150 PHILOSOPHICAL SOCIETY OF WASHINGTON. 
vestment in United States Government bonds, at Six or at four per 
cent., and making use of the banking privileges thus available, 
over investment at a higher rate without such privileges. The 
restrictions caused by the high premium on Government bonds, the 
bank tax, and the necessary specie reserve were all allowed for. 
This paper was discussed by Messrs. Harkness, DE Lanp, 
SmILEy, and others. 
Mr. H. Farquuar presented the following 
FORM OF LEAST-SQUARE COMPUTATION. 
Suppose four unknown constants, A, B, C and D, are to be cal- ° 
culated from equations of condition of the form 
aA + 6B+cC+dD=y. 
Arrange columns in order (1) a’, (2) ab, (3) ae, (4) ad, (5) ay, 
(6) b?, (7) be, (8) bd, (9) by, (10) e*, (11) ed, (12) ey, (18) d’, (14) dy 
Add up first five columns and place under (2) to (5) the quotients 
of their sums divided by 2(1). 
Put the product x) 3(2) under (6), + a ) ¥(3) under (7), 0,32 3(4) 
under (8), A, +(5) under (9), Fer +(3) under (10), sae) under 
(12): en 2(5) under (12), co 5(4) under (13), and aD 2(5) under 
(14), reversing the sign in every case. 
Then add up (6) to (9), placing under the sums of (7) to (9) 
their quotients divided by 2’(6). 
(7 
Put the product ae +’(7) under (10), 76, 2’(8) under (11), 
27) 
¥6) 29) ends (12, mB, 2’(8) under (13), and re 2”(9) under 
(14), reversing each sign. 
yw itil Ds 1, 
Add (10) to (12), putting quotients ach and ech under 
the sums. - 
rig 2”(11 
Put the product dy 2”(11) under (18) and m0) 2”(12) un- 
der (14), reversing the signs. 
