GEOMETRICAL PERSPEOOn. 



171 



UCIMK 



2. Reduce 35o + 70(W =10. 



3. Reduce 



8. Reduce 



,H b + C + d ' 



;; r 

 8. Reduce 4 + 6 = - g + 7. 



7. Reduce -+h=?--+d. 



a o o 



8. Reduce 40 6* 16= 120 14*. 



e-3 c c 19 



9. Reduce r + - = 20 x 



3 - 



10. Reduce g + - & = 20 * 



lo 



11. Reduce 4 = 5. 



12. Reduce 



2=8. 



13. Reduce 



to 

 STV 



14. Reduce x + ;j + jj = 11. 



15. Reduce s + 5 - T = ^ 



16. Reduce 



2 ' 4 

 26. Reduce 2* 9 = 72 + -.-. 



27. Reduce * 11 = 



28. Reduce =- ~ l = ^ 



+ 7. 



29. Reduce 11 ,- = 13 



o 4 



30. Beduoe + = a 



4 



z-3 t + 9 3* + 7 



31. Reduce - + 3. 



O la iiU 



2* 4* 6* * 3* 5* 

 82. Reduce^* __--.- + -__ y + a. 



GEOMETRICAL PERSPECTIVE. XT. 



Wi will oommeBM this lesson by giving a practical 

 of tin* remark* made in the last lesson upon Fig. 71. 



PROBLEM XLII. (Fig. 72). 4 foldiny ttreen of four 

 A, B, c, D. Two of the leave*, A and B, /orm an an/;i of 100 ; 

 C at on angb o/80 mM B j and D at on anglt of 70 toftA c. 

 The icreen u 6/e( high, and each Leaf it 3 feet broad. Height 

 of the eye, 5 feet ; and distance from the picture plane, 9 feet. 

 The eye opposite the centre of the leaf B. 



In drawing the ground plan, make the plan* of the leare* 

 A, B, c, D each 3 feet long, and nnito them according to the 

 angles stated in the question. The PP may be drawn at an/ 

 distance from it, and in any position the draughtsman may 

 consider to be most convenient, with reference to any particular 

 riew of the subject he wishes to represent, bearing in mind that 

 the direction of tight from the telected ttation point of view mutt 

 be perpendicular to the pp. Therefore the line drawn from 

 the centre of the leaf B (opposite to which the eye is directed 

 according to the conditions in the question) most be drawn per- 

 pendicularly to the PP ; and upon it place the SP 9 feet from 

 the PP. The HL and Laso of the picture may be drawn any- 

 where below the PP. From the SP draw vanishing lines to the 

 PP, to produce the vanishing points ; and mark each vp with 

 the letter of tho leaf to which it belongs, to ensure the right 

 direction of the extremities of each leaf respectively. Draw 

 visual rays from each angle of the plan to the PP, in the 

 direction of the SP, afterwards to be drawn perpendicularly 

 from the PP. Produce the plan of one of the leaves, say A, 

 to the PP, for a point of contact ; e f will then be the line of 

 contact upon which to mark the height of the screen /h. 



We must remind our pupils here that they are to foUovc the 

 course of the ground plan when drawing the perspective positions 

 of tho ends of the leaves, viz., the tops and bases ; change the 

 directions at the visual rays, and be guided by their respective 

 vanishing points ; whilst the perpendicular continuations of the 

 visual rays from the PP will determine their widths. Thus 

 inog represent the leaf A ; op kg the leaf B ; p rlk the leaf c; 

 and rims the leaf D. 



In drawing buildings where there are many projections the 

 regulation of following the course of the ground plan, directed by 

 the vanishing points, is important. It saves the trouble of 

 additional lines of contact, when the vanishing points for the 

 various projections are obtained. 



Our next subject will be steps or staircases. 



PROBLEM XLIII. (Fig. 73). A flight of eight descending stept. 

 Length of stept, 12 feet ; width of each, I foot 2 inches; depth of 

 each, 6 inches. Height of eye, 7 feet. Distance of the eye from 

 the PP, 9 feet. Scale, J tnc/i to the foot. 



Draw the horizontal line, and the plane of the picture 7 feat 

 below it. Place the PS and DE 1 and DE- at 9 feet from PS. 

 The first thing to be considered is the inclination of the steps, 

 found by constructing a profile or section of them from DC 1 . 

 Make the distance from DE 1 to a equal to the width of the steps, 

 1 ft. 2 in. ; also the spaces ab,bc, and c d, the same. Draw per- 

 pendiculars from each of these points to e, f, g, and h ; making a e 

 equal to 6 inches ; bf twice that distance ; eg three times ; and 

 dh four times. Rule a line from DE 1 , through the points e,f,g,h, 

 to the TP on the perpendicular line drawn through PS. This 

 last line, e,f, g, h, will represent the downward inclination of the 

 steps. The tread of each step may be drawn through the points 

 e,f, 9, h, parallel to the HL. From TP, with the radius to DE 1 , 

 draw the arc from DE' to DVP, for the distance point of the 

 vanishing point of the inclination. Set off the length of the 

 first step, i k, equal to 12 feet. Draw a perpendicular line 

 through t for a line of contact or measuring line. Draw from i 

 and k to VP. Upon these last lines will be found the angles of 

 tho steps, thus: Set off from i upwards the spaces 1,2,3, i, etc., 

 each equal to the inclined spaces from DK 1 to e; from e to f; 

 from ftog, etc. Rule from each of these points to DTP. Where 

 these lines cut the one from to VP will be found the angles 

 of the steps. The top of each step must be drawn from those 

 intersections directed from PS. because the tops or treads of the 

 steps are horizontal ; and as they retire at right angles from the 

 picture plane, they have the PS for their vanishing point The 

 other ends of the steps upon k must be treated in the same way. 

 The balustrade at the right may be drawn at pleasure, observing 

 that the top of the descending portion vanishes at VP ; whilst 



