bi) the Method of the Least Squares. 51 



dition of equilibrium the difference would be great, though 

 it is likely a slight difference might take place. Indeed, before 

 I saw Mr. Airy's paper, I was in the habit of employing the 

 reduced or geocentric latitudes in the solution of this problem, 

 instead of the apparent or observed latitudes which have been 

 generally used. The difference, however, is not great in a 

 spheroid of small compression, such as our earth, and the em- 

 ployment of the apparent latitudes increases in a small degree 

 the lengths of the computed pendulum near 45° ; but the ef- 

 fect upon the compression is almost insensible. I shall not, 

 however, at present direct my attention to this method by the 

 pendulum of obtaining the compression, but proceed to con- 

 sider that derived from the measurement of arcs. 



Mr. Airy gives the following table of the measure of arcs, 

 which are cei'tainly the most extensive and accurate : 



The method of comparing large arcs has been said to be 

 the more accurate plan of arriving at a correct value of the 

 ellipticity, than by a comparison of single degrees ; though it 

 is not likely to have any great advantage over a comparison 

 of degrees derived from the measurement of large arcs. — As 

 a comparison of single degrees is more easily made than of 

 arcs, I have deduced from the above arcs the value of a de- 

 gree at the middle latitude of each. 



H2 



