Notices respecting New Books. 1 15 



We will now proceed to offer some observations on each of these 

 discussions, and will begin with the second of them. It is scarcely 

 necessary to mention that the mean surface of the earth is nearly or 

 exactly that of an oblate spheroid, whose minor axis coincides with 

 that of the earth's revolution ; that its equatorial radius cannot 

 differ much from 20,925,000 feet; and that its ellipticity, or the 

 ratio which the excess of the equatorial radius over the polar radius 

 bears to the former is about 1 : 300. If it be asked what is meant 

 by the mean figure of the earth, and how it is determined, we may 

 answer that the problem proposed for solution is really this, — Given 

 a certain number of measured arcs of different meridians, to deter- 

 mine the geometrical figure of the surface on which they will most 

 exactly fit. That figure when determined is the mean figure of the 

 earth. There are three principal measured arcs which supply data 

 for this determination : viz. the Russian arc, the latitudes of the 

 extremities of which differ by about 25° ; the Anglo-French arc, in 

 which that difference is about 22° ; and the Indian arc, in which the 

 difference is about 21°. There are also other shorter arcs, e.g. 

 those measured in Prussia, Peru, the Cape of Good Hope, &c. 

 General Schubert, and subsequently Captain A. R. Clarke, have 

 shown that the figure which most nearly represents these measure- 

 ments is an ellipsoid. The calculation of the latter gentleman is 

 based on the data supplied by thirteen stations on the Russian arc, 

 twelve on the Anglo-French arc, eight on the Indian arc, five on the 

 Cape arc, and two on the Peruvian arc. And his result comes to 

 this, that the polar semiaxis is 20,853,768 feet, while the semi- 

 major and minor axes of the equatorial ellipse are respectively 

 20,92G,4S5 feet and 20,921,177 feet, the two latter numbers differ- 

 ing by just a mile. General Schubert makes the difference about 

 half a mile. Archdeacon Pratt is of opinion that the method fol- 

 lowed by these gentlemen is erroneous, inasmuch as it neglects 

 the possible influence of local attraction on the plumbline at the 

 standard stations of the arcs employed. The amount of the uncer- 

 tainty introduced by this possibility is the subject of a very elaborate 

 paper by Archdeacon Pratt, published in vol. xiii. of the Proceedings 

 of the Royal Society. An account of the method pursued in that 

 paper, and of the chief results arrived at, is given in the present 

 work. By a preliminary investigation he shows that the differences 

 between the latitudes of the principal stations on a measured arc, as 

 determined by geodesy, are sensibly unaffected by local attraction ; 

 and consequently that if the latitude of that station to which the 

 others are referred were clear of error depending on local attraction, 

 the method pursued by Captain A. R. Clarke (Bessel's method) 

 would be unobjectionable. But this is by no means the case. Ac- 

 cordingly Archdeacon Pratt investigates the consequences which 

 follow from assuming that there exists a small unknown deflection of 

 the plumbline at the reference-station, producing a small unknown 

 error in the determination of its latitude. He then applies this in- 

 vestigation to determine the semi- major and minor axes, and the 

 ellipticity of the mean ellipses which respectively represent the 



