MACHINERY. 



but the heaviest railway-trains without sensible 

 deflection. 



In beams supported at both ends, the strain is 

 greatest in the middle ; girders are therefore made 

 strongest in the middle, and taper towards the 

 ends. 



Torsion. 



If one end of the axle or shaft of a wheel is 

 immovably fixed, and a power acts at the circum- 

 ference of the wheel (or at the end of a lever or 

 winch), the power may be so increased as to twist 

 the shaft asunder at its weakest point. If a shaft 

 A has twice the diameter of another shaft B, there 

 will be four times as many fibres in the section of 

 fracture of A, to resist the twist, as in that of B. 

 But as the separation takes place by the one end 

 of the fracture turning round upon the axis of the 

 shaft, making the ends of the separating fibres 

 describe circles, those fibres that are furthest from 

 the centre will have the greatest power of resist- 

 ance, and the sum of their moments, or their 

 united effect, will be in proportion to their mean 

 distance from the centre. This mean distance in 

 A is twice that in B ; therefore, the resistance in 

 A is 2 X 4 or 8 times the resistance in B. Gener- 

 ally, the strength of shafts to resist torsion is as 

 the cubes of their diameters. On the other hand, 

 the twisting force that may be applied to the 

 wheel or lever will be less as that lever is longer. 

 The torsive strengths of shafts i inch diameter, 

 and with weights acting at i foot leverage, being 

 found by experiment for different materials ; the 

 strength of shafts of other dimensions are found 

 from these ' constants ' by multiplying by the cube 

 of the diameter, and dividing by the length of the 

 lever. It is evident that the torsive strength of a 

 hollow shaft will be greater than that of a solid 

 one of the same quantity of material, on the same 

 principle that its transverse strength is greater. 



MACHINERY. 



The object of all machinery is to transmit and 

 modify motive-power. It is not, as already ex- 

 plained, to create or multiply power ; for no 

 machine can give off more working-power at one 

 part than has been applied to it at another. The 

 most usual and convenient form of motive-power 

 is rotary or circular motion ; having once a motion 

 of this kind, we can transmit it to any point where 

 it is required, and can alter its velocity, and 

 change it into another kind of motion, at pleasure. 

 The more important elements of machinery by 

 which these purposes are effected, we now proceed 

 to notice. 



COMPONENT PARTS OF MACHINERY. 



Shafts. A rigid bar of metal or wood made to 

 revolve on its axis by any motive-power applied 

 at one part, is capable of conveying and giving off 

 that power at any part of its length to machinery 

 connected with it. A large bar or beam of this 

 kind is called a shaft; a smaller one, a spindle. 



The part of a shaft on which it rests while turn- 

 ing is called the journal or gudgeon. The bear- 

 ings of a shaft are the rests in which its journals 

 or ends turn. The lower bearing of a vertical 

 shaft is called a step. 



Bands or Straps. Bands or straps are used to 

 convey motion from one shaft to another parallel 

 and distant shaft. In fig. 37, A is a drum or 

 pulley with a flat surface, supposed to be fixed 

 on a shaft put 

 in motion by 

 the source of 

 power ; B is 

 another pulley 

 fixed on the 

 shaft S ; and 

 over the sur- 

 faces of the 

 two a broad Fig. 37. 



leather belt, L, 



is stretched tight. As A turns, the friction between 

 its surface and that of the belt carries the latter 

 along with it, and thus B is also made to revolve. 

 The shaft S thus set in motion may be ma'de to 

 communicate rotation to any number of pulleys 

 and spindles, C, E, each of which may drive a 

 separate apparatus. The main stream of driving- 

 power is thus distributed into a number of small 

 rills. 



In order to economise the power, the band 

 should have no more tightness than is just suffi- 

 cient to prevent its slipping ; for it is evident 

 that the greater its ten- 

 sion, it will cause the axes 

 of the pulleys to press 

 the more against their 

 bearings, and thus in- 

 crease the friction of the 

 machine. When the two 

 parts of the band are 

 made to cross each other, as in fig. 38, it works 

 with less tension, owing to its embracing a larger 

 arc of each drum. There is thus some economy 

 of power in this arrangement ; besides that, it 

 serves another purpose namely, that of reversing 

 the direction of the rotation. 



Toothed-wheels. If the two pulleys or drums 

 in fig. 38 were near enough to touch each other, 

 by making the one revolve, the other would be 

 made to revolve with it. This method of com- 

 municating motion serves only when the resist- 

 ance to the driven pulley is very slight. The 

 usual and sure method is to raise projections or 

 teeth on the pulleys ; this contrivance is called 

 toothed-gearing. 



Let C and C' (fig. 39) be the centres of two 

 toothed-wheels in gearing with each other (the 

 centres are not represented in their actual posi- 

 tions, in order to save space). The line CC' is 

 called the line of centres; and the two circles, gg, 

 hh, which touch each other in T, midway between 

 the extreme projections of the teeth, are the pitch 

 circles. The pitch of the teeth of a wheel is the 

 distance, AB, from the centre of one tooth to the 

 centre of the next, measured upon the pitch 

 circle ; and it is evident that for two wheels to 

 work together, the pitch must be the same in 

 both that is, AB must be equal to TD. The 

 breadth of the teeth is made a little less than the 

 intervals between them, that they may have room 

 to engage and separate without becoming locked 

 in consequence of any slight irregularity. 



The actual size of the wheels is not indicated 

 by their solid rims or bosses, ee, ff, but by the 

 pitch circles, gg, hh; and we shall best under- 

 stand what is necessary to the true working of 



