Mr. Donkin on the Composition of two Harmonic Curves. 223 



that the portion transmitted through the reflecting layer shall be 

 incompetent to affect the flame. Then by the introduction and 

 withdrawal of the bat's-wing flame the two sensitive flames can be 

 rendered alternately quiescent and strongly agitated. 



An illustration is here afforded of the perfect analogy between 

 light and sound ; for if a beam of light be projected from B to F', 

 and a plate of glass be introduced at A, in the exact position of the 

 reflecting layer of gas, the beam will be divided, and one portion 

 will be reflected in the direction A F, and the other portion trans- 

 mitted through the glass in the direction F', exactly as the sound- 

 wave is divided into a reflected and a transmitted portion by the layer 

 of heated gas or flame. 



Feb. 19. — Joseph Dalton Hooker, C.B., President, in the Chair. 



The following communication was read :— 



"On an Instrument for the Composition of two Harmonic 

 Curves." By A. E. Donkin, M.A., F.R.A.S., Fellow of Exeter Col- 

 lege, Oxford. 



The interest in such compound curves lies in the fact that, as a 

 simple harmonic curve may be considered to be the curve of pres- 

 sure on the tympanic membrane when the ear is in the neighbour- 

 hood of a vibrating body producing a simple tone, so a curve com- 

 pounded of two such simple harmonic curves will be the curve of 

 pressure for the consonance of the two tones which they severally 

 represent, and thus the effect on the ear of different consonances 

 can be distinctly represented to the eye. 



If the motion of a point be compounded of rectilinear harmonic 

 vibrations and of uniform motion in a straight line at right angles 

 to the direction of those vibrations, the point will describe a simple 

 harmonic curve. 



Thus a pencil-point performing such vibrations upon a sheet of 

 paper moving uniformly at right angles to their direction would 

 draw such a curve. 



The same kind of curve would also be drawn by keeping the 

 pencil fixed and by giving to the paper, in addition to its continuous 

 transverse motion, a vibratory motion similar and parallel to that 

 which the pencil had ; and if the motion of the latter be now r re- 

 stored, a complicated curve will be produced wiiose form will depend 

 on the ratio of the numbers of vibrations in a given time of the 

 pencil and paper, and which w r ill be the curve of pressure for the 

 interval corresponding to this ratio. 



The manner in which these three motions are combined- in the 

 machine is as follows : — Tw<o vertical spindles, A and B, revolving 

 in a horizontal plate carry at their lower ends each a crank, C and 

 D, and at their upper ends each a wheel cut with a certain number 

 of teeth ; these two wheels can be connected by means of an inter- 

 mediate one, as is seen in the figure ; and since either wheel of the 

 pair can be replaced by another with a different number of teeth, the 

 relative angular velocities of the spindles can be regulated at plea- 

 sure. The paper upon which the curve is to be drawn is carried upon 



