1874.] Composition of two Harmonic Curves. 199 



where a and b are the radii of the cranks, and a and /3 are dependent 

 on their relative inclinations to the above-mentioned vertical plane at 

 starting. 



As an example, suppose that a =b, while the ratio of m to n is as 2 to 1 ; 

 then the above equation will represent the curve of pressure for the octave. 

 Similarly, if m is to n as 16 to 15, the resultant 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, 0=55, and D = 27, - = ^L this ratio being nearly = ?, the 



n 



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 reel- 

 full 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 influ- 

 ence on the form of the resultant curve ; the slower it is the more com- 

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

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

 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 con- 

 sonances of tones not of the same intensities. 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 Road, to whom some improvement upon the original model 

 is due. 



