in the 

 equation employed for solution. 



Now let us imagine all the separate pieces of each shell rolled 

 together; the further any shell is from the centre the greater will 

 be the volume per unit area to be filled up, and, consequently, the 

 greater the amount of heat evolved by viscous friction. Hence the 

 difi"erence between the temperatures of two consecutive shells, at 

 any time, will be, in reality, less than that, had the first process 

 alone come into play. Thus it would really take longer to establish 

 any given temperature gradient ; which amounts to saying that the 

 time from consolidation would be increased. To make allowance for 

 this new factor we should require some data as to the heat evolved 

 by viscous friction in the rolling out of sheets of rock material. 



Time from Consolidation. 



Since physicists and geologists differ considerably in the number 

 of years which they would allow for the world's age, it is a matter 

 of great interest to see whether the numerical results arrived at by 

 physicists should not be considerably increased. 



I need scai'cely remark that, in what follows, I am in no way 

 concerned with the effect which any of the alterations suggested 

 below may have upon the position of the theoretical level of no- 

 strain ; for I have already expressed my belief that the main 

 elevations and depressions of the earth's surface have been caused 

 by differential contraction. 



In the determination of the time from first solidification, heat is 

 supposed lost solely by conduction from within outwards, and no 

 mechanical deformation or change of physical state is accounted for. 

 Now, as I have shown above, heat must be generated in that settling 

 together, which is considered to be the probable outcome of con- 

 traction, and this extra heat will, as I have shown, tend to increase 

 the time from consolidation. So far there is a correction to be 

 applied on account of the insufficiency of the equation employed to 

 express all that actually takes place, for this equation takes account 

 only of heat actually conducted from point to point, and does not 

 recognise any heat originated within the cooling mass. 



Again, the final result arrived at is, that the time varies as the 

 square of the temperature of solidification directly, and as the co- 

 efficient of thermometric conductivity inversely. The temperature 

 of solidification is assumed as 7000° F., and the coefficient of con- 

 ductivity as 400. Both these quantities are supposed constant 

 throughout the mass considered, and hence must be taken to have 

 their average values throughout that mass. 



But when the Earth was molten, the pressure at any point within 

 a few hundred miles of the surface, was practically that due to 

 the weight of the overlying mass ; hence it follows that the molten 



