With 3 and 4 sheaves, the weight lifted is the sum of the strains on the seven ropes, b, c, d, e, f, g, h, or 8507 lbs.; but the weight due to 1960 lbs. at a, is 1960 × 7 = 13720 lbs.: hence 850713720 62, or 62 per cent. is utilised, and 38 per cent. wasted.

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(119.) These ratios may be applied generally with approximate accuracy to average pulley-blocks with ropes of other sizes, and we have thus obtained Table 26: thus taking the working strain on common hand-laid ropes from col. 5 of Table 24, we obtain col. 4, and from that, and the theoretical power, combined with the duty, we obtain cols. 5 to 8 in Table 26. Thus for a rope 2 inches girth without any pulley the direct safe load by col. 4 5 cwt.: with 1 pulley, 5 x .88 4.4 cwt.; with 2 and 1 sheaves, 5 × 3 × ⚫78 11.7 cwt.; with 3 and 2 sheaves, 5 × 5 ×·69 = and with 4 and 3 sheaves, 5 x 7 × ·62

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17.2 cwt.;

21.7 cwt., &c.

TABLE 26. Of the SAFE LOAD for PULLEY-BLOCKS, allowing for RIGIDITY of the ROPE, and FRICTION of PIN.

(120.) When pulley-blocks can be so arranged that the power shall act upwards instead of downwards, the last pulley can be dispensed with and economy of power effected. For example, if in Fig. 27 the rope b is continued to Q, the pulley k is useless, all the strains on the different ropes remain as before, therefore the weight lifted is the same, but instead of 1960 lbs. as at a, we now require 1727 lbs. only, the weight due to which is 1727 × 7 = 12089 lbs.; hence 85071208970, or 70 per cent., is utilised, and 30 per cent. lost, whereas in (118) we had 62 per cent. utilised: 8 per cent. being thus saved.

(121.) "Strength of Wire Rope."-Wire ropes are very extensively used for winding purposes in collieries, &c., where the principal objection to them, namely, their great rigidity, is easily overcome by the use of very large pulleys. The breaking weight and safe working load of round and flat iron-wire ropes shown by Table 27 are given by Messrs. Newall and Co.: it will be observed that they fix the working load of round ropes for inclined planes and other ordinary work at 4th of the breaking weight, and for flat ropes (111) used in pits, hoists, &c., where life depends absolutely on the strength of the rope,

TABLE 27.-Of the STRENGTH of IRON WIRE ROPES.

only 4th of the breaking weight, agreeing with (923) and Table 141, which gives in col. 3, for an intermittent dynamic load of the statical breaking weight, which, with Factor 3, becomes

3th.

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(122.) "Strength of Pump-rods."-By Table 1 the mean tensile strength of welded wrought iron 47,266 lbs. per square inch breaking weight with dead load, equivalent by the "ratios" in col. 3 of Table 141 to 47266 × = 15755 lbs. intermittent dynamic breaking weight. Table 137 gives factor of safety 3, hence we obtain 15755 ÷ 3 = 5252 lbs. per square inch working strain: taking it in round numbers at 5000 lbs., we obtain col. 2 of Table 28. Fig. 28 gives the form and proportions of socketjoints for pump-rods, which have been found to work well in practice, and the table gives the sizes of socket, &c., &c., for different diameters from ğ inch to 2 inches.

TABLE 28.-Of the PROPORTIONS of SOCKET-JOINTS for WROUGHTIRON SINGLE-ACTING PUMP-RODS.

Table 29 gives the strain on single-acting pump-rods in practice: col. 10 shows that it seldom exceeds 5000 lbs. per square inch, but at Trafalgar Square it was 6600 lbs., the result being that fractures were frequent.

For double-acting pump-rods the strain is not only intermittent but alternate also, and being accompanied by more or

G

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less violent shocks from the motion of the water, the factor of safety 3, by col. 5 of Table 141 becomes 3÷ 18; hence we have 47266 18 2626 lbs. per square inch working load.

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CHAPTER V.

ON THE SHEARING STRAIN.

(123.) "Single and Double Shear."-When two plates are connected by a rivet or pin, as at A in Fig. 6, and the rivet is severed by a tensile strain applied to the plates, we have a case of single-shearing, and it has been found that the strain is simply proportional to the area sheared, being independent of the form of the pin in cross-section, whether round, square, &c.

In Fig. 8, or at C in Fig. 6, we have two side plates and one central one: it is obvious that to shear the pin a double area has to be severed requiring double strain for the double shear.

Mr. E. Clark made direct experiments on the resistance of 7-inch rivet-iron to single and double shearing: he found that the

tons per square inch. Double-shearing gave as the result of eight experiments :-

tons. The mean of the two = 23.12 tons per square inch: the direct tensile strength of the same iron was 24 tons, from which it appears that the shearing and tensile strains are practically equal to one another, and this is admitted as a general rule: it requires, however, some modification as applied to rivets in joints. It appears that in the process of riveting red-hot in the