FUNCTION OF CRITICISM IN ADVANCEMENT OF SCIENCE. 357 
tinction between potential and kinetic energy, as an incom¬ 
plete statement of a greater truth. Rumford, Carnot, Mayer, 
Colding, Joule, Clausius, and others have sought the mechan¬ 
ical equivalent of heat in various ways, and it turns out to 
be about 426.8 kilogram-meters or 777.9 foot-pounds for this 
latitude. 
Helmholtz sought to ground a theoretic basis for the trans¬ 
formation of energy in the principle of the “ impossibility of 
perpetual motion,” and showed that the mode of transfor¬ 
mation, such as a Carnot cycle, does not affect the result, but 
at first he was unsuccessful in arriving at an analytical ex¬ 
pression. He then introduced the further principle of action 
and reaction, which is equivalent to limiting the operation 
of his cycles to central forces, and proved that rotations as 
well as translations must be taken into the account, and thus 
arrived at the famous theorem of the conservation of energy: 
“ In conservative systems, the sum of the kinetic and the 
potential energies is a constant.” Helmholtz made an appli¬ 
cation of his principle to magnetic, electric, and heat pro¬ 
cesses, but fell into another error, and his result met only 
wdth* opposition, showing how hard it is even for a master 
mind to successfully grasp at the outset the truths of nature’s 
operations. Another thread of the problem was worked out 
by Carnot, Clausius, and Thomson, culminating in the entropy 
theorem, which, coupled with the theorem of conservation, 
gives the two laws of thermodynamics. Stripped of all tech¬ 
nicalities, the first or conservation law is, that energy cannot 
be created or destroyed by mechanical processes ; the second 
or entropy law is, that the energy of a body can be trans¬ 
formed only from higher to lower states of intensity. The 
first law asserts that the sum total, or the energy of the uni¬ 
verse, is constant; the second that the available useful energy 
of the solar system is diminishing in efficiency. 
It cost much labor and effort to arrive at the true mathe¬ 
matical expression for the second law. The early investi¬ 
gators, Carnot, Clayperon, and Horstmann, did not emancipate 
their minds from the erroneous idea that heat is a substance, 
