52 PHILOSOPHICAL SOCIETY OF WASHINGTON. 
For positions of encroachment the law is more complicated, and 
forms an interesting field for mathematical discussion. Where three 
or more atoms are superimposed the problem becomes too complex 
for discussion. It is noted, however, that such compound atom, if 
quiescent from extreme abstraction of heat, would be in a condition 
of elastic equilibrium, ready to respond like a bell to the slightest 
disturbances. In all these cases of interpenetration the law of stress 
would be finite and diminishing, and if the line of encounter should 
chance to be a right line through their centers (a condition infi- 
nitely rare in actual occurrence), they would continue on or repeat 
according to energy of approach; while upon any other lines of 
approach orbital relations would supervene, in modified curves of 
the second order, either hyperbolic, parabolic, or elliptic, according 
to velocity, and with or without partial penetration, according to 
nearness of approach. 
Boscovich, however, did not adopt this solution, although within 
his reach. The problem of the action of a gravitative particle as 
controlled by an attractive center has several aspects of statement, 
which may be confined to four, for practical investigation. In the 
first, where the particle is assumed to be without mass, no discus- 
sion is possible, for the two suppositious points instantly assume the 
same locality, and end the relation. In the second, where the par- 
ticle is endowed with inertia but not magnitude (and the attractive 
locus fixed by postulate), the element of motion enters, but infinite 
terms appear in the equations in the limit, forbidding interpretation. 
Thirdly, when we attribute finite magnitude to the gravitative par- 
ticle for gravitative pervasion, as in actual spherical masses, no in- 
finite terms appear, and we get an intelligible mathematical discus- 
sion, with planetary results for exterior positions, and pendulum 
results for interior positions, as I have heretofore demonstrated ; 
and lastly, when both the gravitating Joct are invested with similar 
attributes of volume and of mass (excluding extraneous notions of 
ordinary collision and repulsion from the problem), the results are 
similar to those of the third hypothesis. I do not introduce any 
of the mathematical discussions here, as the dynamics of the par- 
ticle have been fully treated by mathematicians, though I am not 
aware that any of them have pursued it to physical conclusions. 
It is not likely, however, that there is any matter so simple as 
this modified Boscovichian atom; that is, which can be identified. 
