= Hermann von Helmholtz
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<Hermann von Helmholtz>'s 1847 synthesis connected mechanical, thermal and electrical processes through <conservation of energy>. A modern example exposes the mathematical structure: for a particle with <kinetic energy> $T$ moving under a time-independent <potential energy> $V$, a <conservative force> $\mathbf F=-\nabla V$ gives $dT/dt=\mathbf F\cdot\mathbf v=-dV/dt$, so $T+V$ is constant. This derivation assumes a <conservative force>; the wider experimental question is how an apparent loss of mechanical <energy> reappears as another measurable form of <energy>. His essay helped organize such comparisons into a common conservation programme.<Über die Erhaltung der Kraft by Hermann von Helmholtz>[1847 monograph; conditional particle derivation expressed here in modern notation]{ref}
Physicist and physiologist whose 1847 synthesis connected mechanical and other natural processes through a conservation principle.
\Image[https://upload.wikimedia.org/wikipedia/commons/b/b4/Helmholtz_1876.jpg]
{title=Portrait of <Hermann von Helmholtz>}
{description=Portrait by Franz von Lenbach; reproduced in Leo Königsberger, Hermann von Helmholtz (1906). Public domain (artist died 1904; reproduction published 1906); Commons PD-old/PDM. Source and usage information on the linked Wikimedia file page.}
{source=https://commons.wikimedia.org/wiki/File:Helmholtz_1876.jpg}
{width=260}
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