Wheatstone's Wave Machine at the Science Museum in London. Credit: SCIENCE MUSEUM/SCIENCE & SOCIETY PIC. LIB.

Gaining a visual grip on compound motions in more than one plane is a tricky business, particularly when the mechanism cannot be observed directly. Under these circumstances, the didactic machine or what was called the ‘philosophical toy’ comes into its own.

The most obvious role for such devices is the inducing of the ‘Ah-hah!’ factor — that instant of illumination when we find that we have suddenly acquired the elusive visualization of how a complicated system works in spatial terms.

In addition to instruction in known mechanisms, ‘philosophical’ machines could model hypotheses in a more speculative manner, acting to confirm the feasibility of a theory. Exemplary cases are the armillary sphere, which modelled the Ptolemaic system of the cosmos, and Wheatstone's “Wave Machine”, which gave visible shape to the interference of different wave-forms.

Best known as a pioneer of the electric telegraph, Sir Charles Wheatstone (1802-75) came to his main sciences of acoustics, optics and electricity via the making and inventing of musical instruments. The enduring theme of his creative life may be described as the invention of mechanisms of direct practical utility and didactic cunning that were profoundly in tune with natural law.

Wave motion, such a crucial theoretical model in physics from the time of Thomas Young and Augustin Fresnel in the early nineteenth century to the present day, was the subject of the most compelling of Wheatstone's didactic toys. His wave machine was invented in the early 1840s and produced for sale in handsomely engineered versions. It ingeniously represents the motion of ‘ether particles’ in plane, elliptical and circular polarization through the compounding of two sinusoidal motions at right angles.

White beads of mother-of-pearl are located at the tips of wiry rods that move sinuously in response to a set of more than two dozen wave-shaped, wooden templates inserted in pairs into the machine at right angles to one another. The instructions issued in 1884 by John Newman, “Philosophical Instrument Maker”, give a nice idea of the kinds of shapes supplied: “The slides are marked R & L (right and left) H & V (Horizontal and Vertical); (1) The standard wave; (2) The lower octave, 2:1; (3) The major third below, 5:4.”

Wheatstone's “Sonic Patterns Produced by a Kaleidophone”.

A complementary realization of the ‘musical’ principles governing the ‘molecular vibrations’ in both light and sound was provided by Wheatstone's “Kaleidophone or Phonic Kaleidoscope⃛ for the Illustration of Several Interesting and Amusing Acoustical and Optical Phenomena”. Named after Sir David Brewster's optical kaleidoscope, it used small illuminated mirrors attached to the top of vibrating rods that emerged from a base plate in which varied vibrations were induced. The paths of the oscillating mirrors, traced by the persistent impressions of reflected light, created beautiful and surprising patterns, comparable to the Chladni's figures produced by sand on vibrating plates.

For Wheatstone, as for Brewster, the philosophical toy was designed to induce simple delight in nature's concealed wonders, particularly in the young, and to model in mechanical form profound truths about physical law at the highest levels of understanding.