104 



NATURE 



\May 29, 1879 



A third method ^ is the photographing of the vibrations 

 of a disk set in vibration by the sound to be analysed. 

 The curves are drawn with great sharpness and seem to 

 offer the best means for pursuing this investigation. It 

 was the study of these photographs which led Prof. Blake 

 to consult with Prof. H. A. Newton, of Yale College, on 

 the possibility of producing similar curves by mechanical 

 means. Prof. Donkin, F.R.S., had described a machine 

 by which the combination of any tivo simple tones could 

 be drawn,2 but the apparatus was not available for more 

 complex combinations. The machine now to be described 

 was the result of this consultation. 



Fig. I represents the machine. A, A', A", A"', a'', A'', 

 are "f-shaped pieces of sheet brass, sliding between screws, 

 motion being given to each by a crank-pin entering a slot 

 cut in the cross-bar of the T- Each crank is driven 

 by a pulley which is set in revolution by a string passing 

 completely around it. The wheel b serves to return the 

 string to the tightening pulley, D, which gives or takes up 

 the " slack" when the crank-pulleys are changed. Firmly 

 attached to B, and revolving on the same axle, is a smaller 

 wheel which drives the roller feeding the paper on which 

 the curves are traced. To secure the necessary tightening 

 of the second string, the axle of b is inserted in the end 

 of a wooden bar which slides horizontally under the frame. 

 The strain given by D having tightened the string suffi- 

 ciently, this bar is clamped by the thumb-nut, f. 



The driving roller, G, is covered with sand-paper, and 

 the pressure of the companion roller, h, secures the feed 

 of the paper between them. A small brass vrheel, c, is 

 pressed by the spring of its steel axle on the middle of 

 the paper strip. It has a sharp edge, and prevents lateral 

 motion of the paper liable to result from friction of the 

 pencils. 



E, e', e"„ are strips of brass sliding between screws. 

 Each has a steel spring attached to it, to the end of which 

 a thick piece of brass is soldered. A hole through this 

 brass is tapped with a screw thread, into which the 

 pencils (or tubular pens) fit and are readily adjusted to 

 the desired height, e, k', and e'', have each a steel pin 

 projecting upward from their middle points. Similar pins 

 project from points near the ends of A, a', a", &c. 



A cross-bar connects the pins a', e", and a", the joint 

 at e" admitting simply of revolution, while at a' and A" 

 there are slots in the bar permitting both rotation and 

 sliding, a"', a'', and E, are similarly connected. A third 

 cross-bar connects e and E" with e', having slots at E and 

 e", and a simple rotary joint at e'. 



A is not represented as in action, in order not to com- 

 plicate the drawing and description unnecessarily. It 

 would be connected by a cross-bar with e', and a fourth 

 slider (e'") placed midway between A and E'. 



The operation is as follows : — Imagine a strip of paper 

 fed between the rollers and passing under the pencils. 

 The pulleys revolve by the action of the string, and their 

 cranks give the respective T's movements which are the 

 rectilinear components of the circular movements of the 

 crank-pins. A pencil attached directly to any one of the 

 X-s, would therefore draw on the paper a simple harmonic 

 curve,' whose "period" depends on the diameter of the 

 pulley, and whose amplitude depends on the length of the 

 crank-arm. The connection of the cross-bars with E and 

 e", compels these strips to perform movements which are 

 respectively one-half those of A''-f A"', and A" -j- a'. 

 Hence, from the pencil in e, we get a curve combining 

 A'" and A'i, but having ordinates of one-half their sum ; 

 from the pencil in E", a curve combining a" and A', in 

 like manner. Finally, the cross-bar connecting E and E" 

 determines a movement of e' which is one-fourth the sum 



' Silhmaris American Journal, vol. xvi., 3rd Series, July, 1878. 

 Nature, July 25, 187S. 



' 'RoyaXSocitty Froceedin£s, xxii. p. 196. British Association 'i^^/^W, 

 2I73, xliii. p. 65. 



3 This rnethod of drawing simple harmonic curves is due to Prof. E. C. 

 Pickering. See Journal, Frankhn Institute, vol. Ivii. p. 55. 



of the movements of the four T-s, and, therefore, E' 

 describes upon the paper the curve belonging to the 

 chosen relations of "period," "amphtude," and "phase." 



The relations of these three terms may be varied to any 

 extent (within practical hmits), and with great ease. The 

 accuracy with which a definite period may be obtained 

 without the use of gearing, is quite surprising. 



Specimens of the curves obtained are given in Fig. 2. 



4i 



Nos. I to 8 (inclusive) are combinations of the first four terms 

 of the Harmonic Series : — 



Ratios of vibration 



Amplitudes of vibration ... 



