recorded curves of sound-waves, as taken down automatically by the then newly-invented phonautograph of Scott (see p. 60). It is perfectly marvellous how precise his views were upon the correspondence between the graphic curve or wave-form of a sound and the actual sound itself; a precision amply justified by the experience and the discoveries of the last ten years. This matter of representing sounds--or rather the varying density of the air in the sound-wave--by a graphic curve, was a vital one to Reis. Had he had a less clear view of the nature of sound-waves than that afforded by a graphic _curve_, I doubt whether he would ever have grasped the problem of the telephone--that the final vibrations, or undulations, or oscillations of the armature in the receiver must _correspond with_--must be the very counterpart of--those of the tympanum of the transmitter. The clearness with which Reis saw this is only surpassed by the clearness with which he expressed himself upon it. For him a sound was simply a complicated series of variations in the density of the air, and capable, in all its complexity, of being represented by the rise and fall of an undulatory _curve_. “Every tone, and every combination of tones, evokes in our ear vibrations ... the motions of which may be represented by a _curve_” (p. 54). “That which is perceived by the auditory nerve ... _may be represented graphically according to its duration and magnitude by a curve_” ... (p. 53). “Our ear can perceive absolutely nothing more than is capable of being represented by _similar curves_” (p. 53). The curves with which he accompanied his original memoir--and now reproduced in facsimile, from Legat’s plates, at the end of this volume--are evidence of the thoroughness of his grasp on the undulatory principle. And he explicitly states this principle amongst “the various requisite conditions which must be fulfilled by the transmitting _and receiving_ apparatus for the solution of the problem that has been set” (Legat’s Report, p. 71). He declared that so soon as it should become possible “at any place, and _in any prescribed manner_” (that is to say, whether by electric undulations or by mechanical undulations, as in the string of the toy telephone, or by any other means), “to set up vibrations whose _curves_ are like those of any given tone or combination of tones,” we should then receive the same impression as that tone or combination of tones would have produced upon us. So much for Reis’s principle of correspondence of undulations between the transmitter and the receiver; we have seen how clear and precise, yet how comprehensive it was, and how the general proposition necessarily included within itself, as an intermediate step, the particular minor proposition that the undulations of the current must also be in correspondence with the voice.