Conservation and Innovation : Helmholtz's Struggle with Energy ...

measure this expenditure and compare it in the case of different machines? In the
case of a watermill with an iron hammer, the work must be measured by the
product of the weight into the space through which it ascends. The work
performed by the hammer is determined by its velocity. The motion of a mass
regarded as taking the place of working force is called the living force (vis viva)
of the mass. Living force can generate the same amount of work as that expended
in its production. It is therefore equivalent to this quantity of work. Mathematical
theory has corroborated this for all purely mechanical, that is to say, for moving
forces. After this law had been established by the great mathematicians of the last
century, a perpetual motion, which should make use of pure mechanical forces,
such as gravity, elasticity, pressure of liquid and gases, could only be sought after
by bewildered and ill-instructed people." 306
But here comes the new problem caused by the conversion processes
in the 19th century:
"But there are still other natural forces which are not reckoned among
the purely moving forces, heat, electricity, magnetism, light, chemical forces, all
of which stand in manifold relation to mechanical processes. Here the question of
a perpetual motion remained open." 307
At this stage Helmholtz's argument shows the complete abandonment
of one of the two conceptual roots and main assumptions of his Erhaltung,
namely the hypothesis of central forces depending only on distances. In fact the
conservation of force is here seen as the correlation of forces through constant
coefficients, based on the acceptance of the impossibility of perpetual motion :
" ..it was asked, if a perpetual motion be impossible, what are the
relations which must subsist between natural forces? Everything was gained by
this inversion of the question. It was found that all known relations of forces
harmonize with the consequences of that assumption, and a series of unknown
relations were discovered at the same time, the correctness of which remained to
be proved." 308
Contributors to this line of thought were Carnot in 1824 (despite the
incorrect view of the nature of heat), Mayer in 1842 309, Colding in 1843 310, Joule.
306 Helmholtz "Interaction" pp.489-95
307 Helmholtz "Interaction" Pp.495-6.
308 Helmholtz "Interaction" p.498
309 This is the first published appreciation of Mayer's priority. Helmholtz will repeat it
in 1855 (in the "Bericht" see n.2); in1861 ("On the Application of the Law of the Conservation