^90 Mr Watts on the ElUptkity the Earth, 
39,15554 — ^ — 0,68694728 . ^ , 
39,14600 — a- — 0,64556764 .y =. 
39,14^50 — a? — 0,62460442 ,y = z,, 
39,13929 — a* — 0,61280052 . y = z ^ , 
39,13614 — a- — 0,59751663 .y-z^. 
Now, by the principle of least squares, the values of a: and y 
ought to be determined in such a manner, that the sum of the 
squares of the errors Zj^, Zq, z^^ & c . may be the least possible : 
and to satisfy this condition, it will be requisite to form the 
equations of minimum for each of the unknown quantities x 
and y^ in particular, by multiplying all the terms of each of the 
equations of condition by the coefficient of the unknown quanti- 
ty, taken with its proper sign, and then find the sum of all the 
products. 
By performing this operation successively, with each of the 
coefficients of the unknown quantities, upon all the equations of 
condition, we shall obtain as many different equations as there 
are unknown quantities. These equations will all be of the 
first degree, and it will only remain to determine the unknown 
quantities by the ordinary process of elimination. 
Then the values of x and determined in this manner, will 
be the most proper to represent the best possible observations, 
since they will give a system of errors which differs less from 
die truth than any other system whatever. 
Since, therefore, the coefficient of x is unity in all the equa- 
tions of condition, the equation of minimum relatively to x will 
be found, by taking one-seventh of their sum, and putting the 
quotient equal to zero : Thus we shall find, 
— 39,15036 + a? -f 0,66328595 , y (1.) 
In like manner, if we multiply each equation of condition by 
the coefficient of y in that equation, the following results will 
arise, 
— 29,8238492 -}- . 0,76136670 d- y . 0,57967933 ^ 
— . 27,9691673 q- a- . 0,71419880 q- y , 0,51008004 
— 26,8977882 q- a- . 0,68694728 q- y . 0,47189664 
— 25,2713907 q- a- . 0,64556764 -h y . 0,41675753 
— 24,4485814 q- a; . 0,62460442 q- y . 0,39013081 
— 23,9845795 q- a- . 0,61280052 q. y . 0,37552451 
— 23,3844813 q- a> . 0,59751630 q- y . 0,35702582: 
