Fig. 526.

Fig. 527. Fig. 528.

The Chord dividers, fig. 527, an instrument suggested to the author by Mr. G. A. Ames, for prevention of error and convenience in measuring angles and in navigation problems has the two limbs continued beyond the center, the one terminating in an arc divided with the scale of chords, and the other in an index or reader; thus combining the dividers and the scale in one instrument. Fig. 527 is convenient for all the purposes to which the scale of chords is applied.

The loss of time between the main screw and the nut of the slide lathe or slide rest has been noticed, a similar interval occurs on reversing the direction of motion of change wheels; the effects of either are readily eliminated, but otherwise, they affect the traverse of the tool in screw cutting. An insidious, because less apparent but frequent loss of time, may also occur from separation between the work and its driver; arising in like manner from the reversal of motion, but also from some other causes; this cannot be neglected in accurate screw cutting and these matters may claim a few words.

The teeth of two wheels turning together interlace, one by one upon each, dropping in between two teeth of its neighbour. If their axes be too closely approached the wheels turn stiffly together, and when the axes of a train, or more than one pair are so placed, the motion is no longer even, but spasmodic and liable to jerks. The train of wheels for the slide lathe or spiral apparatus, carried by the arbors, mandrel and screw, it is sufficiently near to consider the circumference as exactly three times the diameter." Should greater precision be required, the proportion that the diameter bears to the circumference may be taken more nearly, as 7 to 22, or still more exactly as 113 to 355. The latter proportion gives a result within one millionth of the circumference ; and possesses the advantage of being easily impressed on the memory, by writing down the first three odd numerals in duplicate, and then bisecting the whole number thus written, 113/355, therefore require to be approached in gear to run easily one with the other, yet without unnecessary freedom or shake between their respective teeth. But, as their agreeable action arises from the small amount of play between the teeth of each pair of wheels, it follows that the contact of neighbouring wheels, is only between the right and left sides of their teeth respectively, when turning to traverse the tool in the one direction, and between their left and right or opposite sides when turning and traversing the tool in the reverse direction. The interval or loss of time, when by reversing the action the contact is transferred from the one to the other set of sides of the teeth, called "backlash," is more or less according to the distance between the axes of the wheels, and other circumstances, but it is always present and appreciable.

* At page 657, Vol. II., it is mentioned that "

When the apparatus is set in motion by the revolution of the mandrel; if the tool be supposed to have traversed the work and to have cut a screw line upon the cylinder, and then to have been returned from the left to the right to its starting point, for the purpose of retracing the same line. Then, on reversing the direction of motion, that the tool may a second time travel from right to left; the change in the revolution of the mandrel is communicated to the work, either on the instant, or so soon as the driver comes in contact with the carrier. But the same reversal of motion, has to take up the loss of time between all the wheels, and between the main screw and its nut, before the tool can start. The tool, remaining thus an instant motionless after the revolution of the work has commenced, cannot drop exactly into the groove it has previously cut on the work; but, it engages against one of its sides only, widening the interval at that spot, at the expense of the thread. As the traverse continues, the loss of time is gradually absorbed, while the groove already cut also assists the tool to glide into its correct line, and the piece taken out of the thread is partial and not continued along it. The spiral apparatus, when used for the coarser ornamental spirals, is driven from the slide rest screw, and the slide lathe sometimes from its main screw; the tool then moves an instant earlier than the work, producing the same effect.

The backlash from the wheels, and that of the nut and slide rest screw, is neutralized by invariably traversing the tool i back, a little distance beyond the commencement of the thread, previously to reversing the motion to recommence. The loss of time being then entirely absorbed, before the tool commences to cut. The tool is never reversed in direction while traversing the work; and all cuts are taken in one direction only, from right to left or from left to right, as the screw required may be right or left handed in thread.

Backlash arising from separation between the carrier fixed on the work and the driver of the running center chuck, is less readily avoided. The act of running back the lathe and slide rest, tends to separate the two, and the liability exists even when they are bound together by wire, or fixed to each other by some of the other methods already alluded to. Some amount of heat is always evolved in cutting a metal screw, and this expanding the length of the work, causes it to move with more or less friction between the two centers as the screw cutting progresses; from which increase after many cuts, there is a risk of the carrier and driver becoming slightly separated, even when attached. Their separation is also more likely to occur when most undesirable, towards the completion of the screw; for the latter, may then move so stiffly between the center of the popit head and that of the chuck, that perfect contact between the carrier and the driver may not arrive, until brought about by the resistance of the cut.