15)0 Theory of Continuous ('<i/<-ul<ttiny Mac/lines, fyc. [June 19, 



then a measure of the ratio of the increase of space to that of time, 

 and in the limit is a measure of their differential coefficient, that is 



(since v= ) a direct measure of the velocity of the moving body. 

 dt 



The author afterwards found that this idea had been suggested some 

 time previously by a correspondent in " Engineering." Quite recently 

 (May 24th) a speed indicator on this principle, but with a cone 

 instead of a disk, was exhibited before the Physical Society, and at 

 the same meeting the Secretary himself showed the disk and roller 

 speed indicator which he had re-invented. 



The disk and roller has, however, two kinds of defects, which 

 account for its practical failure for the foregoing purpose, and render 

 its accuracy as an integrator almost a matter of impossibility ; though 

 in the latter case the error for reasons which are explained is more 

 difficult to detect. These kinds of defects are : 



(1.) Those which are the mechanical result of the principle of action 

 itself; 



(2.) The limited range of action of the instrument. 



(1.) The very conditions under which the mechanism acts are con- 

 tradictory, and are shown to lead to three special defects : 



(i.) Grinding action between the edge of the roller and the face of 



the disk, 

 (ii.) Necessity for the application of force, in order to change the 



position of the roller, 

 (iii.) Error in numerical results. 



These defects are considered, and a modification of the disk-globe 

 and cylinder-indicator of Professor James Thomson, which was de- 

 signed to obviate them, is suggested for the converse process. 



(2.) The second kind of defect led the author to modify the disk 

 and roller, so that a range of action, in theory infinitely great, was 

 obtained. This is not so easy to use, the graduation of the scale 



having to be made according to an equation y= , instead of 



R x 



simply y=Rj!, as in the first form; but it was new, and led to the 

 fact being made clear that there was a close analogy between these 

 two forms and two forms of what may be called the " sphere and 

 roller mechanism," which with certain results were communicated 

 to the Physical Section of the Bristol Naturalists' Society in November 

 last. 



It was the endeavour to overcome the frictional defects of the disk 

 and roller which still remain in this form of mechanism, and to render 

 the application of the sphere and roller possible for practical pur- 

 pjses, that led to the investigation which forms the real subject of 

 the paper. 



