226 



THE POPULAR EDUCATOR. 



probably they will be better understood from the table, as the 

 positions of the several parts will be easily recognised. We 

 recommend our pupils to go through this experiment with a 

 table, it will help them better to understand the positions of 

 objects in the problems that will be given in the course of these 

 lessons. 



In ground-plan perspective the rule for finding the vanishing- 

 point is : 



Draw a line from the station-point, SP, parallel with the 

 ground-plan, as far as the plane of the picture, PP, from which 

 draw a perpendicular line to the horizontal line, HL ; this will 

 give the vanishing point, VP. 



In order to assist the pupil in comprehending this, we request 

 him to turn to Fig. 7 in the preceding page, and he will 

 notice first the ground-plan, of a line only, A B, at an angle with 

 the PP. It must be remembered that this line, PP, is the plan 

 or projection of the whole surface of the picture, supposed to be 

 in an upright position, and as we cannot draw upon a piece of 

 paper so placed, it is necessary to rabat it that is, turn it down 

 and lay it flat upon the table. This is done by bringing down 

 the picture-plane, and all the points of intersection of visual rays 

 and points of contact (anywhere, so that there may be sufficient 

 space to make the drawing), towards the station-point, SP 

 we have marked it BP, " base of picture, or plane of picture, 

 brought down." From this line we arrange the height of the 

 eye, or horizontal line. Now to find the vanishing point for 

 the line represented by its ground-plan : Draw a line from SP 

 to VP, parallel to A B, and draw a perpendicular line from VP 

 to VP 1 . VP 1 will be the vanishing point for the given line 

 represented by the plan A B. This must be learnt at once, as it 

 will be wanted in almost every case of ground-plan perspective. 

 It does not signify whether the given line is inclined or parallel 

 to the horizon; it is the plan only of the line we use for 

 finding the VP, as will be seen when we come to problems 

 relating to inclined lines and planes. 



We advise the pupil to work the problems that we shall 

 bring under his notice in the course of these lessons to a 

 ecale of half an inch to the foot that is, if we say he is to 

 draw a line five feet long, he will make it five half inches ; 

 and, to save a great deal of repetition, we will settle at once 

 that the height of the eye, HL, from the ground is five feet, 

 and ten feet from the picture-plane. This scale may be 

 employed until we propose another, when we come to other 

 problems. 



PROBLEM I. (Fig. 7). Draw the perspective view of a given 

 line, A B, five feet long, lying on the ground, forming an angle 

 with the picture-plane of 35, and touching the picture-plane ; the 

 eye to be opposite the centre of the given line. 



Draw a line, PP, to represent the picture-plane; from any 

 point, A, draw a line, A B, at an angle of 35 with PP (see Les- 

 sons in Geometry, Problem XX., Vol. I., page 256), and make it, 

 according to the given scale, five feet long ; find the centre of 

 A B in c, and from c draw a line perpendicularly to the picture- 

 plane to any length ; mark the point d on PP. Anywhere 

 below, draw the base of the picture, BP, parallel to PP, and 

 draw the line HL parallel to BP or PP. From d make d SP 

 equal to ten feet. Now find the vanishing-point, vp l , as we 

 have already explained. Because the end of the given line A B 

 touches the PP at A, therefore A is the point of contact of the 

 line A B ; mark it PC. Bring it down perpendicularly to the 

 line BP to PC 1 . Draw a line from PC 1 to VP 1 , and somewhere 

 upon this line will be the perspective view of the given line, A B, 

 to be found thus : As the line A B touches or is in contact with 

 the PP, therefore the perspective view will commence at PC 1 ; 

 the other end B, away from PP, is found by drawing a visual 

 ray, v B, from B towards the SP, stopping at the picture-plane, 

 from which it is taken perpendicularly until it cuts the line 

 PC 1 and vp 1 in o ; a o is then the perspective representation 

 of the given line A B. Make the space between a and 6 some- 

 what darker than the rest of the line. 



We advise the pupil to repeat this problem until he knows 

 the method of working by heart, then to turn the line or plan 

 the other way ; and, again, increase or diminish the angle of 

 inclination with the picture-plane. Also change the height 

 of the eye, or horizontal line, and the distance of the eye from 

 the picture-plane; these various positions of the object will 

 very materially assist the pupil in understanding % the method of 

 working the problem. 



LESSONS IN ENGLISH. XXI. 



WOBDS THAT ARE BOTH PREFIXES AND SUFFIXES. 

 SOME of the words which we treated of in the last Lesson as 

 nncombined suffixes, may also be regarded as uncombined pre- 

 fixes. The same word stands before and after its stem. You 

 may take, as an instance, to cast-down, and down-cast. In this 

 instance the meaning varies, but does not greatly vary ; to 

 cast-down is used physically, and dotun-cast signifies dejected, 

 sorrowful. Besides this difference, there is a difference also as 

 to the function of the two words, for the former is a verb, the 

 latter is an adjective. Rarely, perhaps, does the import remain 

 the same, if the position of the adverb is altered. Make a prefix 

 a postfix (or suffix), and in general you produce a greater or less 

 modification of meaning. Indeed, some of the most delicate 

 shades and hues of thought expressed in the English language 

 are connected with, if not dependent on, the varied use of these 

 movable particles. It may, therefore, be proper to go into 

 some little detail on the point. 



It is not all the prefixes and suffixes that usage permits to 

 take their stand before or after their principal word. Out enjoys 

 the privilege, and makes free use thereof. Look at these 

 examples : - 



cast-out, 



bid-out, 



grow-out, 



do-out, 



live-out, 



out-cast. 



out-bid. 



out-grow. 



out-do. 



out-live. 



cry-out, 

 laugh-out, 

 look-out, 

 right-out, 



out-cry, 

 out-laugh, 

 out-look, 

 out- right. 



An out-cast is one who undergoes the result and consequences 

 of being cast-out. Corresponding with out-cast, is out-law. But 

 though we may say to out-law, we cannot say to law-out. Out- 

 post is again different from out-cast, for out-post does not make 

 the idea of action so prominent as does out-cast. In this respect 

 out-cast is not unlike out-lay. Out-lay may be reversed ; thus, 

 lay-out. But while the verb is lay-out, the noun is out-lay. To 

 bid-out, is to bid with a clear, loud voice ; but to out-bid, is to- 

 bid more than another. To grow-out is very different from to 

 out-grow. A young brother, by becoming taller, out-grows an 

 elder brother ; and the elder brother, who is thus surpassed, 

 may be grown-owt at the shoulders so as to be hump-backed. 

 To do a person out of anything, is to cheat him ; but to out-do a 

 competitor is to excel him. If my children live-out the century, 

 they will out-live me. By crying-out lustily, boys make a great 

 out-cry. That shameless man, by laughing-out so loud and so 

 long, out-laughed all the company. If you look-out at the 

 window, you will have a pleasant out-look. 



" We have taken all the out-lying parts of the Spanish monarchy." 

 Temple. 



" But for public dormitories, how many a poor creature would kave 

 been obliged to lie-out of doors in the nights of the last severe winter !" 

 Anon. 



" Oh, my lord, 



Yon said that idle weeds are fast in growth ; 

 The prince, my brother, hath out-grown me far." Shakespeare. 

 " Albert has grouin-out of his clothes." 4non. 



" But breathe his faults so quaintly 

 That they may seem the taints of liberty ; 

 The flash and out-breafe of a fiery mind." Shakespeare. 

 " A fire breaking-out in the cellar, consumed the whole house." 

 Anon. 



" Nor they which use 

 To out-drinfc the sea." Donne. 



" You have ctrunfc-out the cask. Children cannot well drink out of 

 goblets." Anon. 



" Re looked and saw what numbers numberless 



The city gates out-poured." Milton. 



"Pour-Gilt a glass of wine for the famished woman." .Anon. 

 " The workmen, in standing-out for the wages, have out-stood the 

 appointed time." Anon. 



" Sense and appetite out-wte reason." SoiitTi. 



" A large majority of the constituency voted the old member out." 

 Anon. 



" Better at home lie bed-rid, idle, 



Inglorious, unemployed, with age out-worn. " Milton. 



" This reverent leecher, quite u-orn out 



With rheumatisms, and crippled with his gout." Dvyden. 



" By Shakespeare's, Johnson's, Fletcher's lines, 



Our stage's lustre Rome's out-shines." Denham, 

 " Out of Zion, the perfection of beauty, God 7iat?i sTiined." Psalm 1. 2. 



