It is conceivable that animal life might have the attribute of using the heat of surrounding matter, at its natural temperature, as a source of energy for mechanical effect . . . .The influence of animal or vegetable life on matter is infinitely beyond the range of any scientific enquiry hitherto entered on. Its power of directing the motions of moving particles, in the demonstrated daily miracle of our human free-will, and in the growth of generation after generation of plants from a single seed, are infinitely different from any possible result of the fortuitous concurrence of atoms.
At what time does the dissipation of energy begin?
Symmetrical equations are good in their place, but ' vector ' is a useless survival, or offshoot from quaternions, and has never been of the slightest use to any creature.
Fourier's theorem is not only one of the most beautiful results of modern analysis, but it may be said to furnish an indispensable instrument in the treatment of nearly every recondite question in modern physics.
There cannot be a greater mistake than that of looking superciliously upon practical applications of science. The life and soul of science is its practical application.
Simplification of modes of proof is not merely an indication of advance in our knowledge of a subject, but is also the surest guarantee of readiness for farther progress.
The vortex theory [of the atom] is only a dream. Itself unproven, it can prove nothing, and any speculations founded upon it are mere dreams about dreams.
[Of the ether] it is no greater mystery at all events than the shoemakers' wax.
[Referring to Fourier's mathematical theory of the conduction of heat] ... Fourier's great mathematical poem.
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