1864.] Archdeacon Pratt on Local Attraction in Geodesy ^ ^c. 253 



On the degree of uncertainty whicli 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 

 obtaining the Mean Figure free from ambiguity by a comparison 

 of the Anglo-Gallic, Russian, and Indian Arcs ; and Speculations 

 on the Constitution of the Earth^s Crust." By the Venerable J. H. 

 Pratt, Archdeacon of Calcutta. Communicated by Prof. G. G. 

 Stokes, Sec. U.S. Received October 5, 1863*. 



1. In former communications to the Royal Society I liave shown that Local 

 Attraction, owing to the amoimt it in some places attains, is a more trouble- 

 some element to deal with in geodetical operations than had generally been 

 supposed. The Mountains and the Ocean were shown to combine to make 

 the deviation of the plumb-line as much as 22"-71, 17"-23, 21"-05, 34"'16 

 (or quantities not differing materially from them) in the four principal sta- 

 tions of the Great Arc of India between Cape Comorin and the Himma- 

 layas— viz. at Punnoe (8° 9' 31"), Damargida (18° 3' 15'), Kalianpur 

 (24° 7' 11"), Kaliana (29° 30' 48") ; and how much these might be in- 

 creased or lessened by the effect of variations of density in the crust below 

 t was difficult to say. Deviations amounting to at least such quantities as 

 7"*61 and 7"*87 were shown to exist in the stations of the Indian Arc, 

 arising from this last cause (see Phil. Trans. 1861, p. 593 (4) and (5)). 



M. Otto Struve has lately called attention to similarly important de- 

 flections caused by local attraction in Russia — and especially to a remark- 

 able difference of deflection at two stations near Moscow, only about eighteen 

 miles apart, amounting to as much as 18", which is attributed to an invi- 

 sible unknown cause in the strata below (see Monthly Notices of the Royal 

 Astronomical Society, April 1862). 



2. It is 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 a country, and (2) determining 

 the Mean Figure of the Earth. I have pointed out the effect on mapping 

 in India, as far as determining the latitudes is concerned, in a former paper. 

 I propose now to consider the subject generally with reference to any 

 country, and taking into account the longitudes as well as the latitudes. 

 The effect upon the determination of the mean figure of the earth I discuss 

 at greater length. By a change, I venture to call it a correction, of Bessel's 

 method of applying the principle of least squares to the problem, I obtain 

 formulae for the semiaxes and ellipticity of the Mean Figure involving ex- 

 pressions for the unknown local deflections of the plumb-line at the standard- 

 or reference-stations of the several arcs made use of in the calculation. 

 These formulae at once show the great degree of uncertainty which an ig- 

 norance of the amount of local attraction must introduce into the determi- 



* Read November 26, 1863. See Abstract, vol. xiii. p. 18. 



