Length of a Degree of the Terrestrial Meridian. 227 



Table of measured lengths of portions of Terrestrial Meridians. 



Substituting the lengths of the degrees which are given, and for 

 convenience numbered, in the table, for L and the corresponding 

 latitudes for ■\^, in formula (4), and proceeding agreeably to the man- 

 ner just before explained, we obtain ten values for each of the quan- 

 tities a and a. The measured degrees which are numbered 1 and 



1 . 1 



2, give a = „-p7.3 a:=3958.554 miles : 1 and 3 give «^=<^ii;' « = 



1 

 3962.184 m.: 1 and 4 give a=„Y_3 0=3961.954 ra. : land 5 give 



a=g^^5a=3962.17m 



2 and 3 give «=; 



1 



0=3962.287 m. 



d08.6' 



, . 1 1 



2 and 4 give a=^-^3 a = 3961.925 m. : 2 and 5 give a =77r\ ' «= 



1 

 3962.111m.: 3 and 4 give a ^^g^s a = 3961.327 m. : 3 and 5 give 



1 1 



a=— -.5 0=3962.176: 4 and 5 give a=ir7r^, a = 3961.977 m. 

 314 ^ 305 



The discrepancies in the different values are doubtless owing to un- 

 avoidable errors, arising from the local irregularities of those portions 

 of the earth's surface where the degrees were measured. But if we 

 take the mean of all the values, we shall, in all probability, diminish 



the effect of these errors. 



The means are, oTp for the measure of 



the oblateness, and 3961.6667 English miles, for the equatorial ra- 

 dius of the earth. There is a method of combining the quantities 

 in the table, to determine a, invented by Lagrange, which is called 

 ' The ..;'£-thod of the least squares,' and which consists in making the 

 sum of the squares of the errors a minimum when compared to each 

 of the unknown quantities of the problem. Doctor Bowditch has 

 improved this method, and with the five measured degrees in the 

 1 



table, has obtained a= 



312 



There is also another method due to 



