348 Mr. Ivory on the Figure of the Earth, 



Now, put A — 45° 43' 12", and a degree of longitude at that 

 latitude, will be equal 



42487*8 x(l +-001661)= 42557*4 fathoms. 



But 77865 m -75 reduced to fathoms at 62° of Fahr. is equal to 

 42578*2 fathoms, which is 20 fathoms more than the calcu- 

 lated quantity. If this discrepancy appear very great, we shall 

 only remark, that it is very small in comparison of the differ- 

 ences of the degrees deduced from the partial arcs, and that 

 it supposes not quite so much as 1"J of time, for the sum of 

 all the accumulated errors in the amplitude of the large arc. 

 Unless we possessed some means of estimating with tolerable 

 exactness the error really existing in the degree of the parallel, 

 the discrepancy we have found can hardly be deemed suffi- 

 cient to throw any doubt upon the elliptical elements which 

 agree so well with all the most exact measurements that have 

 been made on the earth's surface. 



If the earth be really an elliptical spheroid, there can be 

 little doubt that the ellipticity must be very nearly what we 

 have found it to be. But the solution of the problem would 

 be greatly improved, and the results obtained would be more 

 exact and more certain, if the measurement of the meridian 

 in England were extended as far north as possible. An arc 

 of 8° or 10° north of Dunnose, would be the most valuable 

 addition that in the present state of this research can be made 

 to the data for determining the figure of the earth. Another 

 very profitable addition would be the extension of the Indian 

 arc, already the largest we have except the French measure- 

 ment; and more especially if it could be extended southward 

 nearer the equator. Supposing the difference between A and 

 A' to be small, it will readily appear that the coefficient of s in 

 the formula (A) will be equal to zero, or so small as to render 

 the term insensible, when 



Cos (A + A') = - £ and A + A' = 109° 28'. 

 Thus if, by means of the formula mentioned, we compute 

 the expression of the length of an arc extending northward 

 from Dunnose about a degree beyond Portsoy, to latitude 

 58° 55' 30", it will be found that the length of this large arc 

 is almost independent of the ellipticity e, and equal to an arc 

 of the equator. The reason is that, in latitude 54° 44', the 

 radius of curvature of the meridian is equal to the radius of 

 the equator, and the degree of the meridian having its middle 

 point in that latitude is equal to A , that is, to a degree of 

 the equator. Thus the length of the portion of the meridian 

 contained between the extreme north and south points of Bri- 

 tain depends chiefly on A> and very little on the other ele- 

 ment 



