MECHANICAL DRAWING SHADING.] 



APPLIED MECHANICS. 



793 



a proper notion of the cylindrical surfaces intended 

 to be shown. The drawing requires shading to give the 

 full effect ; and after another example of simple shadow- 

 ing, we will endeavour to show how the shading may be 

 eifected. 



Referring now to Fig. 47, showing a plan and section 

 of a cylinder open at top, we have to inquire as to the 



Fig. 47. 



form of shadow in the sec- 

 tion cast on the inside by 

 the cylindrical side. Tak- 

 ing any points 6 / d on the 

 inner circle in plan, and 

 drawing lines from them at 

 45 till they meet the oppo- 

 site limb of the circle in the 

 points c g e tracing up 

 these points by lines to the 

 elevation, and also the 

 points bfdtob 1 f 1 d^, and 

 from the latter drawing 

 lines at 45 to meet the 

 others, we get the points 

 c \ 9i e i> m tne boundary of 

 the shadow. The point a, 

 where a line at 45 touches 

 the circle, being traced up 

 to a 1 in the section, gives 

 the commencement of the 

 shadow ; and the outline being filled in by a dark tint, 

 nts the appearance of an interior cylindrical shadow. 

 Like the exterior shadow shown in Fig. 46, shading is 

 required in order to give the notion of a curved surface. 

 We shall, therefore, now proceed to discuss the ques- 

 tion of shading ; which consists in placing on a drawing, 

 tints of various degrees of lightness or darkness, so as 

 to represent the comparative amounts of reflected light 

 from the different portions of the surface represented. 

 We are not aware that the question of shading mechanical 

 drawings has ever been discussed on geometrical grounds, 

 like that of shadowing ; it is, therefore, with considerable 

 diffidence that we venture to offer some considerations 

 which may furnish a clue to the proper variations of 

 light and shade on projections. A skilful draughtsman 

 has little difficulty in bring up a very correct, and even 

 an artistic effect of light and shade on mechanical draw- 

 ings ; but we believe that it is to a practised eye and an 

 expert hand that he owes his success. In shadowing, he 

 trusts to the same elements of success ; but as the out- 

 line of every shadow can be determined with mathe- 

 matical accuracy, on the supposition of parallel rays of 

 light proceeding at certain angles to the planes of pro- 

 jection, on the same supposition we think the variations 

 of light and shade can also be determined. It must be 

 confessed that, even if the lights and shades of a projec- 

 tion were determined in quantity, so that we could say 

 such a part of a surface must have twice or thrice the 

 darkness or the light of such another part, we should still 

 labour under the difficulty of carrying out these dimen- 

 sions of light and shade. We might, however, approach 

 them by applying repeated dark tints to the shaded parts; 

 making the number of equal tints laid on above one 

 another, correspond with the degree of darkness deter- 

 mined on. But even without attempting any mathe- 

 matically accurate mode of carrying out the theory in 

 practice, we may at least derive useful hints from its 

 investigation. 



If we suppose the circle in Fig. 48 to be the plan of 

 a cylinder, of which we wish to represent a shaded 

 elevation, one half A D B would not be shown ; the 

 other half has its circumference divided into eight equal 

 parts. We will suppose parallel rays of light R, R,, 

 R,, R., R 4 , R B , R,, to come at the proper angle (45), 

 and to DC reflected from the surface of the cylinder in the 

 directions r, r,, r 2 , r 3 , r t , r s , r t , respectively. These 

 directions of the reflected rays are of course determined 

 by 1 1 rawing them so as to make the same angles with the 

 radii C A, C 1, C 2, <fcc , as the incident rays make with 

 those radii, but on opposite sides of them, according to 

 the well-known optical principle that rays of light are 



VOL. X. 



reflected from a surface at the same angle as that with 

 which they strike it. Now, of all those rays, that striking 

 the point 3 is reflected most directly to an eye situated 

 in the line C E, at a great distance from C, 3r s being 



Fig. 48. 



Fig. 49. 



parallel to C E, and therefore the elevation of the point 

 3 should be the brightest. Again, the points 2 and 4 

 would appear equally illuminated, because the reflected 

 rays 2 r s and 4 r 4 lie at equal obliquities to C E ; but 

 each of those points would appear less illuminated than 

 the point 3, because of this obliquity. Farther, the 

 points 1 and 5, whence the rays are reflected parallel to 

 A B, mark the places where the illumination of the sur- 

 face ceases ; and were it perfectly smooth and polished, 

 all beyond 1 towards A, and beyond 5 towards 6, would 

 be perfectly dark. The portion 6 to B, receiving no light 

 at all, would be represented in shadow. In the elevation 

 then, if the points in the circumference of the plan be 

 projected, and the surface darkened by lines or tints in 

 accordance with the deficiency of reflected illumination 

 at its different parts, we get a geometrically shaded 

 representation of a cylinder. 



For the interior surface of a cylinder shown in section, 

 the light and shade of the different parts may be found 

 in a similar way, as marked in Fig. 49, where the point 5 

 giving the direct reflection will be the brightest, the 

 points 4 and 6 ha\ing equal intensity of light, but each 

 less than 5, because of the obliquity of the reflected 

 rays ; the part A 1 2 3 4 quite dark, because the light is 

 intercepted by the edge A ; the point 7, whence the ray 

 is reflected parallel to A B, the last part of the illumi- 

 nated surface ; and 7 B dark, because the rays are 

 reflected backwards. The section shows the shading in 

 accordance with this variation of reflected lights, the 

 lower part of the interior being completely shadowed in 

 the form marked in Fig. 47. 



The shading of other curved surfaces might be deter- 

 mined in a similar way ; but as cylindrical surfaces are 

 those which most commonly occur in drawings of ma- 

 chinery, we consider it sufficient to have pointed out 

 the principles upon which the shading of them may 

 be determined. A little practice will soon enable a 

 draughtsman to give a rounded effect to drawings of 

 such surfaces ; and a little attention paid to this will 

 often render plain and explicit a drawing, which would 

 otherwise be comparatively obscure. The lights, shades, 

 and shadows to complete drawings need not be deter- 

 mined by geometrical projections, which would often 

 involve great labour without adequate results. A 

 draughtsman accustomed to make drawings of ma- 

 chinery, forms, in his own mind, a very accurate con- 

 ception of the solidity, projections, and hollows of the 

 various parts, and throws in the shades and shadows by 

 eye, in such a manner as to give a tolerable notion of 

 these variations of surface. It is well, however, that 

 the beginner should know the principles on which 

 shading must depend, and he will then be better pre- 



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