COTTON-SPINNING MACHINERY. 307 



However^ to make the nature of the differential motions 

 more readily comprehended by persons wholly unac- 

 quainted with these compound motions^ I may take a 

 supposed case to illustrate them. Let a travelling car- 

 riage, drawn by horse or any other moving power, have a 

 common windlass fixed in it, with a rope wound upon the 

 barrel and extending thence some yards behind, let the 

 outer end of the rope be fastened to another carriage to be 

 drawn after the first by the rope j then it is evident that 

 the two carriages will move with the same speed so long 

 as the tow-rope continues without any change of length, at 

 whatever speed the first carriage be driven. But let a 

 man in the leading carriage have charge of the winch to 

 lengthen or shorten the rope (by winding it on or un- 

 winding it from the barrel of the windlass) ; then the rate 

 of taking up or giving out of . the rope will be the exact 

 measure of the difference of speeds of the two carriages at 

 each of the rates at which the leading one^ may be driven. 

 Let the one move, say, ten miles the hour, the other must 

 follow at the same rate whilst no change is made in the 

 distance between them ; but if the rope be wound up at 

 the rate of one mile an hour, or unwound at the same 

 rate, it follows that the speeds will respectively be as ten 

 to elevea, and as ten to nine miles per hour, — and so on 

 with every change made in the connecting link between the 

 two moving bodies. In this case the will of the man at the 

 winch regulates the differences of these principal moving 

 bodies. But again, the wheels of the two carriages may 

 be of different diameters, and then their rotative motions 

 will differ accordingly; and these revoh'ing speeds will 

 have their differences made to accord with the varying 

 motions of the carriages. Now such are the kind of 

 differences to be provided for in the bobbin and fly frame. 

 The invention of Mr. Houldsworth provides a correct 

 substitute for such giving and taking of a rope to main- 



