I860.] On Local Attraction. 35 



M. Otto Struve has lately called attention to similarly important 

 deflections caused by local attraction in Russia — and especially to a 

 remarkable difference of deflection at two stations near Moscow, only 

 about eighteen miles apart, which is attributed to an invisible 

 unknown cause in the strata below. 



It has become, therefore, an important inquiry : — What degree of 

 uncertainty does Local Attraction, if not allowed for, introduce into* 

 the two problems of geodesy, viz. (1) obtaining correct Maps of any 

 country, and (2) determining the Mean Figure of the Earth. 



These matters are discussed in the present Paper ; and I would 

 here observe, that the paper is complete in itself, and does not require 

 a study of the previous communications. 



2. With regard to the construction of Maps from Survey operations 

 I show, as before in India, that no map in any other part of the 

 world will be affected except in the way already stated, if the length 

 of every measured arc of latitude is not greater than twelve degrees, 

 and a half, and of every measured arc of longitude not greater than 

 fifteen. Now in point of fact, however long the great arcs (such as. 

 the Anglo- Gallic, the Russian, and the Indian) may be, they are. 

 always broken up into much smaller portions, so as to bring them, 

 very far within the above-mentioned limits. Hence the maps 

 constructed from geodetic operations will always be relatively correct, 

 in themselves ; but the precise position of the map. on the terrestrial 

 spheroid will be unknown by the amount of the unknown deflection 

 of the plumb-line in latitude and longitude at the place which fixes 

 the map. 



In India the effect of the Himalaya Mountains and the Ocean, 

 taken alone, would throw out the map by nearly half a mile. And, 

 as already stated, there is no way of discovering with certainty how 

 much this is increased or diminished by the effect of variations of 

 density in the crust. If, however, the calculations which I give in 

 the third section of this Paper are accepted, they show that the effect 

 of variations in the density of the crust below almost entirely 

 counteracts that of the mountains and ocean at Damargida in 

 latitude 18° 3' 15-', and the displacement of the map is almost 

 insensible if fixed by that station. If fixed by the observed latitude 

 of any other station, the map will be out of its place by the local 



