270 



Archdeacon Pratt on the effect of 



"When these are substituted in the semiaxes, they give 



= 20928 190 - 2161 = 20926029, = 20927234 - 766 = 20926468, 



Cg = 20926529 - 457 = 20926072, 

 *i = 20847200+8064 = 20855264, = 20861620-6288 = 20855332, 



^3=20855535- 183 = 20855352. 



These three results are remarkably near each other ; they differ from 

 their average, 20926189 and 20855316, in no case by so much as 300 feet, 

 and in most cases by much less. I think, then, that we may safely infer 

 that this average ellipse is in fact the mean figure of the earth. This being 

 the case, T^ Tg, T3 are the same as t^, t^, t^ ; and therefore tlie deflections 

 of the plumb-line in the meridian at the standard stations of the Anglo- 

 Gallic, Russian, and Indian arcs are l"-37, 2"-22, 0"-033, all in the south- 

 ern direction*. 



14. The values, then, which I would assign to the semiaxes and ellipti- 

 city of the Mean Figure of the Earth are as follows : — 



a=20926180, 5=20855316 feet, e= !— . 



295-3 



If these are substituted in the formulae (1) of paragraph (6), we have 

 U=--0'3581 and V=0-8819. 



§ 4. Speculations regarding the constitution of the Earth^s Crust, 



15. If the reasoning in the last section, which has led to so satisfactory 

 a result, be correct, I think we may draw some useful inferences regarding 

 the constitution of the earth's crust. 



By substituting the values of U, V, t^, t^, t^ in the formulae similar to 

 m+aU+/3V+^ for the fifty-five stations of the eight arcs, which will be 

 found at p. 766 of the Ordnance Survey Volume, every one of the results 

 will be small. These results are the corrections of the latitudes of the 

 stations in referring them to the mean ellipse ; that is, they are the deflec- 

 tions of the plumb-line in the meridian at those stations owing to local 

 attraction, or the attraction arising from the departure of the actual figure 

 of the earth from the mean figure. 



Fifteen of these formulae I here select, adding one new one for Dehra 

 about 56 miles to the north of Kaliana, the northern extremity of the 

 Indian arc. They are as follows : — 



* The numerical calculations in paragraphs 7 to 13 inclusive have been tested at the 

 Government Trigonometrical Survey OflSce in Calcutta. 



