April 23, I860.] SPOTTISWOODE ON TYPICAL MOUNTAIN RANGES. 99 



'* In this way the calculus of probabilities, though one of the 

 most abstract and refined branches of mathematics, and in itself in- 

 capable of interpreting any natural phenomena, may still serve as 

 a check and a guide to the physical philosopher, by pointing out 

 where he may and where he may not employ his study of causes, 

 with reasonable hope of a successful result." 



The Chairman, in returning the thanks of the Society to Mr. Spottiswoode 

 for his communication, said this subject of the direction of mountain chains 

 had for a considerable period given rise to discussions among geologists, and 

 had formed a subject to which M. Elie de Beaumont in France had given his 

 most mature consideration. 



General J. E. Portlock, r.e., f.r.g.s., said he would only oifer a few words 

 on a subject so complicated to point out the value of such researches. Every- 

 body is now aware that the earth is not in the condition in which it proceeded 

 from the hands of the Creator. The mountains were not originally in the 

 position or under the circumstances in which we now saw them, but they have 

 been lifted up to their present position. It naturally occurs to us to inquire 

 how this work had been performed ? Was there a regular progression in it, 

 was it done all at once, or was it done in successive epochs ? This is a point 

 which has engaged the attention of geologists for many years past. M. Elie de 

 Beaumont has particularly made it the object of his inquiries, and has esta- 

 blished that there were at least twelve successive epochs of disturbances, or of 

 elevation, each of which produced some evidence of the direction of its action 

 on the surface of the earth. Now, an inquiry, such as Mr. Spottiswoode has 

 entered upon, will, by the aid of high mathematical analysis, lead us to this 

 kind of conclusion. We are looking at a range of mountains ; we examine not 

 merely their present direction, but their magnitude and weight. We consider, 

 therefore, each range in its length, its height, and consequently its magnitude 

 and weight, and by the calculus of probability we arrive at the conclusion that 

 such particular line exhibits the direction in which the greatest amount of force 

 had been applied ; and that is assumed as the typical direction, or the direction 

 in which nature had applied an elevatory force in the greatest and most general 

 way. Of course, there will be diverging lines : on one side diverging in the one 

 direction, and on the other diverging in the opposite ; but these balance each 

 other, and we arrive at a typical direction, which is not merely the mean as 

 referred to direction alone, as was the case in the investigations referred to by 

 Mr. Spottiswoode, but a result in which the weight of each part is taken into 

 consideration as a necessary element in determining the direction and magnitude 

 of the force which had been applied to the elevation of the chain. This, of 

 course, is a most valuable elementary result as a guide to the physical inquirer 

 in his researches, when endeavouring to bring positive facts under the domain 

 of some definite law, and on this ground General Portlock looks upon every 

 application of mathematical science to natural questions to be of the very 

 utmost importance. 



The Chairman, before adjourning the meeting, called attention to a series of 

 beautiful illustrations of Texas and Mexico, which had been exhibited to the 

 Society by the Abbe Domenech, who was about to publish in this country a 

 work on that region, Avhich would soon appear. The Abbe Domenech had 

 spent six years in those countries, and he (the Chairman) was persuaded, from 

 what he had heard from his contemporaries in France, and particularly from, 

 missionaries, that no person could be more thoroughly relied upon or more 

 completely enabled to delineate the features of the tract he had explored. 



