322 MM. iStruve and Dollen on the Correction 



such case allow ourselves to be satisfied with theories, the 

 opinion will perhaps no longer seem strange that even in such 

 cases as that of Sohehallien, and all the more in those of wide- 

 spread irregularities of uncertain constitution, the justification 

 of the said correction lias yet to be proved. No doubt about 

 it exists of course in the mind of him upon whom lies the obli- 

 gation of furnishing this proof. This is naturally the business 

 of the one who asserts that the utility of the observed latitudes 

 for the purpose of determining the figure of the earth is 

 damaged by neglecting these corrections. Oar wish, how- 

 ever, for as thorough an understanding as possible respecting 

 a subject so full of importance induces us to examine it more 

 closely, and to give our opinion as to the manner in which 

 the desired proof might be satisfactorily conducted. To this 

 end there seem to be three ways open to us : —First, there are 

 certainly cases in which the origin of the existing surface- 

 inequality can be declared with confidence, so far at least 

 that not a doubt need remain that it has any connexion what- 

 ever with the distribution of density in the proximate interior. 

 This presentment will receive confirmation by remembering 

 the constant changes produced by water on the form of the 

 earth's surface. The accumulations thus brought about by 

 transference from distant and often extensive areas, are exactly 

 analogous to the pyramid referred to above ; and with due 

 regard to the circumstances, corrections to the latitudes of 

 adjacent points may, in such cases, be deduced which, if these 

 latitudes are to be employed for determining the mean figure 

 of the earth, we may regard as fully justified. Secondly, we 

 may be convinced, in some particular case, of the practical ab- 

 sence of a compensating effect in the interior of the earth ; and 

 this may happen if we can prove the opposing or, more cor- 

 rectly the corresponding, disturbance of the latitude on the other 

 side of the disturbing mass, let us say, of the mountain : it is 

 to be remarked that this is always practicable, and presents no 

 very great, and certainly comparatively few difficulties. When 

 once the work has been performed which is necessary for de- 

 termining the form and mass of the mountain, all that remains 

 is the determination of a second latitude, and the trigono- 

 metric connexion of the two points of observation with each 

 other and with the mountain. Then, if this condition is 

 fulfilled — that the difference of the two observed latitudes is 

 greater than it should be according to the geodetic distance, 

 and that by just so much as the sum of the disturbing in- 

 fluences of the mountain upon the latitudes taken singly — it 

 may well be admitted that on the whole the observed latitudes 

 approach more closely through consideration of these influences 



