FIOUBE OF THE EARTH. Ql 



our present uncertainty respecting them can have on the sub- 

 ject in question, I have employed three different estimates of 

 the oblateness -£fa yffc , and y^. With respect to the radius 

 of the equator, that is ascertained with sufficient precision by 

 the mean of the arc extended from Greenwich to Formen- 

 tera, corresponding to latitude 45 418". The value of the 

 degree in toises is 5/010,5, and it is highly probable that in 

 this estimate the error does not amount to so much as half a 

 toise, as it is deduced from an entire arc of 12° 48' between 

 the two extremities, the latitudes of which have been deter- 

 mined with extreme care, and by a great number of obser- 

 vations. 



The following are the logarithms of radius at the equator By assuming 

 ,.,x, , , f , ii r^i * hree different 



which I have employed as adapted to each degree or oblateness, estimates of 



and opposite to them are placed the corresponding computed oblateness the 

 estimate of the entire arc between Clifton and Dunnose. t ^ e resu i t , 



-r] 6,5147,400 2° 50^21,972 



3 -i 6,5147,485 2° 50' 21,974 



tK- . . . 6,5147,570 2° 50' 21,976 



so that the greatest difference is but 0",38> Let us suppose 

 it 0',4, or evenO",5, for the second calculation was made only 

 by means of the western series of triangles, and the third only 

 was the eastern j but even then the error arising from uncer- 

 tainty in the elements is not half the difference we find 

 between the results of computation and of observations of the 

 fixed stars. It appears, therefore, that these elements are by 

 no means to be neglected as a method of verification ; and in 



fact the quantity of 1^,38 is so small, that it is extremely dif- 



/- , . .... , prove too 



ficultto ascertain this quantity with the very best instruments. sma ll to be in 



Of this we shall find further proof hereafter j but as this dis- general ascer- 

 cussion is not without its use, I shall enter into some, details on 

 this subject. 



The measurement in Lapland was performed by means of The same 

 a double metre, and with a repeating circle of Borda, sent by shewn from 

 the National Institute of France. In order to see to what ob^^tions • 

 degree of accuracy the arc computed would agree with that 

 obtained by observations of the pole star above and below 

 the pole, I assumed an oblateness of -g-i^- and as logarithm of 

 adius I had 6,5147500 expressed in toises and in round num- 

 bers. 



