62 Mr HOLDITCH, ON ROLLING CURVES. 



No continuous motion of B can therefore be derived from that of 

 A, if they be continuous curves, unless their outlines be treated like the 

 pitch lines of ordinary wheels, and be indented with small teeth at 

 regular distances; these teeth, as in the usual forms, projecting nearly 

 as far beyond the pitched line or circumference as they extend within 

 it. If this be done, it will be found that the circumference of A will 

 retain its hold on that of B in all positions, as well on the receding 

 as on the advancing sides of the curve. A continuous uniform rotation 

 of one curve will produce a rotation of the other, not uniform, but 

 continually varying in its angular velocity, as the ratio of the radius 

 of A to that of B; this becomes then a commodious contrivance for 

 converting an equable angular velocity into an unequal one, and is 

 sometimes so used by Mechanists. Fergusson's well-known Cometarium 

 was constructed on this principle: it is to be found in use in some 

 silk machinery, where it is introduced for the purpose of correcting the 

 unequal action of the common excentric in laying the silk upon the 

 bobbins; it has also been used by Messrs Bacon and Donkin, in their 

 printing machinery. I am informed by Professor Willis, who drew my 

 attention to the subject of these curves, and furnished me with the 

 above practical information, that the copious collections of Messrs Lanz 

 and Betancourt, and that of Borgnis, furnish no example of the appli- 

 cation of rolling curves to the purposes of machinery ; which may there- 

 fore be considered to have been unknown to them. 



When two such curves roll on each other, let r be the distance of 

 their point of contact from the centre of rotation of the first curve, 



and the angle made by r with a fixed radius; then -r— is the tan- 

 gent of the angle the curve makes with r\ and r t and 0, being corre- 

 sponding quantities in the second curve, ^— l is the tangent of the 



angle it makes with r t , and as r and r t are in the same straight line, 

 and the curves must have a common tangent at the point of contact, 

 these two angles must be equal, and 



rd9 rd6 i 

 '-' dr ' ' dr.' 



