18 Archdeacon Pratt on Local Attraction in Geodesy, ^c, [Nov. 26, 



III. "On the degree of uncertainty which Local Attraction, if not 

 allowed for, occasions in the Map of a Country, and in the mean 

 figure of the Earth as determined by Geodesy : a method of ob- 

 taining the mean figure free from ambiguity, from a comparison 

 of the Anglo-Gallic, Russian, and Indian Arcs : and speculations 

 on the Constitution of the EartVs Crust/' By the Venerable 

 J. H. Pratt, Archdeacon of Calcutta. Communicated by Pro- 

 fessor Stokes, Sec. R.S. Received Oct. 5, 1863. 



(Abstract.) 



After referring to a former paper in which he had shown that, in the 

 Great Indian Arc of meridian, deflections of the plumb-line amounting to 

 as much as 20" or 30" would be produced if there were no sources of com- 

 pensation in variations of density beneath the surface of the earth, and 

 after alluding to a remarkable local deflection which M. Otto Struve had dis- 

 covered in the neighbourhood of Moscow, the author proceeds to consider, 

 in the first instance, the effect of local attraction in mapping a country 

 according to the method followed by geodesists, in which differences of 

 latitude and longitude are determined by means of the measured lengths of 

 arcs, by substituting these lengths and the observed middle latitudes in the 

 known trigonometrical formulae, using the mean figure of the earth, although 

 the actual level surface may differ from that belonging to the mean figure 

 in consequence of local attraction. He concludes that no sensible error is 

 thus introduced, either in latitude or longitude, if the arc do not exceed 

 12^° of latitude or 15° of longitude in extent, but that the position of the 

 map thus formed on the terrestrial spheroid will be uncertain to the ex- 

 tent of the deflection due to local attraction at the station used for fixing 

 that position. In the Great Indian Arc this displacement might amount to 

 half a mile if the deflections were as great as those calculated from the 

 attraction of the mountains and the defect of attraction of the ocean, irre- 

 spective of subjacent variations of density ; but the author shows in the 

 next two sections that some cause of compensation exists which would rarely 

 allow the actual uncertainty to be of any considerable amount, unless the 

 station used for fixing the map were obviously situated in a most disadvan- 

 tageous position. 



The author then proceeds to examine the effect of local attraction on the 

 mean figure of the earth, considering more particularly the eight arcs which 

 have been employed for the purpose in the volume of the British Ordnance 

 Survey. He supposes the reference station of each arc to be affected to 

 an unknown extent by local attraction, and obtains formulae giving the 

 elements of the mean figure obtained by combining the eight arcs, these 

 formulae involving eight unknown constants expressing the deviations due 

 to local attraction at each of the selected stations. By substituting reason- 

 able values for the unknown deflections, he shows that local attraction s 

 competent to affect the deduced mean figure to a very sensible extent. 



