allowed, but for a rush of say 5,000 feet, some increase upon the acknowledged minimum is desirable in the interests of durability, although efficiency may remain unaffected. For example, the pulleys used upon the high speed engine running at 7,000 feet are just under 55 diameters, otherwise the driving might have proved less favorable.

ARC OF CONTACT, SLACK ABOVE.

Before dismissing the consideration of pulley diameters, it will be well to notice another phase of the same question, viz: that which deals with the arc of contact.

It needs but little reasoning to prove that rope contact reaches its zenith when both pulleys are equal in size, but when unequal the utmost quantity realizable is that carried by the smallest pulley whether it be driver or driven. The full value of this assessment however, also depends upon centre distances, as may be readily inferred by reference to the geometrical formula, Figure 18.

FIGURE 18.-ARC OF CONTACT, SLACK ABOVE.

First measure the length of the two radii crossing at E from

A to D off point B, and from B to C off through the centre at A gives F E.

point A. A line carried The line A H is gained

140°

by taking the vertical of the top pulley line, while equally dividing the angle A H E by C produces the angle F AG which represents an arc of 175 degrees. By bringing the small circle to the second position and repeating the same formula the arc FAG 2 is constructed and gives only 146 degrees. (164 degrees is an error).

ARC OF CONTACT, SLACK BELOW.

The formula is somewhat altered in order to ascertain the arc of contact for any distance of centres with slack below. Therefore, mark the distance from A to D and B to Cat E which gives the curve radius for the under slack and constructs the

E

FIGURE 19.

angle FA G by the lines E F and A G, the latter vertical with the upper line over top of circle, thus declaring an angle of 140 degrees.

This formula will be found useful for ascertaining the depths of drives by what may be termed the ultimate slack.

Generally speaking it is advisable to discount the transmitting value of the ropes by the amount of difference between the actual arc of contact and 170 degrees, upon which the power table on pages 362 and 363 is based, but when the pulleys are comparatively large, these differences may be neglected.

For evidence of the fact that by adding sufficient rope to make up for deficient contact, driving may be successfully accomplished when pulleys are almost touching; we need only

refer to the case of an engine in Dundee, from which spur gear was removed and rope pulleys fixed upon the same centres, permitting a clearance of only eight inches between the rims, 360 horse power is thus comfortably transmitted with sixteen ropes 134 inches diameter. At a mill in the north of France the pulleys are so close that a finger would scarcely pass between them.

TRAILING SPAN OF ROPES.

The arc of contact is also affected by the position occupied by the trailing span of the ropes which when above the pulleys undoubtedly gives the maximum bearing surface. This position is not always attainable, nor is it under all circumstances desirable. For example, an erractic delivery of power or variable load may set up oscillations in the responsive ropes of such

FIGURE 21.-TRAILING SPAN.

violence as to fling them entirely off the pulleys. Now if the direction of rotation is so arranged as to bring the trailing span below the pulleys, any tendency on the part of the ropes to wander from their appointed track is held in check by the pull on the tight side, while gravitation tends to control the vibrations on the slack side.

ing this is to run them through a wooden guard or grid. The construction need not be very elaborate and the frame work may be made of ordinary timber securely bolted together, so as to rigidly hold the oaken blades corresponding to the number of ropes, plus one. The blades are four to six inches wide and have rounded edges. The guard should be fixed fairly near the driven pulley, but actual distance can be best arranged after making practical trials.

LONG CENTRES.

The contiguity of rope pulleys just mentioned gives rise to suggestions bearing upon the opposite extreme, that is, as to the greatest distance at which power many be transmitted with unsupported ropes. Again referring to the diagram Figure 21, it will be readily observed that in under driven installations

FIGURE 23.-TOWER OF ROPE DRIVE.

centre distances are governed by the size of the pulleys employed, and should allow sufficient clearance between the ultimate slack of the trailing span (say about 10 per cent. of the centres) and the tight portion of the ropes.

Over driven installations with slack below, obviously permit a greater latitude, and centres may be, in fact are, pretty successfully extended to distances of overside 100 feet, without intermediate support. In lengthy drives of this sort, it is however,