92 Observations on the Measurement of 



elements are well known, and the errors that can arise 

 from any uncerlainty in them, are not so considerable as is 

 generally supposed. The cblatenc-ss and the diameter at 

 the equator are the only elements wanting in the calculation: 

 for the purpose of seeing what effect our present uncertainty 

 respecting thoni can have on the subject in question, I have 

 employed three different estimates of the oblateiiess -g-a-jr* 

 ^fo, and -j-j-^. With respect to the radius of the equator, 

 that is ascertained with sufticient precision by the mean of 

 tlie arc extending from Greenwich to Formentera, corre- 

 sponding to latitude 45° 4' 18". The value of the degree 

 in toises is 57010,5, and it is highly probable that in this 

 estimate the error does not amount to so miich as half a 

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

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

 termined with extreme care, and by a great number of ob- 

 servations. 



The following are the logarithms of radius at the equator, 

 which I have employed as adapted to each degree of oblate- 

 ness, and opposite to them are placed the corresponding 

 computed estimates of the entire arc between Clifton and 

 Dunnose. 



3^ .... 6,5147,400 2° 50' 21,972 



^^ 6,51}7,485 2° 50' 21,974 



■j-l-g. 6,5 147,570 2° 50' 21,976 



so that the greatest difference is but 0",38. Let us sup- 

 pose it o",4, or even 0",5, f(jr the second calculation was 

 made only l)v means of the w estern series oF triangles, and 

 the third only with the eastern ; but even then the error 

 arising from uncertainty in the elements is not half the 

 difference we find between the results of computation and 

 of observations ot" tlie 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 l",38 

 is so small, that it is extremely difficult to ascertain this 

 quantify with the, very best instruments. Of this we shall 

 find further proof hereafter ; but as this discussion is not 

 without its use, I shall enter into some details on this sub- 

 ject. 



The measurement in Lapland was performed by means 

 of a d'Mible metre, and with a repeatmg circle of Borda, 

 sent bv the National Institute of France. In order to see 

 to what 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 ^J-^^, and as 

 logarithm of radius 1 had 6,5 147500 expressed in toises 



and 



