This contrivance consists in the use of two screws, the threads of which may have any strength and magnitude, but which have a very small difference of breadth. While the working point is urged forward by that which has the greater thread, it is drawn back by that which has the less; so that during each revolution of the screw, instead of being advanced through a space equal to the magnitude of either of the threads, it moves through a space equal to their difference. The mechanical power of such a machine will be the same as that of a single screw having a thread, whose magnitude is equal to the difference of the magnitudes of the two threads just mentioned. Thus, without inconveniently increasing the sweep of the power, on the one hand, or, on the other, diminishing the thread until the necessary strength is lost, the machine will acquire an efficacy limited by nothing but the smallness of the difference between the two threads. This principle was first applied in the manner represented in _fig. 142._ A is the greater thread, playing in the fixed nut; B is the lesser thread, cut upon a smaller cylinder, and playing in a concave screw, cut within the greater cylinder. During every revolution of the screw, the cylinder A descends through a space equal to the distance between its threads. At the same time the smaller cylinder B ascends through a space equal to the distance between the threads cut upon it: the effect is, that the board D descends through a space equal to the difference between the threads upon A and the threads upon B, and the machine has a power proportionate to the smallness of this difference. Thus, suppose the screw A has twenty threads in an inch, while the screw B has twenty-one; during one revolution, the screw A will descend through a space equal to the 20th part of an inch. If, during this motion, the screw B did not turn within A, the board D would be advanced through the 20th of an inch; but because the hollow screw within A turns upon B, the screw B will, relatively to A, be raised in one revolution through a space equal to the 21st part of an inch. Thus, while the board D is depressed through the 20th of an inch by the screw A, it is raised through the 21st of an inch by the screw B. It is, therefore, on the whole, depressed through a space equal to the excess of the 20th of an inch above the 21st of an inch, that is, through the 420th of an inch. The power of this machine will, therefore, be expressed by the number of times the 420th of an inch is contained in the circumference through which the power moves.