“NEW HAVEN, JUNE 2, 1897.

    “MY DEAR MR. BOSTWICK: 

    “I regret that I have allowed your letter to lie so long
    unanswered.  It was in fact not very easy to answer, and when one
    lays a letter aside to answer, the weeks slip away very fast.

“I do not think that you state the matter quite right in regard to the mixture of fluids if they were continuous.  The mixing of water as I regard it would be like this, if it were continuous and not molecular.  Suppose you should take strips of white and red glass and heat them until soft and twist them together.  Keep on drawing them out and doubling them up and twisting them together.  It would soon require a microscope to distinguish the red and white glass, which would be drawn out into thinner and thinner filaments if the matter were continuous.  But it would be always only a matter of optical power to distinguish perfectly the portion of red and white glass.  The stirring up of water from two pails would not really mix them but only entangle filaments from the pails.

“To come to the case of energy.  All our ideas concerning energy seem to require that it is capable of gradual increase.  Thus the energy due to velocity can increase continuously if velocity can.  Since the energy is as the square of the velocity, if the velocity can only increase discontinuously by equal increments, the energy of the body will increase by unequal increments in such a way as to make the exchange of energy between bodies a very awkward matter to adjust.

“But apart from the question of the increase of energy by discontinuous increments, the question of relative and absolute motion makes it very hard to give a particular position to energy, since the ‘energy’ we speak of in any case is not one quantity but may be interpreted in a great many ways.  Take the important case of two equal elastic balls.  One, moving, strikes the other at rest, we say, and gives it nearly all its energy.  But we have no right to call one ball at rest and we can not say (as anything absolute) which of the balls has lost and which has gained energy.  If there is such a thing as absolute energy of motion it is something entirely unknowable to us.  Take the solar system, supposed isolated.  We may take as our origin of coordinates the center of gravity of the system.  Or we may take an origin with respect to which the center of gravity of the solar system has any (constant) velocity.  The kinetic energy of the earth, for example, may have any value whatever, and the principle of the conservation of energy will hold in any case for the whole solar system.  But the shifting of energy from one planet to another will take place entirely differently when we estimate the energies with reference to different origins.

    “It does not seem to me that your ideas fit in with what we know
    about nature.  If you ask my advice, I should not advise you to try
    to publish them.