154 GAUSS ON GENERAL PROPOSITIONS REGARDING FORCES 
duced a new and distinctive circumstance; the direction of 
the force is not in the connecting straight line, but is perpen- 
dicular to the plane passing through p» and the direction of ds ; 
and the intensity of the force depends not on the distance 
alone, but also on the angle which rv makes with ds. If this 
sin §.uds 
7 
angle be called 6, then is the measure of the moving 
force which ds exerts upon »; and an equal force in the pa- 
rallel and opposite direction is exerted by »% on the element of 
the current ds, or on its material conductor. 
If we assume with Ampére that the elements ds, ds! of two 
galvanic currents act attractively or repulsively on each other 
in the straight line which joins them, then the phenomena 
require us to consider this force as acting in the inverse 
ratio of the square of the distance ; but as having, at the same 
time, a somewhat less simple dependence on the direction of the 
elements of the currents. We shall restrict ourselves in this 
treatise to the three first cases, or to those forces which are ex- 
erted by one element upon another in the straight line which 
joins them, and which are therefore simply in the inverse ratio 
of the square of the distance; although several propositions 
will be found applicable, with slight alterations, to the other 
cases also, the more detailed development of which must be re- 
served for another treatise. 
2. 
We denote by a, b,c the rectangular coordinates of a mate- 
rial point, from which an attracting or repelling force emanates ; 
and we denote its accelerating force, at an indeterminate point 
O, the coordinates of which are x, y, z, by 
oe a ek a eh 
aa OS gr eet re 
where » expresses for the first case mentioned in the preceding 
article, the quantity of matter existing at the first point; and 
for the second and third cases, the quantity of magnetic or elec- 
tric fluid. Resolving this force in directions parallel to the 
three coordinate axes, we have its components 
eu (a—z) ep (b—y) ep (C—2) 
RRS qe ae evi 
where « = + 1, or = — 1, according as the force is attractive 
or repulsive, which is always decided by the qualities of the 
