814 Royal Society : — 



portion of the earth's crust, or that between one sedimentary portion 

 and another, has not hitherto been taken into account*. The author 

 has investigated the problem assuming the crust of the globe to consist 

 of any number of strata of different conductive powers and bounded 

 by parallel surfaces, the problem being much simplified by consider- 

 ing their surfaces as plane instead of spherical. Then, assuming the 

 temperature of the crust of the globe to be due entirely to the trans- 

 ference of heat from its central portions to its surface, it is shown 

 that the increase of temperature in descending vertically through 

 any two strata, ought to be in the inverse ratio of the conductive 

 powers of those strata, whether the two strata belong to the same 

 group of stratified beds, or to two different groups in different local- 

 ities. Such at least must be the result unless we introduce very 

 arbitrary and, as the author conceives, entirely inadmissible hypo- 

 theses into the problem. 



For the purpose of testing this theory in its application to our 

 own globe, four or five cases of Artesian wells and vertical shafts are 

 especially referred to, in which the temperature has been carefully 

 observed at greater depths than at any other places in Western 

 Europe, or probably in any other part of the globef. The cases 

 spoken of are the following : — 



(1) An Artesian well near Geneva. — Depth=225 metres ; increase 

 of depth for 1° (F.) = 55 feet. 



(2) An Artesian well at Mondorff in the Grand Duchy of Luxem- 

 bourg. — Depth=730 metres ; increase of depth for 1° (F.) = 57 feet. 



(3) An Artesian well at New-Saltzwerk in Westphalia. — Depth 

 = 644"5 metres; increase of depth for 1° (F.) = 54 feet. 



(4) The Puis de Grenelle at Paris.— Depth=546 metres ; increase 

 of depth for 1° (F.) = 60 feet. 



(5) A coal shaft at Duckenfield, near Manchester. — Depth=1400 

 feet ; increase of depth for 1° (F.)=G5 feet. 



(6) A coal shaft at Monkwearmouth. — Depth about 1700 or 1800 

 feet; increase of depth for 1° (F.) about = GO feet. 



The general rate of increase of temperature in our own deeper 

 coal-muies is that of about 1° (F.) for GO feet in depth; and the 

 same result has been obtained for many parts of the chalk in North- 

 ern France. 



These cases present a remarkable approximation to uniformity, 

 whereas the conductive powers of the strata which have been pene- 

 trated are very different. Cases (4) and (j>) present the best means 

 of comparison. The Puis de Grenelle passes through nearly 500 

 metres of chalk, the conducting power of which is estimated by the 

 author at somewhat more than '25, while the mean conducting 

 power of the rocks through which the coal shaft at Duckenfield 

 passes, is estimated, by means of experiments performed on speci- 

 mens of these rocks, at rather more than '5. This is about twice as 



* Except in the case in which Poisson investigates the state of temperature of 

 a sphere surrounded by a single concentric spherical shell of different conductivity. 



t In a great majority of instances observations of this kind have not been 

 made with sufficient care to be relied on. 



