M. P. Tchebychef on a Modification of Watt's Parallelogram. 51 



triotism " added themselves to the exalted value which I attached 

 to his researches. I held, and still hold, him to be one of the 

 noblest workers of this age ; and my estimate of his labours is 

 not a shade lowered by this other conviction, that he must, in the 

 history of science, accept Dr. Mayer as his scientific brother, — 

 that the Thinker and Generalizer is fit to stand, and will be caused 

 to stand, beside the Experimental Philosopher. To permit Dr. 

 Mayer to remain in the position in which I found him, would be 

 to fasten on myself the guilt of that neglect of which the plea 

 of ignorance alone acquits his contemporaries. In every sen- 

 tence that I have written in his favour I have felt that strength 

 which perfect single-mindedness can alone impart, and, fearless 

 alike of his fate and of my own, I now commit his reputation, 

 and my conduct concerning it, to the impartial judgment of 

 mankind. 



Royal Institution, June 1864. 



V. On a Modification 0/Watt's Parallelogram. 

 By P. Tchebychef*. 



THE mechanism known as Watt's parallelogram furnishes a 

 solution of the following practically important problem : 

 To produce, to a sufficient degree of approximation, rectilineal 

 motion by a combination of circular motions. 



The degree of precision attainable by contrivances of this kind 

 depends obviously upon the number of its disposable elements, 

 and in this point of view the parallelogram of Watt is far from 

 being satisfactory. In its structure, for instance, two rods more 

 are employed than in the mechanism a fleau, and yet the mo- 

 tion produced is the same. In attempting to produce approxi- 

 mate rectilineal motion by means of either of these two contri- 

 vances, the motion really attained is an oval one, which has at 

 most live elements in common with the desired rectilineal motion. 

 Now this degree of approximation is unquestionably small when 

 we take into consideration the degree of complication presented 

 by Watt's parallelogram. The latter, as is well known, pos- 

 sesses four disposable elements, each of which, as therein em- 

 ployed, furnishes two arbitrary parameters — its length and its 

 direction. Seeing, therefore, that, on the whole, eight parame- 

 ters are involved, we are justified in seeking a contrivance of the 

 same degree of complexity as Watt's parallelogram, but capable 

 of furnishing a much more rectilineal motion — one, in fact, 



* From the Bulletin de V 'Acad. Imp. des Sciences de St. P&ersbourg, 

 vol. iv. p. 433. 



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