ON GRAPHIC METHODS IN MKCHANICAL SCIENCE. 431 



diagram. The two defects in this class of iustrument are : first, the 

 comparatively small scale of the recorded results ; and, secondly, the slight 

 variation which occurs owing to different kinds of paper being used for 

 diagrams on which the planimeter has to operate. A class of instruments 

 has therefore been invented called precision polar planimeters, the first 

 attempt in this direction being by Mr. Hohmann, of Bamberg, in 1882, m 

 coujunction with Coradi, of Zurich. In this planimeter what corresponds 

 to the rolling wheel of the Amsler planimeter works on a prepared 

 disc, which in°turn is driven by rollers from the paper, so that the result 

 is very much magnified. At the same time the roller itself always works 

 upon the same surface. A number of such instruments have since been 

 devised, many of which were exhibited among the scientific instruments 

 at the international Inventions Exhibition at London, 1885, and the 

 more important have been described in a paper on integrators by the 



In all these planimeters the roller slips over the surface, but there is 

 another totally different class of instrument in which no slipping of the 

 roller as it moves to and fro is supposed to take place. Such a plani- 

 meter was suggested by the late Professor Clerk Maxwell. ^ On such a 

 principle also the disc, globe, and cylinder integrator of Professor James 

 Thomson has been designed. This mechanism has been used by Sir 

 William Thomson in his tide- calculating machine already referred to, 

 and obtains the harmonic analysis of the tides for subsequent operations 

 with the tide-predicter. 



Instruments of this class have been designed by Professor Vernon 

 Boys, Mr. Abdank Abakanowicz, and the writer. These instruments 

 are referred to in the paper by the writer already mentioned, and also m 

 a recent treatise on ' Integraphes.' ^ This treatise commences with an 

 explanation of the properties of the integral curve, and then proceeds to 

 describe integrators in which the area of a figure is measured by the 

 height to which a roller rises in the curve of its movement round the 

 periphery of the curve to be integrated. A number of integrators, or 

 instruments for drawing an integral curve, designed by Mr. Boys, M. 

 Zmurko, and Mr. Abdank Abakanowicz, are then described. The work, 

 which contains 150 pages, then proceeds to describe the application of 

 these instruments to various mechanical problems, such as bridges, earth- 

 works, naval arcliitecture, electric machines, and for obtaining the work 

 performed by engines. ^ . , . , ,, 



A new planimeter is made by Messrs. Richard Freres m which there 

 is no contact between the paper and the totalising mechanism, but 

 which employs the old principle of the disc and roller. The following 

 explanation is supplied by Mr. Berly. Messrs. Richard Freres' manager :— 



' The surface is the function TetZa;, e being the ordinate, x the abscissa. 

 The planimeter executes exactly this sum of differentials ; it is composed 



' 'Mechanical Integrators,' by Professor Hele-Shaw. Min. Proc. Inst. C.E., vol. 



^^^3 ""Description of a New Form of Planimeter, an Instrument for Measuring the 

 Areas of Plain Figures Drawn on Paper,' by James Clerk Maxwell. Trans. Uoyat 

 Scottish Soc. of Arts, 1855. . .. i, 



3 Les LitrrfrapJies. La Courhe integralc et ses Ajiplicatiom, par AbdanK ADaKa- 

 nowicz. Gautliier-Villars, Paris, 1880. 



