^20 Col. Henri/ James, on the [April 23, 



The elements of the spheroid, given in Airy's " Figure of the 

 Earth," are 



Polar diameter = 7899 • 1 miles. 

 Equatorial . = 7925 • 6 miles. 



1 

 Ellipticity . • = 299-3 



Our most recent determination, therefore, slightly increases the 

 ellipticity, and we increase the equatorial diameter of the earth by 

 about one mile. 



One of the chief difficulties which is encountered in the investi- 

 gation of the figure of the earth, arises from the local attraction at 

 the stations at which the observations for latitude are taken, in con- 

 sequence of the irregular distribution of the masses of matter in the 

 mountains or hills near the stations, or the unequal density of the 

 matter beneath the surface of the earth. 



Thus, for example, when observations are taken on the north 

 end of the hill at Dunnose, in the Isle of Wight, and also at the 

 south end, the great mass of the hill being between the two stations, 

 the difference of latitude is found to be greater than is due to the 

 actual distance between the stations ; and this, because the attraction 

 of the mass of the hill has drawn the plumb line in each case to- 

 wards it, and made the celestial arc greater than the geodetic. 



The detailed survey of Edinburghshire having been published 

 with the contours, or zones of equal altitude, engraved on the plans, 

 and thus furnishing accurate information as to the relief of the 

 ground, the superintendent of the survey undertook, in 1854, to 

 investigate the amount of the local attraction at Arthur's Seat ; and 

 this the jmore readily, as it would furnish the data for computing 

 the mean density of the earth itself. Observations for latitude were 

 taken at the north and south ends of the mountain, and also on the 

 summit, and the geological structure and specific gravity of the 

 rocks composing it ascertained. 



The attraction of the mountain was computed, by supposing it 

 divided into a number of vertical prisms, and summing their sepa- 

 rate attraction, resolved into the direction of the meridian. 



The attraction of each prism is, according to the known laws of 

 gravitation, proportioned to the mass, and inversely proportioned to 

 the square of its distance ; similarly, the attraction of the earth 

 is in proportion to its mass, and inversely as the square of the 

 distance from the centre, the ratio of these attractions is equal to 

 the tangent of the angle of deflection. This will be obvious from 

 the inspection of a diagram, on which the attraction of the earth 

 is represented by a vertical line, and the attraction of the moun- 

 tain by a short line drawn at right angles to it, showing the 

 extent to which the plumb line is deflected or drawn towards the 

 mountain. 



