388 



THE POPULAR EDUCATOR. 



breadth of the Meander, a river of Phrygia, is twenty-five feet. 8. Tha 

 parasang, that is, Persian measure, contains thirty stadia, or eighteen 

 thousand seven hundred and fifty feet. 9. The calculation of the 

 entire journey, the expedition and retreat, which is described by 

 Xenophou, was two hundred and fifteen stadia, one thousand one 

 hundred and fifty-five parasangs, thirty-four thousand six hundred and 

 fifty stadia. ; and the length of time of the expedition and retreat was 

 a year and three months. 10. The friendship of one intelligent person 

 is better than the friendship of all unintelligent people. 11. This was 

 vhe number of the army of Cyrus : of the Greeks there were ten thou- 

 sand four hundred hoplites, two thousand five hundred targeteers ; but 

 of the Barbarians with Cyrus, there were one hundred thousand, and 

 scythe-bearing chariots about twenty. 



EXERCISE 71. ENGLISH-GREEK. 



1. Elf oweToc <pi\o; ton ' kpr 



2. Ta 



errj 



rcfT. 3. 'OXo? 6 api0/AO? Trj? 6<3ou OTTO TIK M a X1? v Ba/SuKuvi it ra Kort/aipa 



%aKo?tot ciKotri <rra6ia ftvpia oKTaK*crx(X*a efcuccxrta, xpofov 6c TO TrX^Cov 

 OKTW firivev. 4. *O apitffjiov TOW o-Tpareu/naTo? ean Tpr/iup(0( eciaKmx(A(o< 



TOW uTpaT(a>Taii/ Tpttr/it/pfwi* evi'uicoa'<a)y Ka< f e^MKoi'Tit. 6. llopri<Tav v rt; 

 /la^t? Tpiv Tpter/jiMptot Kai c^uKKrxt^iot t uKu<T(oi Ka< TrevrrjKoi'Ta TU*** aT^uTfafTU)^ 



KUU UpUCtTCt <3pt7Tat'fl0OpU Q,fJL<f>t tKUTUV KCIi 7Tf T^JKUfc-TU. 



GEOMETRICAL PERSPECTIVE. XII. 



IN proportion as the number of lines and angles increase, which 

 compose the subject to be represented in perspective, so there 

 will follow a greater amount of working lines, drawn in various 

 directions from the picture plane. Under these circumstances 

 it will frequently be necessary to use more than one line to 

 represent the PP, in order to prevent the confusion which must 

 occur when working all the details from one PP only. Therefore 

 we are at liberty to use any number of lines as picture planes 

 an advantage fully 

 appreciated by 

 every draughts- 

 man when engaged 

 in making highly- 

 finished drawings 

 of very elaborate 

 subjects. The kind 

 of work to which 

 these lessons are 

 but an introduc- 

 tion, and which 

 must fall to the 

 lot of those who 

 have studied per- 

 spective for some 

 practical purpose, 

 will not be re- 

 Btricted to cubes, 

 blocks of wood, 

 and the simple 

 objects wo have 

 elected for our 

 practice, and to 

 assist us in ex- 

 plaining the prin- 

 ciples. We know h -n, J T f a- 

 the same rule for 



drawing a block in perspective is applied again in drawing a 

 church or a palace; but respecting the latter, that which 

 increases the labour, and not unfrequently perplexes the stu- 

 dent, is the increased amount and the great variety of details. 

 We intend still to confine ourselves to simple examples, so 

 long as we have any new rule to give or fresh principle to 

 explain ; let these be well learnt, then the application of 

 them to more extensive and important subjects will be easy. 

 We now, therefore, introduce the practice of additional picture 

 planes, and that our explanations may, we trust, be clearer, 

 we will simplify the process by proposing a problem with 

 reference to two slabs or bloclcs only, of the same size, and each 

 in the same position with regard to the PP. By this time our 

 pupils will be prepared with the fact, that if an object touches 

 the picture plane its real length is represented upon the picture; 

 and as it retires from or beyond the picture, the space it occupies 



upon the PP diminishes. Turn to Fig. 24, Vol. II., page 360, 

 where the slabs of the pavement touching the PP are drawn to 

 the size given by the scale ; also / e, the perpendicular edge of 

 the cube in Fig. 33, Vol. III., page 9, is another example. Af ti-r 

 this remark, it will be seen that the object may be made to touch 

 the PP in more than one place, if it is placed at a distance from 

 the PP, by means of one or more of its lines being produced to 

 the PP as points of contact. Therefore, if we have the option of 

 placing a line representing the PP anywhere in conjunction with 

 one of these points of contact, besides our usual practice of 

 putting it below the drawing, we have the advantage of distri- 

 buting the measurements, which might be crowded upon this 

 one line, upon other lines similarly placed for the same purpose. 

 Any further remarks will be made as we proceed with the method 

 of drawing the following problem : 



PROBLEM XXXV. (Fig. 57). Two slabs or rectangular bloclcs, 

 each of the same dimensions, 6feet long, 4 feet broad, and Ifoot thick. 

 One block is above the eye, the otJier below, resting on the ground; 

 in every other respect the conditions of each are tlie same. Their 

 long sides are 40 with the PP; their nearest angles 3 feet to the 

 left of the eye, and 2 feet within tlie PP. Height of the eye, 4 

 feet, and distance of nearest angle to the eye 10 feet. The vertical 

 space between tlie blocks is 6 feet. 



Our motive for employing two blocks of the same dimensions 

 and position, with the one exception named, is that we shall find 

 it easier to explain ; and we hope our pupils will more clearly 

 understand the use of the PP when placed above the eye, and by 

 which we intend to show that the proportions of the object can 

 with equal capability be arranged upon a line above the HL, as 

 upon one below it. By this use of two lines to represent the 

 PP, the base of a column can be worked from the PP below, and 

 the capital from the one above. The same may be observed 

 when representing windows, balconies, etc., in the upper storeys 

 of a large building. From PS on the HL draw the semicircle 



DE I E r>E 2 . (We 

 have stated the 

 distance of sight 

 in a way frequently 

 done in some of 

 the military exa- 

 mination papers, 

 for the purpose of 

 drawing attention 

 to it. It is said 

 that the distance 

 from the nearest 

 angle to the eye is 

 10 feet, and that 

 the object is 2 feet 

 within or beyond 

 the PP ; therefore 

 the eye will be 8 

 feet from the PP, 

 which length will 

 be the radius for 

 describing the 

 semicircle through 

 E.) The distance 

 of the nearest an- 

 gle of the object 



S to the left of the 



eye will be at b; c 



the nearest point of the object to the PP, from which lines 

 must be drawn to both vanishing points ; the perspective 

 lengths of c d and c e must be cut off by lines to their 

 respective distance points in the way already explained in 

 Lesson IX., Vol. III., page 271. The line c d, which has been 

 drawn to vp 1 , must be produced to the PP in h. The thick- 

 ness of each block is 1 foot, that being added to the verti- 

 cal space between them will be 8 feet ; therefore the perpen- 

 dicular line, or line of contact, must be 8 feet from 7*. to i. 

 Another PP through i must be drawn parallel to the HL. Now, 

 as the blocks in this case are the same in their dimensions and 

 positions, the upper one could be very quickly and conveniently 

 drawn from the lower one, by raising perpendicular lines from 

 the angles ; but we avoid this for a special reason : that is, we 

 wish our pupils to go through the construction again, upon and 

 from the upper PP, in the same way as they did from the lower; 



PP 



