MATHEMATICAL SECTION. - PHL 
wi 
214 
Add (13) and (14); when vrs =D. 
2”(12 a ChE) 
Then, under (12), enter eee ae Fag? = ( 
> 9 Dx Dy le 
Next, under (9), enter 6) re ~ Ee = B. 
20) | 3ta) 208) 22) 
Be) eat) pe ek 
Nores.—[1] The sign of summation is distinguished by an ad- 
ditional stroke for every additional quantity introduced under the 
column added up. 
[2] These additional quantities, under the columns of squares, 
(6), (10), and (13), will evidently all be negative. 
[3] This form may be extended to any number of unknown 
quantities, by insertion of ae, etc., between (4) and (5), be, etc., 
between (8) and (9), and so on. Modifications where there is a 
smaller number of unknown constants, and where one of them has 
the coefficient always unity, will be obvious. 
[4] One of the quantities a, }, etc., will, in many computations, 
be zero when another one is significant, and vice-versa ; as when one 
unknown quantity changes in the course of a series of observations. 
In this case we may save some columns by arranging our equation 
thus: a, A, + a, A, + 0B + etc. =y (where a, a, = 0, always). 
Here two sums are found under columns (1) to (5), two quotients 
under (2) to (5), and two additional quantities placed under each of 
the other columns before they are summed up. The remainder of 
the work then proceeds as before, except that the Jast step will be 
duplicate. 
[5] It will be found advisable always to make 4a, 2%, etc., as 
nearly zero as possible, so that the products will be smaller and 
there will be less danger of error. 
[6] The computation is to be checked by applying A, B, etc., 
and finding the residuals of y. Then 2 (a Ay), ¥(a 4b), etc., should 
all be zero. 
[7] Where but two unknown quantities are to be found, one of 
them with the constant coefficient unity (as A + b) B =), other 
methods will usually be preferable. Two of these will be given. 
I. If the values of 6 are symmetrical, so that b = 2? + b',,2+0’,, 
& + 0’,, etc., here all that is necessary to find B is to subtract the 
Lastly, under (5), enter D— B=. 
