106 
PHILOSOPHICAL SOCIETY OF WASHINGTON. 
35th Meeting. November 30, 1887. 
The Chairman presided. 
Eleven members present. 
Mr. E. B. Elliott continued his remarks, begun at the last 
meeting, on 
THE QUOTIENTS OF SPACE-DIRECTED LINES. 
[Abstract.] 
Mr. Elliott said that the quotient of two space-directed lines is 
not a line, but is abstract. It is a quantity which applied as a mul¬ 
tiplier to one of the space-directed lines will produce the other. 
He then gave as an illustration of this principle its application to 
the problem of the mutual action of the elements of electric currents. 
Let M and p! represent, respectively, in length, current strength, 
and direction, two elements of electric currents. 
p and p' represent, respectively, in length and direction, the 
lines connecting the centers of the elements. 
d represent the angle made by the element p with the line 
connecting the elements p. and //; that is, with p. 
ip represent the angle made by the element p! with its rectan¬ 
gular projection in the primary plane; that is, the plane 
determined by the element p. and the connecting line p. 
ip represent the angle made in the primary plane by the rec¬ 
tangular projection of the element // and the connecting 
line p'. 
The effect of the action of p on p! will be as the product of the 
' current strength, the length, and the direction of the elements, and 
inversely as the square of the distance, and the direction of the ac¬ 
tion will be expressed by the following formula: 
U - X U ^ = cos 0 cos cos (p — sin 0 cos ip sin 0 
P . . 
-}- [cos 0 cos ip sin ^ -f sin ^ cos ip cos i 
-f- cos ^ sin ^. j 
-|- sin 6^ sin ^ . ij; 
in which the first line denotes action (transference) in the direction 
of the line connecting the centers of the elements; the second line 
