71 
kinetic energy at any distance s and the maximum kinetic 
energy, it represents the potential energy. We learn, there- 
fore, from this last equation that the sum of the kinetic and 
potential energies is constant, and equal to the kinetic energy 
when the latter is greatest. After the pendulum has passed 
the lowest point of the arc, s changes its sign, and the pen- 
dulum ascends on the other side until it reaches the distance 
—s', when the motion again ceases ; and if we do not consider 
the resistance of the air or the friction between the pendulum 
and its support, it will vibrate back and forwards without 
limit of time. The change in the sign of s and s' makes no 
difference in the formula, as s 2 and s ' 2 are still of the same 
sign. 
Assuming in all this the invariability of the unit of gravi- 
tating force, the theorem that the kinetic and potential ener- 
gies make together one unvarying sum has no more to do 
with religion than has the statement that if I am travelling 
with a view to reaching a certain distance, the space I have 
already travelled and the distance I have still to travel make 
together a constant sum, namely, the whole distance. By 
assuming the invariability of the unit of force, I need scarcely 
say I do not mean “ assuming that it cannot vary/ - ’ but 
“ assuming that, under ordinary circumstances, it does not 
vary.” 
The Chairman. — I need not ask whether I am to return the thanks 
of the meeting to Lord O’Neill for his exceedingly well-reasoned paper. 
His lordship has invited corrections and additions, hut I am only afraid 
that the debate will drop still-born on account of the general agreement, 
which I am sure there will be with what he has said. I would call particular 
attention to his having so strongly brought out the principle that we ought 
not to consider a thing impossible because we cannot conceive how it can 
take place The simple fact of a stone falling to the ground is inconceivable 
as regards the “ how,” and Lord ObN eill has brought out strongly that no 
philosopher has ever been able to give a satisfactory explanation of it. 1 have 
not read the investigations of my friend Professor (Jhallis ; but it is well 
known that the action of gravity at a distance perplexed no less a mind than 
that of Sir Isaac IS ewton ; and it is to ordinary faculties perfectly inconceivable 
how one body can act upon another through space. While we know by our 
every-day experience that this kind of action does take place, it ill-befits us 
to say we will not believe in a thing because we cannot see how it is possible. 
If any member present has any of those corrections or remarks to make 
which Lord U’JN eill has so modestly invited, the Society will be glad to hear 
them. 
Mr. D. Howard, F.C.S.— I am afraid it would require considerable 
boldness to attempt corrections of Lord O’Neiil’s paper; but there is 
