of Latitudes for Locct I Attraction . 317 



ing influence of neighbouring surface-inequalities upon the 

 direction of the plumb-line. We do not share this opinion 

 with him : nay, we consider such correction for this purpose 

 not even justifiable. 



In order to present these differences of opinion in a clearer 

 light, we must examine more closely the nature of the chief 

 problem of geodesy — namely, the determination of the figure 

 of the earth, and the effects of local attraction. At my in- 

 stance Herr Dollen has undertaken this introductory presenta- 

 tion of the argument ; and I think it best to give his own 

 words, as his statements contain many thoughts which may 

 be new to even experienced geodesists, and which certainly 

 deserve consideration. At the conclusion of his exposition I 

 will add a few remarks on my own account, in order to con- 

 firm what he has said. 



Herr Dollen says : — " Let us for the present set aside the 

 question of the linear dimensions of the earth ; then the 

 problem before us, of determining the figure of the earth, in 

 the sense in which alone it is regarded in all researches of the 

 higher geodesy, will be none other than this : To determine 



THE RELATION" OF THE DIRECTION OF GRAVITY TO THE LOCALITY 



at any place upon the surface of the earth ; or, in other words, 

 to determine the law according to which the direction 



OF GRAVITY VARIES WITH CHANGE OF POSITION ON THE SURFACE 

 OF THE EARTH. 



" It is essential to grasp this definition in its full significance, 

 and especially to make clear to one's self, and to keep constantly 

 before one's mind, what is the difference between the figure of 

 the earth as we shall hereafter speak of it, and the figure of 

 the earth as known in common parlance ; remembering always 

 that even in this common usage notice is not taken of those 

 slight unevennesses (inappreciable as compared with the mass 

 of the whole earth) which we call mountains and valleys. In 

 order to grasp this difference fully, let us confine ourselves to 

 the simplest conception, representing the earth as a perfect 

 sphere, for instance, of a homogeneous but rigid mass ; our 

 arc-measurements would in that case present us with a sphere, 

 as the figure of this earth, only if there were no rotation about 

 an axis. Should this rotation exist, the figure of this earth, 

 still actually spherical, would, according to the teaching of 

 geodesy, be that of a spheroid or ellipsoid of revolution, with 

 shortened axis. Alteration of the rate of the earth's rotation 

 would alter only the proportion of the axes of this spheroid ; 

 any alteration, however, in the assumed uniformity or homo- 

 geneity of the mass in the interior of the earth might change 

 the geodetic figure of the earth in endless ways, the exterior 



