352 Captain A. R. Clarke on the Course of 



the silicates and the compounds of the mineral kingdom gene- 

 rally, in a manner similar to that by which we have sought to 

 discover in organic compounds the proximate constituents and 

 their functions (that is, by a careful study of their decomposi- 

 tions, substitutions, and syntheses), then we may certainly expect 

 soon to gather results as splendid as those which organic che- 

 mistry has so lavishly presented to us. 



The future province of the mineralogical chemist is, therefore, 

 not simply to analyze minerals and to determine their empirical 

 composition, and then from this empirical composition empiri- 

 cally to construct rational formulae, but to create new methods 

 of investigation, and from their results to deduce arguments to 

 elucidate the chemical constitution of such minerals. 



HI. On the Course of Geodesic Lines on the Earth's Surface. 

 By Captain A. R. Clarke, RE., F.R.S* 



THE geodesic line has always held a more important place 

 in the science of geodesy among the mathematicians of 

 France, Germany, and Russia than has been assigned to it in 

 the operations of the English and Indian triangulations. Here, 

 indeed, it has been completely set aside, partly because the long- 

 arcs measured are in the direction of the meridian (itself a geo- 

 desic line), and partly because the angles of a geodesic triangle 

 cannot be actually observed. If we consider three points on a 

 spheroid and suppose them joined by geodesic lines, then the 

 angles of this triangle will differ slightly from the angles which 

 would be measured by a theodolite ; in other words, the angle 

 in which geodesies proceeding from A and B intersect in C dif- 

 fers from the angle contained by the two planes which, contain- 

 ing the normal at C, pass through A and B. But the difference 

 of length between the plane curve distances C A, C B and the 

 corresponding geodesic distances, we can show to be immeasu- 

 rably small for any such distance as two or three degrees. It 

 may also be proved that the calculation of spheroidal triangles 

 as spherical is only correct when the observed angles have been 

 reduced to the geodesic angles. Still the difference is so very 

 small for such triangles as are formed by mutually visible points 

 on the earth's surface that it has been generally disregarded. 

 But it would be somewhat hasty in the advancing state of science 

 to conclude that geodesic lines have no necessary place in geo- 

 desy. Both the extreme precision now attained in the mea- 

 sures of base lines and angles, and the vast extents of country 

 over which triangulations are being carried, make the considera- 

 tion of even the smallest refinements not superfluous. If pro- 

 * Communicated by the Author. 



