1879.] 



Studies in Acoustics. 



361 



1 oo 



2 o 



a J 



Juh— (gut), 

 aw — (law). 



3. . . , ah % 



a — (bad). 



4. 



5 e 



. All the subsidiary vowels, such as uh, aw, a, take up intermediate 

 positions in this scale, so that, in fact, we may say that there is a 

 vowel spectrum, in which the different sounds merge into each other 

 by almost imperceptible gradations, and hence, probably, the difference 

 in dialectical pronunciation. 



11. In the following investigation, a method opposite to that of 

 Messrs. Fleeming Jenkin and Ewing has been adopted, i.e., the 

 question has been attacked by the method of synthesis. It has been 

 assumed that vowels are compounded of a prime sound and certain 

 upper partials, and the number of these partials has, for convenience, 

 been taken as 8, although there are many more. Indeed, we have 

 taken in some cases, the 10th, 12th, and 16th. Now, since each 

 partial can be considered as a simple harmonic curve, if we assume 

 the pitch of a prime to be constant, then it would be possible, by 

 means of a machine, to represent and vary each partial in phase and 

 in amplitude. For this purpose an instrument was constructed, which 

 we call " the synthetic curve machine," in which a number of toothed 

 wheels, A, B, C, D, E, F, Gr, H, &c. (figs. 3 and 4) are mounted on 

 steel pins or axes rigidly fixed on a board, so that they will revolve 

 together, and the numbers of their teeth are so calculated that 

 during one revolution of the wheel A, B will make two, C three, 

 D four, E five, F six, Gr seven, H eight revolutions, and so on. The 

 wheel I has, on its prolonged axis, a small crank, by means of 

 which the whole system of wheels can be rotated. On the sam& 

 axis is a pinion I', gearing into the wheel J, which, by means of a 

 chain T, gives motion to a sliding table R. Each head of the pins 

 on which the eight wheels revolve, has, in its centre, a small pit or 

 hollow, in which rest the pointed ends of eight steel rods (one of 

 which B' only is represented in fig. 4), held in position by eight 

 springs b. To the rod on the wheel A is attached, near its point, one- 

 end of a silken thread V, passing over the roller N', the other end 

 being attached to the rod on wheel B, The rods on wheels C and D, 

 E and F, Gr and H are similarly connected. The four rollers N" are 

 mounted on two levers U and IT, and these are connected by links to 

 the lever V, which is finally linked to the lever P. This lever P is 

 pivoted at p, and by means of the spiral spring S keeps the levers, 

 links, and silk threads in a state of tension. On the longer end of 

 the lever P is pivoted another lever 0, which carries at its shorter end 



