ON GRAPHIC METHODS IN MECHANICAL SCIENCE. 417 



3. ' For testing locomotives and carriages. This only differs fi-ora 

 No. 2 in the clockwork, which is arranged to drive the paper at the rate 

 of about I inch per second for a short interval of time,' 



In the discussion which followed the reading of this paper Mr. Milne 

 explained instruments made by him for the same purpose ; Mr. Dawson 

 and M. Kapteyn also mentioned other instruments for a similar purpose. 

 Quite recently an account has been given by Mr. Yarrow, in a paper ' 

 read before the Institution of Naval Architects, of an instrument, called 

 by him the ' Vibrometer,' for investigating the results of a new method 

 of balancing marine engines in torpedo-boats. This instrument consists 

 of a drum provided with suitable clockwork, a.nd resting on a circular 

 plate. The circular plate is hung by three indiarubber suspenders to a 

 frame, which is rigidly connected with the hull of the boat. The circular 

 plate can slide freely up and down on three guides, and form part of this 

 frame. A pencil or style is attached to the frame, and placed in contact 

 with the clockwork drum. It is clear that since the pencil partakes of 

 any movement of the hull, while the barrel of the circular plate has a 

 free vertical motion, any up-and-down movement of the hull will be 

 recorded on the revolving drum, the axes of which are, of course, vertical. 

 By means of this instrument many important facts concerning the 

 vibration of the vessel were ascertained. 



g. Instruments for graphically recording the results of mathematical 

 operations have been frequently designed. In the year 1845 Mr. F. 

 Bashforth read a paper, an abstract of which appears in the British 

 Association report, and which he afterwards further expanded in a 

 pamphlet, and by means of lithographed diagrams explained the machine 

 itself. Concerning the action of the instrument mentioned in the 

 pamphlet ^ he remarks : — 



' Persons engaged in testing theory by experiment have frequently 

 derived great assistance from mechanical contrivances, which give rapid 

 and near approximations without the trouble in every separate case of 

 going through tedious multiplications and additions. The proposed 

 machine would be capable of giving the values of S {b cos (nft + a)} or of 

 tracing the curve p='2!,{b cos (nO + a)} , where n is any +ve or — ve, 

 integer or fraction. It might be employed to find the numerical roots of 

 equations, correct, probably, to two places of decimals, to trace curves 

 representing the intensities of the different kinds of light in the rings 

 given by polarised light, or to illustrate the effect of the several terms 

 (separately or together) of the value of u in the lunar theory. The 

 accuracy of the values given by this machine would very nearly corre- 

 spond to those of the slide rule — the first two figures would be corfect, 

 the third doubtful.' 



Probably the most important instrument of this class is the mechanical 

 tide-predicter, one form of which was constructed for the Tidal Committee 

 of the British Association. In this machine, which has been described ^ by 

 Sir W. Thomson (Lord Kelvin), there are ten shafts, giving respectively 

 the following tidal constituents : — 



' Evgineering Review, May 5, 1892. 



- 'Eeprint of a description of a Machine for Finding the Numerical Roots of 

 Equations and Tracing a Variety of Useful Curves.' By E. Bashforth, B.A. Cam- 

 bridge, Metcalfe, 1822. 



' ' The Tide-gauge, Tidal Harmonic Analyser, and Tide-predicter.' Min. Prac. 

 Inst. C.E., vol. Ixv. 1890. 



1892. ' E E 



