Length of a Degree of the Terrestrial Meridian. 227 
Table of measured lengths of portions of Terrestrial Meridians. i 
Country. _ |Latitude yp of vai in point of meas-|Mean ec Han bse rong degree 
Peru, 1° 31’ 00.34” North. 60467.7 No. 1. 
India, 13° 06’ 31.00” « 60492.8 « 2, 
France, na” 51° 02.65" ~™ COTES ITS, 
England, oe (2 FTbe" 60824.1 “ 4, 
Sweden, 66° 20’ 09.91” 60954.8 “ 5, 
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 2 and a. The measured degrees which are oe 1 and 
2, give ae sp a =3958.554 miles: 1 and 3 give a a7 a= 
3962.184 m.: 1 and 4 give ee a=3961.954 m.: 1 and 5 give 
1 . 1 
a= 3 4? 4=3962.17 m.: 2 and 8 give o =555  a=3962.287 m. : 
” . 1 u 1 
2 = 4 give a= 375° a==3961.925 m.: 2 and 5 give a=37)’ = 
I 
3962.111m.: 3and4 givea=355> a=3961.327 m.: 3 and 5 give 
= a=3962.176: 4 and 5 give ate a = 3961.977 m. 
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 
takethe mean of all the values, we shall, in all probability, diminish 
the effect of these errors. ‘The means are, 318 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 «, invented by Lagrange, which is called 
‘ The method 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 
Pe a 1 
table, has obtained aa" There is also another method due to 
