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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.^[ref]

Physicist and physiologist whose 1847 synthesis connected mechanical and other natural processes through a conservation principle.