Fig. 415.
Work may be very securely fastened together by the employment of what are called differential screws, the principle of whose action may be explained with reference to [Fig. 415], which is extracted from “Mechanics.” It represents a piston head and piston rod secured together by means of a differential screw nut. The nut contains an internal thread to screw on the rod, and an external one to screw into the piston head, but the internal thread and that on the rod differ from the external one, and that in the head by a certain amount, as say one tenth of the pitch. The nut itself is furnished with a hexagonal head, and when screwed into place draws the two parts together with the same power as a screw having a pitch equal to the difference between the two pitches.
Fig. 416.
When putting the parts together the nut is first screwed upon the rod b. The outside threads are then entered into the thread in the piston c, and by means of a suitable wrench the nut is screwed into the proper depth. As shown in the engraving, the nut goes on to the rod a couple of threads before it is entered in the piston. The tightening then takes place precisely as though the nut had a solid bearing on the piston and a fine thread on the rod, the pitch of which is equal to the difference between the pitches of the two threads. [Fig. 416] shows its application to the securing of a pump plunger upon the end of a piston-rod. In this case, as the rod does not pass through the nut, the latter is provided with a cap, which covers the end of the rod entirely.
Fig. 417.
The principle of the differential screw may be employed to effect very fine adjustments in place of using a very fine thread, which would soon wear out or wear loose. Thus in [Fig. 417] is shown the differential foot screws employed to level astronomical instruments. c d is a foot of the instrument to be levelled. It is threaded to receive screw a, which is in turn threaded to receive the screw b, whose foot rests in the recess or cup in e f. Suppose the pitch of screw a is 30 per inch, and that of b is 40, and we have as follows. If a and b are turned together the foot c d is moved the amount due to the pitch of a. If b is turned within a the foot is moved the amount due to the pitch of b. If a is turned the friction of the foot of b will hold b stationary, and the motion of c d will equal the difference between the pitches of the threads of a and b. Thus one revolution of a forward causes it to descend through c d 1⁄30 inch (its pitch), tending to raise c d 1⁄30 inch. But while doing this it has screwed down upon the thread of b 1⁄40 inch (the pitch of b) and this tends to lower c d, hence c d is moved 1⁄120 inch, because 1⁄30 - 1⁄40 = 1⁄120.