for resolving Transcendental Equations. 439 



to that with which the latter arm itself revolves, it being under- 

 stood that the point of attachment of the center B is to be capable of 

 adjustment to a greater or less distance from C; a condition which 

 excludes the use of toothed wheel work. The following is the 

 simplest construction which has occurred to me for accomplishing 

 this purpose. 



(23.) The horizontal index axis C is surrounded by a grooved 

 wheel ghi, (figs. 4, 5,) which lies behind the index plate (not re- 

 presented in those figures) and the cross-piece and slider, and is 

 not attached to the axis so as to turn with it, but on the con- 

 trary is fixed to the index plate by screws so as to prevent all 

 rotation. The end f of the cross-piece is penetrated by an axis,/ 

 seen in projection in tig. 5, but lengthwise in fig. 6, whose ex- 

 tremities (to avoid shake and loosening) are pivoted in a bifurcated 

 and recurved prolongation of the cross-piece, which is seen in 

 fig. 6 at ef. This axis carries on it two wheels also grooved, cd, c'd', 

 both firmly united to the axis, and therefore incapable of moving 

 unless together as one wheel. A string or band passes round the 

 groove in gh and cd, so that when the axis C is made to revolve, 

 and therefore the wheel erf is carried round gh, the latter remain- 

 ing immoveable, the relative rotation of the one wheel about the 

 other will wrap and unwrap the string round the groove gh, and 

 thus produce a rotation of the wheel cd on its axis f, just as it 

 would do if all the rest of the apparatus stood still, and the wheel 

 gh alone was turned the other way round the axis C. Thus a 

 rotation equal and contrary to that of C, or, if the wheels/* h, cd, 

 be of unequal size, in any constant ratio to the latter rotation, is 

 communicated to the wheels cd, c'd. From the latter of these 

 let a string be led round a groove in the wheel ah, whose axis 

 is the pin B on which the second slider revolves, and which 



