242 E. B. Hunt on the Nature of Forces. 
find a constant of force increment, for all the points in which a 
straight line from the origin cuts the various curves of the sys- 
tem. The significance of this result is obvious when we con- 
sider that radiation gives shape to the formula. By farther dis- 
cussion, it would be seen that the increment for a given ordinate 
varies inversely with the abscissas and directly with the ordinate 
for a given abscissa. ‘ 
If the series of parallel curves corresponding to y=" be con-. 
structed for all values of y’ from plus infinity to minus infinity 
any possible attraction or repulsion curve for which the force varies 
: ae irks : : 
as = will coincide with some one of this series. No two curves 
of this series when referred to the same origin and axes can 
made to intersect. This property is general for all central force 
curves, in which y varies as ma taken in sets for each value of m 
from zero to plus infinity. This signifies that if any number of 
central forces acting from the same centre according to the same 
law are in equilibrio at one point, they must be so at all distances. 
Also if any number of attractions and repulsions act from one 
1 : 1 
point as their resultant also acts as —. Thus 
v 
Ya T Ya FYarF SC. Yr —Yrr— Yn — KC, = Yo OF Y= 
Yotyarty'art &e. —yr—y'e ye &e. _ ya ot Yt 


- 
which is of the original form. Hence all forces emanating from 
a centre and varying as ya are equivalent to a single resultant 
i anueca ee é 
varying as ~; which is wholly attractive or wholly repulsive: and 
other forces than those varying as za of we must suppose more 
‘than one kind of matter. 
If we suppose an atom to exercise two central forces, one al- 
tractive and one repulsive for which 2 has different values, their 
curves will intersect or the forces will balance at one aD 
one distance. Thus if the ordinary attraction, yaa and any 
only 
