20 REPORT—1848. 
In the following table will be found the results of the first series of experiments, 
in which is given—the distance in inches between the nearest points of the spheres 
(a) ; the measures or quantity of electricity requisite to produce an attractive force 
of 1 grain (6); the measures or quantity of electricity requisite to produce discharge 
at the given distance (c) ; the force of attraction at the instant of discharge (d). 
Table I. 
i . Attracti 
Pintonee in ee |: Page | an oni 
mele | Lessin. | dncharge. | of Gncharge 
01 6 26 18 to 19 
0-2 g— 52 38 
0:3 11 78 50 
0-4 13 104 64 
05 154+ ee eee 
08 20 208 108 
1-0 23 260 127 
15 30+ 390 169 
20 38+ 520 187 
a b iB d 
The electrical apparatus employed in these experiments was the same as that for- 
merly described, and consisted of a common balance so circumstanced as to measure 
the relative attractive forces ; a unit-measure for measuring the quantity of electri- 
city; a large electrical jar, and a Lane’s discharging electrometer placed in connec- 
tion with the former, by which the relative quantity requisite to produce discharge 
at a given distance could be estimated. 
In the above table, the last column d is deduced from columns 6 and ¢ by the now 
well-established law of electrical action, viz. that the force is as the square of the 
quantity of electricity ; the four last numbers in column c are deduced from the ge- 
neral law of the discharging electrometer, as observable in the preceding experiments 
of that column, and are taken as the number of measures which would be requisite 
to produce discharge at the given distances in column a, supposing the electrical jar 
capable of containing the given quantity. 
Now, on reviewing these results, there does not appear to be any general law or 
relation between the numbers representing the force, as measured by the balance 
and given in column d, and the comparative quantities of electricity required to pro- 
duce discharge, as given in column c; so far the experiments do not appear to fur- 
nish any very satisfactory result. 
On examining the question, however, more attentively, it will be seen that the 
calculated force in column d is not really the force at the instant of discharge, taken 
between the nearest points of the spheres, that is to say, the points upon which the 
whole force is finally concentrated, and between which the discharge takes place, as 
evidenced in the balls of the discharging electrometer ; hence column d does not ac- 
tually represent the force in these points at this instant; it, in fact, only represents 
the general attractive force upon the whole of the opposed hemispheres, or rather in 
two points qq! taken within the opposed surfaces, in which we may suppose the 
whole force to be collected, and to be the same as if operating from every point or 
the hemispheres. 
The author proceeds to show how these points q q' may be determined, and ac- 
(2+ 2an)*—a 
cording to the formula z= = , in which x= distance of points g q' 
under the surface a = distance of the nearest points of the sphere, and » = radius. 
Supposing both spheres equal and radius = 1, then, according to the author’s ge- 
neral results, brought under the consideration of the Section at the last Meeting, we 
have the total force between the spheres in the inverse ratio of the squares of the 
distances between the points gq’, or calling F the total attractive force we have 
1 
Petia S 
a(a+2r) 
ee eee 2 
