226 Royal Society. 



curve represents the effect on the ear of a diatonic semitone, while 

 the ratio 81 to 80 would give that of the comma. In both these 

 curves, and more especially in the latter, the beats which would 

 ensue on actually sounding the two tones together are shown with 

 remarkable distinctness. 



As the machine is provided with a set of change-wheels, many 

 different curves can be produced, while the form of each can be 

 more or less changed by altering the relative positions of the 

 cranks before bringing the idle wheel into gear. It is also possible 

 to obtain very large values of m and n in the above equation by 

 using two idle wheels on the same axis, which shall come into gear, 

 the upper one with the wheel on the one spindle, the lower one with 

 that on the other. 



Thus, suppose A and B are the numbers of teeth on the spindle- 

 wheels respectively, C and D those on the idle wheels, and let A 



gear with C and D with B ; then — = — — . Now, by properly 

 choosing the four wheels, large values of m and n may be obtained. 



If, for instance, A=81, B= 80, C= 55, andD=27, — = ; this 



n 2187 



2 

 ratio being nearly = -, the corresponding curve will represent the 



effect of an octave slightly out of tune. The period of such curves 

 as these being very long, it is necessary to have a good supply of 

 paper ; and this is arranged by carrying a reelful on the horizontal 

 frame, from which it is slowly unwound between the rollers. The 

 rate at which this takes place has a good deal of influence on the 

 form of the resultant curve ; the slower it is, the more compressed 

 will the latter appear. Instead of using paper, the curves, pro- 

 vided the periods are short enough, may be drawn on slips of black- 

 ened glass, which can be carried along between the tapes connecting 

 the rollers ; they can be at once placed in a lantern and thrown on 

 a screen. 



The width of contour of any curve depends on the radii of the 

 cranks : these may have any value between and half an inch ; and 

 therefore the limit of possible width at any part will be two inches ; 

 so also, by altering the radii, a series of curves may be produced 

 corresponding to the consonances of tones not of the same inten- 

 sities. Since the maximum width of any curve will be double the 

 sum of the radii of the cranks, the paper is cut to a width of two 

 and a half inches, within which all curves which can possibly be 

 drawn will be comprised. 



The instrument is constructed by Messrs. Tisley and Spiller, of 

 Brompton Eoad, to whom some improvement upon the original 

 model is due. 



