Penny Blood: Serial Sensation and Working-Class Entertainment — page 162: what you’re looking at

Machine-transcribed from the original scan — historical spelling and the odd misread are preserved.

cu, x1.] THE REVELATIONS OF THE PLUMB-LINE. 145 However the very next paper in the Phil. Transactions' disposes of the difficulty in a very satisfactory manner. It was communicated by the late Astronomer Royal about a year after Archdeacon Pratt’s great paper appeared. This paper 1s short and simple, and with the author’s permission the following passages are extracted from it. ‘Although the surface of the earth consists everywhere of a hard crust, with only enough of water lying upon it to give us everywhere a couche de niveau, and to enable us to estimate the heights of the mountains in some places, and the depths of the basins in others; yet the smallness of those elevations and depths, the correctness with which the hard part of the earth ellipticity, the usual formula is | length of arc (J) equatorial radius (a) A is also affected by the mountain attraction, which we may call H. Consequently =i— $e (A+ 8 sin A Cos 2x). A=f (a, U, p, H, e). Consequently if the observed value of \ be not such as accords with the usually assumed value of e when H is determined, some different value of e« may be found which will bring X into accordance with its observed value. And this is the mode in which Archd. Pratt proposed to explain the difficulty. Eliminating a from the above equation by means of another measured are, the latitude of whose middie point is M, he obtains the following approximate formula: ar 2 d 8 (cos 2u — cos 2d) * In order to give this as small a value as practicable he takes the Russian arc for the other, for which M=70°, and after applying the formula to the case in hand, finds | de = if we put 51, for e. ‘‘Hence for an error of 5'°236 in defect in the amplitude, the effect on 5: 236 | the ellipticity will be to diminish it by ——— isa °73 mi of its whole value under the most favourable circumstances.” ‘‘On the computation of the Effect of the Attraction of Mountain-masses as disturbing the Apparent Astronomical Latitude of Stations in Geodetic Surveys.” By G. B. Airy, Esq., Astronomer Royal. Feb. 15, 1855. Phil. Trams. Royal Soc., Vol. 145, p. 101. F. IO — nearly, or by nearly fs part GONG oOo (CO)