46 REPORT — 1873. 



tlie ratio of the numbers of vibrations in a given time of the pencil and paper, and 

 which will be the curve of pressure for the interval corresponding to this ratio. 

 The way in which the machine combines these three motions is as follows. There 

 are two vertical spindles capable of revolving in a horizontal plate. At the lower 

 end of each a crank is fixed ; and at the upper end of each a toothed wheel can be 

 screwed on : this pair of wheels can be connected by a third intermediate one. 



The paper upon which the curve is to be drawn is carried upon a rectangular 

 frame, capable of sliding horizontally up and down. The frame has a pair of hori- 

 zontal rollers at each end, between which the paper passes as the rollers turn ; and 

 a uniform motion is given to them by means of a long pinion working into the 

 teeth of a wheel fixed on one of them, and up and down which the frame slides. 

 This long pinion is turned by one of the vertical spindles. A connecting-rod is 

 carried from the crank of this spindle to the frame, by means of which a vibratory 

 motion is communicated to the latter, which motion, though not truly har- 

 monic, is, owing to the length of the connecting-rod and small radius of the 

 crank, quite sufficiently so for practical purposes. A similar and parallel motion is 

 given to a small glass pen Ijy means of a connecting-rod from the other crank. 

 This pen is so arranged as to rest upright with its point upon the paper. If the 

 intermediate wheel be now put into gear with those on the spindles, and either of 

 them tm-ned by a winch provided for the pm'pose, a curve corresponding to the 

 ratio of the numbers of teeth on the spindle-wheels will immediately be dra'wn. 



The general form of equation to the curves which the instrument can produce 

 will evidently be 



y=a sin {jnx-\-a)-\-h sin (/M'-|-i3). 



Here a and h are the radii of the cranks, which can be altered at pleasure from to 

 half an inch ; in and n are limited by the numbers of teeth of the wheels with which 

 the instrument is provided, while a and /3 depend on the phases of the cranks, i. e. 

 the relative position they are in with respect to the vertical plane passing through 

 their axes when the intermediate wheel is brought into gear with them. 



As an example, by taking 7h = .54, «=27, « = J=half an inch, the curve drawn 

 will be that corresponding to an octave. Substituting a wheel of 55 teeth for that 

 of 54, the curve alters its form to that representing an octave out of tune. Again, 

 the numbers 48 and 45, which have the ratio \j, woidd give the curve corresponding 

 to a diatonic semitone. The form of this curve, as of all others where the ratio 

 approaches unity, shows very distinctly the beats which would ensue upon sotmding 

 the corresponding consonance. 



Since it is possible to vary the radii of the cranks at pleasure, the curves corre- 

 sponding to the consonance of two tones of unequal intensity can also be drawn. 

 The length of paper within which the period of any curve is contained depends on 

 the rate at which the rollers tm-n. Since this can be regulated at pleasure, by means 

 contrived for the purpose, the curves may be either extended or compressed ; that 

 is, the period may be made either long or short. The general form of any curve, 

 however, is better seen in the latter case. The maximum width of contour in any 

 curve is equal to twice the sum of the radii of the cranks. Thus when these are 

 each half an inch, the curve will be two inches wide. 



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

 to whom several improvements on the original model are due. 



On an Improved Form of Aneroid for determining Heights, with a means 

 of adjusting the Altitude-scale for various Temperatures. By Rogers 

 Field, B.A. 



The author begins by stating that the object aimed at in designing this improved 

 form of aneroid was to simplify the correct determination of altitudes in cases such 

 as ordinarily occiu- in England, and that the instrument is therefore arranged to 

 suit moderate elevations, say of 2000 feet and under, and is not intended for consi- 

 derable elevations. 



The table which is adopted in graduating the aneroid described is that given 



