18 Prof. J. Thomson on the true and extended 



were solid previously to their elevatory movements; and that 

 they also possessed lines of structure is more than probable, 

 since the fragments contained in the granite veins, in the el- 

 vans, and in the two systems of mineral veins, exhibit the 

 same concretional forms as those into which the corresponding 

 rocks are now divided by weathering or mechanical action. 



Thus I have endeavoured to substantiate my former state- 

 ment, that the elevatory force could not have acted on a solid 

 mass without the interference of lines of structure ; a circum- 

 stance which would produce, according to Mr. Hopkins, such 

 considerable modifications in the resulting phsenomena, that 

 "to a mass thus constituted these [his physical] investigations 

 must not be considered as generally applicable." 



When I commenced this reply, it was my intention to have 

 offered a few remarks on Mr. Hopkins's lengthened comments 

 on the hypothesis which I have advocated concerning the 

 origin of mineral veins in primary districts; but as it is im- 

 material, in the present case, whether the veins, granite, and 

 slate are or are not all contemporaneous, I think it best not 

 to have our attention diverted from the point at issue, which 

 must be determined by facts, and not by the gratuitous postu- 

 lata of either hypothesis. 



I cannot, however, conclude without again acknowledg- 

 ing the great obligation geologists are under to Mr. Hopkins 

 for his interesting investigations; and, though differing from 

 him on some points, I am not insensible to the great advantages 

 which must accrue to geology in controlling wild specula- 

 tions by the application of the rigid laws of physical science. 



Penzance, Nov. 8, 1836. 



V. On the true and extended Interpretation of Formultje in 

 Spherical Trigonometry, By James Thomson, LL.D.^ 



Professor of Mathematics in the University of Glasgow.* 



l.Xl^HILE the rules and theorems given in the modern 

 ^^ books on trigonometry, in reference to spherical tri- 

 angles, are sufficient for all practical purposes, yet there are 

 some peculiarities and some curious relations of such triangles, 

 which have either been overlooked in all the works with which 

 I am acquainted, or have been merely glanced at in casual or 

 passing remarks ; and hence, as may be expected, some parts 

 of the theory are still imperfectly developed. I shall proceedf 



* Communicated by the Author. 



t The formula; quoted in this paper will be found in my Elements of 

 Plane and Spherical Trigonometry, and in most of the modern treatises on 



the Subject. 



