The substantial conception of work (energy) is by no means a necessary one. And it is far from true that the problem is solved with the recognition of the need of such a conception. Rather let us see how Mayer gradually endeavored to satisfy that need. He first regards quantity of motion, or momentum, _mv_, as the equivalent of work, and did not light, until later, on the notion of living force (_mv²/2_). In the province of electricity he was unable to assign the expression which is the equivalent of work. This was done later by Helmholtz. The formal need, therefore, is _first_ present, and our conception of nature is subsequently gradually _adapted_ to it. The laying bare of the experimental, logical, and formal root of the present principle of energy will perhaps contribute much to the removal of the mysticism which still clings to this principle. With respect to our formal need of a very simple, palpable, substantial conception of the processes in our environment, it remains an open question how far nature corresponds to that need, or how far we can satisfy it. In one phase of the preceding discussions it would seem as if the substantial notion of the principle of energy, like Black's material conception of heat, has its natural limits in facts, beyond which it can only be artificially adhered to. FOOTNOTES: [Footnote 39: Published in Vol. 5, No. I, of _The Monist_, October, 1894, being in part a re-elaboration of the treatise _Ueber die Erhaltung der Arbeit_, Prague, 1872.] [Footnote 40: _On Matter, Living Force, and Heat_, Joule: _Scientific Papers_, London, 1884, I, p. 265.] [Footnote 41: "Atqui hoc si sit, globorum series sive corona eundem situm cum priore habebit, eademque de causa octo globi sinistri ponderosiores erunt sex dextris, ideoque rursus octo illi descendent, sex illi ascendent, istique globi ex sese _continuum et aeternum motum efficient, quod est falsum_."] [Footnote 42: "A igitur, (si ullo modo per naturam fieri possit) locum sibi tributum non servato, ac delabatur in _D_; quibus positis aqua quae ipsi _A_ succedit eandem ob causam deffluet in _D_, eademque ab alia istinc expelletur, atque adeo aqua haec (cum ubique eadem ratio sit) _motum instituet perpetuum, quod absurdum fuerit_."] [Footnote 43: "Accipio, gradus velocitatis ejusdem mobilis super diversas planorum inclinationes acquisitos tunc esse aequales, cum eorundum planorum elevationes aequales sint."]