the change gears travelling with it. For wheels of over 8 ft. to 10 ft. the base and the table go in the floor, and the horizontal arm is removed from the top of the pillar, and bolted to the table. In this way provision is made for wheels from 12 ft. to 14 ft. in diameter. For wheels over these sizes the arm is bolted by its flange to a flange on an extension slide, which is bolted to the table. The change wheels are disconnected, and reconnected as required. See Bevel Gears Machine-Moulded, Spur Gears

-Machine-Moulded.

In reference to the methods of withdrawing blocks, these include vertical, horizontal, and diagonal, or angular lifts. By far the largest numbers are lifted vertically. All spur blocks are lifted thus, so are those for racks. All bevel wheel blocks can be lifted similarly. But those for helical spurs, and bevels, and for worm, and screw or angle wheels cannot be withdrawn bodily upwards. They can be, and are, drawn horizontally bodily. But the method is clumsy, and is rather of the nature of a makeshift, because so heavy a mass must be moved to effect this. In Scott's machine the whole horizontal arm has to be moved. In the table and jib machines the whole jib has to be moved. There are stops used for resetting the block to correct radius, but the method is not satisfactory, being wasteful of time and labour, and liable to cause slight errors. Then there is the desirability of a slide for angular withdrawal, useful in the case of helical bevels. Generally, therefore, a convenient compromise is effected by dividing the tooth block itself in such fashion that a portion is withdrawn vertically by the machine slide, and a portion or portions are withdrawn subsequently by the hand, in a horizontal, or diagonal direction, as is convenient. The portion lifted vertically forms no portion of the actual wheel, being a backing or support only for the teeth, the portions withdrawn subsequently are the teeth themselves. There are many ways of jointing adopted. See Helical Gears.

In order to avoid the necessity for jointing blocks in this way, which is, however, often convenient for other reasons than that of facilitating withdrawal, Messrs Buckley & Taylor's special carrier was designed. This

permits of the withdrawal of a block either horizontally, or at any angle. It is bolted to the machine slide by a piece which terminates at the bottom in a disc with curved slots, on which the plate, with vee'd edges can be set, and tightened at any angle. The slide is fitted to this with a setting-up strip, and is traversed along it by means of a handwheel and screw. The carrier is hinged, so that it can be set and tightened in any position.

Gear Wheels-Strength of. The strength of wheels is estimated by two methods—one as that necessary to sustain a dead load, the other as that required to transmit a definite amount of work, as HP. In the first case speed is not estimated, in the latter it becomes a vital element in the calculation. If a wheel is revolving very slowly, dead load alone need be considered. If a wheel is revolving rapidly, the HP. transmitted is, as in the case of rapidly moving bodies, the convenient unit of work on which to base calculations.

A

Fig. 93.-Tooth Loaded as a Beam.

If the strength of teeth is estimated to resist a dead load simply, they are regarded as cantilevers, or beams, fixed at one end, and loaded at the other, Fig. 93. The strength of such beams varies directly as the breadth B, as the square of the depth or thickness t, and inversely as the length L. Therefore it is to the depth t that increase of strength is chiefly due, and this in wheel teeth equals the thickness of tooth there, and is proportionate to the pitch. The strength mainly increases as the square of the pitch, because L and B are usually made proportionate to the pitch. So, conversely the pitch is proportionate to the square root of the pressure. The formulæ become therefore—

W being the breaking load in lb., and M being a constant multiplier representing the unit strength of the material used for the gearing, and being equivalent to the breaking strength in lb. of a cantilever of that material, 1 in. square, and 1 in. long; taken at 6,000 lb. in cast iron.

Since the curvatures of teeth vary much, and ast measured at the root will vary slightly with variations in diameters of the wheels, it is usual in the formulæ to reckon t as being equal to the thickness on the pitch line, because that is then an invariable proportion, 48, of the pitch; being less than 5 pitch to allow for flank clearance in cast gears. Also, to make allowance for wear, it is properly taken as less than this, or as suggested by Professor Unwin, 36 pitch. The pressure is only concentrated on the extreme end of the length L at certain periods, that is as the teeth are entering, and leaving gear. At all other times the stress is less. But in basing the formulæ on the first contingency the position of greatest stress is taken, otherwise the formule would not be reliable.

Excessive increase of breadth B may not tend directly to increase of strength. For here the inaccuracy of practice comes into play. The teeth may be and often are not at precise right angles with the wheel faces, or the wheels may not be hung precisely true on their shafts. For these reasons some formulæ assume that the load is concentrated on one corner only of the teeth, tending to break off a triangular prism, as at A, Fig. 93. Wheel teeth do often break in that fashion, showing that the load is concentrated on the corner. But they as often break nearly straight across, in a more or less jagged irregular fashion. Moreover, there is less excuse now for accepting this contingency, because machine-moulded gears are practically free from error; and in pattern gears only those of exceptional width should be very much tapered. Then they can, in many cases at least, be so hung on their shafts that the taper of one is in the reverse direction to that of its fellow. After wheels have become worn a little they come into perfect contact, so that inaccuracy of contact occurs only when they are new, and at maximum strength. When weakened, their contact is absolutely true.

The proportions between the pitch and breadth vary. But B is seldom less than twice the pitch, or more than four times the pitch.

The requirements of modern engineering are too exacting to permit of the indiscriminate use of formulæ such as these just noted. There is a vast deal of difference in the manner in which gears have to be driven. Some are driven slowly and steadily, others in a more irregular fashion, while in other cases very violent shock comes into play, stressing the material in a trying fashion. Formulæ are prepared, therefore, in which these influences are estimated, and embodied. The Unwin formula evolved for the strength of wheel teeth is

p = K

where p pitch,

K

=

= a multiplier,

b = breadth of face,

P = the whole pressure transmitted.

This is a general formula for wheels subject to ordinary shock only, and is therefore applicable to the majority of gears. The multiplier K in this equation is taken at 0707 for iron wheels, and 0848 for mortice wheels, and these values correspond with stresses of 4,400 lb. per square inch in iron teeth, and 1,650 lb. per square inch for wooden teeth. ? denotes the ratio of the pitch to the breadth of wheel face, and introduces a factor not taken account of when the stress is supposed to act only upon one corner of the tooth, or when the face width happens to be less than twice the pitch, which very seldom happens.

A rule taken from a standard American work on gearing which appears to be practically identical with this of Unwin's is as follows:-To determine the pitch for a castiron gear; multiply the force to be transmitted by the ratio of the pitch to the face width, extract the square root of the product, and multiply the result by 078 for violent shock, 07 for moderate shock, or 05 for little or no shock. The equation for moderate shock therefore stands :

Having to do with force in rapid motion other conditions come into play. Work increases directly as velocity, so that if the rim of a toothed wheel travels at the rate of 4 ft. in a second that velocity will represent twice the number of units of work which would be done by the same wheel under the same conditions of pressure moving at the rate of 2 ft. per second. Horse power is only a convenient expression to represent 33,000 foot pounds of work per minute. The HP., therefore, of wheels varies directly as their velocity; a wheel moving twice as fast as the same wheel under the same conditions of pressure will develop twice the HP. in the former case as in the latter. But the pressure stress on the teeth varies inversely as the velocity, an important point.

Since a HP. 33,000 lb. lifted 1 ft. high per minute, we have:

H = HP.,

v = velocity at the circumference of pitch line in feet per second, the latter being the most convenient formula.

General Joiner, or Universal Joiner. A combination type of wood-working machine which is specially adapted to the requirements of shops where an extensive plant cannot be laid down. Fig. 94, Plate VI., shows an example which comprises the following:-A circular saw on a rising and falling spindle, to which cutter-blocks for tonguing, grooving, and rebating may be attached. Planing and moulding spindle taking work 12 in. wide by 4 in. thick. Band saw with pulleys 24 in. diameter, sawing up to 9 in. deep. Circular moulding apparatus, with vertical spindle capable of working mouldings up to 4 in. deep. A tenoning apparatus with cutters for cutting complete tenons at one operation. A special table may also be provided for slot-mortising and boring. It will be seen that all the operations in joinery can be done on this machine, with the added convenience that the parts are located close together, so that one man may finish a piece of work rapidly. Alternatively, another helper could be doing some operation, such as bandsawing, as a preliminary to further work. The machine is driven primarily from the pulleys at the end of the frame on the extreme left. Generating Circle.-See Gears. Generating Machines.-See Bevel Gear and Spur Gear Generating Machines. Generating Stations. See Central Stations.

Geometrical Mean. The geometrical mean of two quantities is the square root of their product. Thus the geometrical mean of 4 and 9 is 6; for 4 × 936, and √36 = 6; 9 is as many times greater than 6 as 6 is greater than 4. Stated generally, a: m :: mb or ab = m2, where a and b are the two numbers, and m the mean. Geometrical Progression. A geometrical progression is a series of numbers increasing or decreasing by a common ratio or constant factor. 1, 3, 9, 27 is an increasing series; 3, 3, a decreasing series. The common ratio (which is found by dividing any term by the one preceding it) is 3 in the first example, and in the second.

3

3

189 84 5,

Algebraically, a geometrical progression is stated, a, ar, ar2, ar3, and so on, where a is the first term and r the common ratio. Since the index of the 3rd term is 2, of the 4th term 3,

German Silver.-Also called nickel silver, is an alloy of copper, zinc, and nickel. The proportions vary, one of the best alloys being produced by 4 parts copper, 2 zinc, and 2 nickel ; another alloy is obtained from 6 copper, 3 zinc, and 1 nickel. Spoons and forks, pots, dish covers, and bar fittings are largely made of German silver, its whiteness, and toughness, and the facility with which it takes a polish making it highly valuable for these purposes. It is frequently electroplated, and this is desirable in the case of articles where acids would act on the copper present, and produce verdigris. It is employed extensively in electrical work, for resistance wires.

Gib.-A shouldered strip of metal used as a backing for a cotter, to prevent opening out of a strap by the friction of the cotter. Examples may be noted in Figs. 57 and 58, Vol. IV. The term is also applied to Adjusting Strips. A gib-headed key is thus distinguished from one having no head, the gib being required when the key can only be drawn out by its head.

3

16

Gimbal Joint.-See Universal Joint. Gimlet.-A boring tool for wood, used chiefly for holes for screws. It is not employed in larger sizes than ordinary shell bits, a medium size being in. or in. diameter. Being turned by its handle it does not bore so quickly as a bit operated by a brace, and consequently the latter is always preferred, unless, as is sometimes the case, a gimlet is more convenient. Gimlets are made in twist and in shell form, and less frequently in a combination of the two, and also with a twist like an auger bit, but the most popular form has a comparatively slight twist, and its full diameter is some distance back from the point. In all cases gimlets are provided with screw points.

Girard Turbine.-A wheel of the impulse type, in which the water is under atmospheric