APPLIED MECHANICS. [jfEOHAinOAL DRJLWISTO - 



eye view, having nearly the form which an object would 

 present to the eye of a bird soaring above it 



SECTIONS. For drawing the exteriors of all solid 

 bodies, bounded by straight lines and flat surface*, these 

 projections are generally sufficient. But it is often neces- 

 sary to make such drawings an shall give a correct notion 

 of the iiiti<rii>r o instruction of bodies. 



Suppose, for instance, we wished to have a cubical 

 box constructed of wood, having a certain thickness, 

 and fitted with a vertical partition of a certain height, 



i..- ::. 



and at a certain distance 

 from the ends. In order 

 to indicate this by a draw- 

 ing, we must show its 

 internal construction. To 

 effect this, we may still 

 use the three planes of 

 projection ; but as these 

 planes are imaginary sur- 

 faces, we may easily con- 

 ceive some of them to 

 pass directly through the 

 substance of the box : in other words, we may conceive 

 the box to be sawn or cut across in any direction, and 

 the form presented by the parts so cut, to be projected 

 on the plain's (Fig. 12). Thus, if a horizontal and a 

 vertical cut were made, as indicated by the dotted lines, 

 A A and B B, we should have a plan and a side elevation 

 of the cut surface, in which the thickness of the wood, 

 and the position and height of the partition, would be 

 clearly shown. These views would be called sections, or 

 the drawings of cuttings. The horizontal projection 

 would be a sectional plan, and one of the vertical pro- 

 jections would be a longitudinal or transverse section, 

 while the other would still remain as an end or side 



Fig. is. 



13, which would be seen on unfolding the paper of pro- 

 jection, enough of the form, thickness, position, an<l 

 height of the partition would be represented to enable 

 a workman to construct the box. 



Now, if the part of the paper containing the end eleva- 

 tion were cut away from the rest, and turned round, so 

 as to bring the letters on it into a more convenient 

 position for reading them, as in Fig. 14, the accuracy 

 of the drawing would in no respect be altered, provM. 1 

 always, that it were clearly understood what elevations, 

 plans, or sections, the different parts of the drawing 

 were intended to represent. 



PERSPECTIVE. There is another mode of consider- 

 ing this question. The rays of light by which the eye is 

 enabled to perceive 

 the form of an object, 

 proceed from every 

 point of the object, in 

 straight lines to the 

 eye. Suppose, then, 

 one face of a die were 

 presented directly to the eye, as in Fig. 15, the rays of 

 reflected light, proceeding from every point in the surface 

 of the die to the eye, would all converge or draw together 

 towards the small opening which the pupil presents ; and 

 entering there, would produce the image which enables 

 the spectator to see the object. This would be the case 

 however far off, or however near, the eye were to the 

 die ; but the greater the distance, the less the conver- 

 gence of the rays, or the more nearly are they parallel to 

 each other, as may be clearly seen by the diagram, Fig. 

 16, where an arrow is supposed to be the object, and the 

 rays of light proceeding from its extremities are indicated 

 by the dotted linos, to an eye at the various positions, 

 a, 6, and c. While those to the eye, at o, converge very 



Fig. is. 



C..M- 



elevation. The dotted lines A A and D D, on the end 

 elevation and section, correspond with the horizontal 



Fig. 14. 



pbne of toction ; and the lines B B and C C, on the end 

 elevation and plan, correspond with the vertical plane of 

 section. In a drawing, then, of a box, such as in Fig. 



rapidly, those to b also converge, but more slowly, and 

 those to c more slowly still But if we could conceive 

 the eye removed to an incalculably great distance from 

 the object, and suppose that its powers of vision were 

 still sufficient to perceive it, the convergence of the rays 

 would be immeasurably slow : or, in other words, the 

 rays would be so nearly parallel, that we could not 

 appreciate any convergence at all. Retaining, then, 

 this conception of extreme distance, we may nay, with- 

 out error, that the rays are quite parallel. We have, 

 in nature, actual cases of this kind ; for the fixed stars 

 are so very distant that no difference can be traced in the 

 ion of rays of light coming from them to the earth, 

 at different parts of her orbit, although the distance 

 across that orbit is nearly two hundred millions of miles. 



Now, we have already shown that the different pro- 

 jections of an object are formed by supposing parallel 

 lines to be drawn from the different points of it to certain 

 planes ; and if we suppose these parallel lines to be rays 

 of light, such as we have described, proceeding to an 

 immeasurably distant eye, we attain a mode of under- 

 standing what these projections moan. According to 

 this notion, the plan or horizontal projection is the view 

 whii-h an object would present when we look directly 

 down on it, or directly up to it, from a great distance ; 

 the side and end elevations are the direct views of the 

 side and end respectively ; and sections are the direct 

 views of the object when cut or sliced across in any 

 direction. Bearing this in mind, we may then be pro- 

 pared to make mechanical drawings of most objects with 

 facility. 



Suppose, for example, we had to draw an object such 

 as mathematicians mn<l call a hexagonal prism that 

 is to say, a solid uyuro having six equal oblong sides 

 and two six-sided uuiia. Supposing it to gland on one 



