MATERIALS AND STRAINS.] 



APPLIED MECHANICS. 



795 



instance, the point D, corresponding to the 40 division 

 of the Protractor, would be marked on the paper ; and 

 the instrument being removed, a straight line drawn 

 through C and D would lie at 40 to the line C B, or at 

 140 to the line C A. The Protractor, being semi- 

 circular, contains two quadrants, each of 90, making up 

 180, and the arcs, or angles, are numbered, from D up 

 to 180, from each of its extremities. 



Fig. 2 represents a Trigonometrical Scale, which is 

 easily made, and is very useful in mapping or spherical 

 projection. A quadrant, or arc of 90, A B, is divided 

 equally into arcs, each of 10, or into smaller divisions, 

 if required. The chords of those arcs are struck by 

 circles drawn from the centre A, cutting the line A B. 

 The base A C, or horizontal radius, is equally divided. 

 The vertical radius C B is divided by lines, squared 

 across from the divisions of the qxiadrant, and thus 

 forms a scale of sines. The vertical line A E being out 

 by lines, or radii, drawn from C, and produced through 

 the divisions of the quadrant, forms a scale of tangents ; 

 and the length of those extended radii, being laid down 

 by describing circles from the centre C, upon the vertical 

 line C F, forms a scale of secants. For drawing the 

 meridians and parallels upon the projections of a sphere, 

 either for geographical or for astronomical problems, 

 these divisions are essential. 



Fig. 3 represents the ordinary Compasses, or Dividers ; 

 and Fig" 4 and 6 show the Pen and Pencil-holders, 

 which a substituted for one of the legs of the Com- 

 passes when circles are to be drawn on paper. 



Fig. 6 represents the Parallel Ruler, consisting of 

 two straight rulers, connected together by two equal and 

 equally inclined radii. The edges of the two rulers 

 being parallel to one another in any one position, main- 

 tain their parallelism when they are opened or closed ; 

 and thus, the one edge being laid to any line already 

 drawn, another line can be drawn along the other edge, 

 parallel to the first line at any required distance from it. 



For remarks as to the use of those instruments, the 

 reader may be referred to the Chapter on Practical Geo- 

 metry. It may be farther observed here, that in laying 

 down dimensions on paper, whether full size or to any 

 scale, they should be always pointed off directly from 

 the rule or scale on the drawing. The Compasses should 

 be used only for dividing circular curves, to which 

 straight scales cannot be applied. When they are used 



for straight dimensions, errors are introduced which do 

 not occur when the draughtsman restricts himself to the 

 scale. First is the chance of error in setting the points 

 of the Compasses to the divisions of the scale. Secondly, 

 the spring of the Compasses themselves. Thirdly, the 

 uncertainty in the pricking of the paper. And lastly, 

 the inaccuracy in drawing through the prick marks ; to 

 say nothing of the tear and wear of the scales, arising 

 from the application of the sharp points to them, and 

 the unseemly appearance of the drawing when full of 

 prick marks. 



SCALE OF DRAWING. For the draughtsman em- 

 ployed in devising, on paper, work to be executed in 

 solid materials, we strongly recommend that he should, 

 as much as possible, endeavour to draw all details of 

 their full size. Scale-drawings, especially of large works, 

 are absolutely required to show the combination of all 

 the parts in one machine or engine, full-sized drawings 

 of which would be of most inconvenient size. But, in ad- 

 dition to the scale-drawings of the whole, it is the prac- 

 tice of the best engineers to execute full-sized drawings 

 of details. One great advantage of this is, that the 

 draughtsman sees better on the full size what should be 

 the best forma, dimensions, and combinations of the 

 parts in respect of strength, efficiency, and economy of 

 material and labour ; and another advantage consists in 

 the facility with which the workman can read off the 

 drawings, or transfer to the solid materials he labours 

 on, the dimensions and forms marked out : he has only 

 to apply his rule to the drawing and to his work, and 

 make them agree. Farther, as it is customary for work- 

 men to use rules divided into inches, and these again 

 into halves, quarters, eighths, and sixteenths, the 

 draughtsman should make his dimensions such as can be 

 measured in those fractions. We have known numerous 

 workmen who perfectly comprehended the eighth or six- 

 teenth part of an inch, but had not the remotest concep- 

 tion of what was meant by the tenth or the twentieth 

 part. Were the dimensions even figured by tenths, the 

 workman would read it in quarters, eighths, or six- 

 teenths, and would most probably err in reducing it 

 from the one denomination to the other. It is, there- 

 fore, preferable, in the first instance, to draw or figure 

 the dimensions in a denomination which the workman 

 will employ ; and thus a fruitful source of error will be. 

 avoided. 



CHAPTER III. 



STRENGTH OF MATERIALS. 

 Content*. MATERIALS AND STRAINS TENSION AND INTERNAL PRESSURE COMPRESSION TRANSVERSE STRAIN 



DEFLECTION AND DISPOSAL OF MATERIALS RULES FOE CALCULATING TORSION SHAFTS CLIPPING OB SHEARING 



STRAIN. 



to the fibres so as to break the body across, as in a beam 

 loaded in the middle. In resisting a strain of this kind, 

 the cohesion and elasticity of a body are both exercised. 



4. Torsion or twisting, or a force applied at the end of 

 a lever so as to turn one end of the body round its axis, 

 while the other end is fixed, as in a shaft or axie. 



6. Clipping or shearing, or a power applied to divide 

 or cut a body across its fibres. 



All the possible strains to which materials, whatever 

 be their forms and arrangements, can be subjected, are 

 of one or more of these classes. We therefore propose 

 to consider them separately, and endeavour to apply the 

 results of experiment and observation to their discussion, 

 endeavouring to avoid, as far as possible, mere abstract 

 mathematical investigations. We cannot, however, al- 

 together dispense with mathematical aid, but shall 

 endeavour to place the reasoning as much as possible on 

 such a footing, that a student having a moderate ac- 

 quaintance with the general principles of mathematics, 

 may have little difficulty in following it. We must pre- 

 mise that the whole subject is as yet in an unsettled 



MATERIALS AND STRAINS. The materials with 

 which the practical mechanic has principally to deal are 

 metals, such as steel, wrought-iron, cast-iron, copper, 

 brass and gun-metal, lead, tin, and zinc ; timber, such 

 as oak, teak, ash, beech, and other hard woods ; fir, pine, 

 cedar, and other soft woods ; stones, bricks, mortars, 

 and cements ; cordage, straps and bands, and the like. 

 The strains to which these materials may be subjected, 

 may be classed under five heads : 



1. Tension, or a strain applied in the direction of the 

 fibres of the body, so as to pull it asunder, as in the case 

 of ropes, bands, tie-rods, and chains. The strength of a 

 body to resist a strain of this kind, is called its cohesion, 

 or the force with which its parts are held or knitted to- 

 gether. 



2. Compression, or a strain applied also in the direc- 

 tion of the fibres so as to crush a body, as in the case of 

 a column. Compressive strain is exactly opposite to 

 tensive strain ; and the power of a body to resist it 

 seems to depend chiefly on its elasticity. 



3. Transverse strain, or force applied perpendicularly 



