LESSONS IN 



^ are indicated only in tho elevations. Sometime* when tho 



; is a simple one for iuatancc, a plain wull its coarse 



.ml thickness will !> shown in tlu i'l;i:i, mid its lu-i^lit marked 



it tho end, as (10*5 foot), moaning Unit it 



is to bo built I" ( -t <! inches high. Fig. 9 in the plan . 



,i <>/ a cottage. It will bo seen that if tho plan bo drawn 

 . n>. ndirulurly dottud line* must bo drawn parallel with 

 ii.-r fp>:n -..!> angle, and from tho terminations and 

 f each line, \vhirh will dotcrmino the extent of tho 

 ; >ii and of it- several parts, but not its height. If tho 

 a bo drawn first, the perpendicularly dotted lines are 

 projected downwards to pvodaco the plan. In orthographic pro- 

 i wo usually draw a lino to represent the meeting or axis 

 of tho two planes of projection, tho horizonal and tho vertical, 

 which, us iu Fig. 10, we have marked xy; therefore it must bo 

 remembered that all above that line is understood to be tho 

 ' plane of projection upon which the elevations are drawn, 

 and all below it (If l'.ni-i.t>itt<tl. />/<n<. upon which tho plans aro 

 drawn. Tho plan of a circle when parallel with tho ground is a 

 circle of tho same size indicated by the scale. Tho elevation is 

 a straight lino only, equal to the diameter (Fig. 10). If tho circle 

 is standing on its edge perpendicularly to tho ground, then its 

 plan is a straight lino only, and tho elevation is a circle (Fig. 11). 

 To illustrate tho positions (Fig. 10), let tho pupil hold a penny- 

 piece horizontally before, and level with, his eyes ; ho will see 

 the edge, the elevation; then let him place it upon tho ground, 

 and look down upon it ; ho will soo tho whole circumference, 

 the plan. Reverse tho position of the penny, and do tho same 

 for Fig. 11. Wo trust there will bo no difficulty now in under- 

 standing the position of tho eyo with respect to both planes of 

 projection. As we intend to devote tho present Lesson to the 

 consideration of this subject, preparatory to moro important 

 questions in perspective, we will give our pupils a few simple 

 problems for practice, reserving others of a more complicated 

 nature till they are required in future Lessons. 



PROBLEM II. (Fig. 12). A rod, 4 feet long, is parallel with, 

 and 2 feet from, both planes ; draw its plan and elevation. Scale 



1 inch to tlie foot. First draw x y, tho axis of the planes, and 

 draw a 6, 4 feet long, parallel with and 2 feet from xy; then 

 from the extremities a and u draw perpendicular lines to c and 

 d ; mark c and d 2 feet above x y, and join them ; e will bo tho 

 elevation, and/ tho plan. 



PROBLEM 111. (Fig. 13). When the same rod is at an angle 

 of 40 with Hie vertical plane and parallel with the Iwrizontal 

 plane. Draw a line c g at an angle of 40 with xy, make ef 

 equal to 2 foot, and draw fa parallel to x y : a will bo tho plan 

 of one end of tho rod 2 feet from the vertical plane ; upon e g 

 and from a make a b, tho plan, equal to 4 feet : draw the per- 

 pendicular lines a c and b d, and draw c d, tho elevation, 

 parallel with and 2 feet above x y. 



PROBLEM IV. (Fig. 14). When a rod is at an angle of 40 

 with the ground and parallel with the vertical plane. Draw e g 

 at an angle of 40 with xy, and draw tho perpendicular ef 



2 feet from xy, also fc parallel with xy; cut of? cd, equal to 

 4 feet, the whole extent of the rod : from c and d draw per- 

 pendiculars cutting x y to a and b; join ab, for the plan, 

 parallel with x y. 



When tho object is at an angle with both planes, the angle of 

 inclination with the horizon is made on tho horizontal piano. 



PROBLEM V. (Fig. 15). Let the rod have one end on Uie ground, 

 and let it rise at an inclination of 50, and let its plan be at an 

 angle of 40 with the vertical plane. Draw tho lino eag at the 

 given anglo 40 J with tho vertical piano ; npon this lino tho plan 

 will bo represented. Draw a h at an anglo of 50 with o g, and 

 mako a m equal to tho length of tho rod ; from m draw TO n per- 

 pendicular to ag; an will then bo tho plan of tho rod when 

 inclined to tho horizon at 50. Draw ncd and o b at right 

 angles with x y, and make c d equal to m n ; join 6 d; tho lino 

 b d will bo the vortical elevation. That this may be moro clearly 

 anderstood, we will draw tho eidograph of the problem, Fig. 16, 

 that is, tho figure or appearance it would present when placed in 

 conjunction with the two planes of projection (Fig. 8 is also an 

 fidograph). In Fig. 16 a o is tho given rod, and an is its plan. 

 Now in order to get tho inclination of a o, the rod, which is raised 

 from the paper at an inclination of 50, must bo rabatted, that 

 is, thrown down upon tho horizontal plane ; the course of tho 

 dotted aro o m will show this. Wo must construct tho anglo of 

 the inclination of the rod upon the horizontal plane, that is, tho 



anglo it forms with tho ground; therefore man will be equal 

 to oan; thi* wan the reason the angle man in Fig. 15 WM 

 made 50. By comparing Fig*. 15 and 16, the same letter* 

 lii:in- used in both, tho corresponding linen will be Men, and it 

 will bo understood why c d in Fig. 15 U nude equal to m n, 

 because, as in Fig. 16, mn i equal to no, the dirtanoft of the 

 upper end of tho rod from tho ground, and no i* equal to c d, 

 therefore m n is equal to cd. 



PROBLEM VI. (Fig. 17). The fnutrvm of a right square 

 pyramid rests with its base on a horizontal plane, the length* of 

 the edges of the top and base being retpectivcly 1*3 and 2*4 

 incl^s, and the height 2'8 inches; draw its plan and elevation. If 

 a pyramid bo divided into two parts by a plane parallel to it* 

 base, tho part next tho base is called a frustrum of a pyramid, or 

 sometimes a truncated pyramid. Draw the square abac, the plan 

 of tho base 2-4 inches side (see Lessons in Geometry, Problem 

 XVIII., Vol. I., page 255), and within it tho square efh g, the plan 

 of the top 1 *3 inch side. In order to place tho plan of the top BO 

 that tho edges shall bo equidistant from the edges of tho plan 

 of tho base, proceed as follows : Draw the diagonals c b and 

 ad, make en equal to 1*3 inch, and draw nh parallel to 

 cgfb; draw gh parallel to cd; the rest will be evident, M 

 tho angles are in tho diagonals, and the sides are parallel to a b 

 and a c respectively. Having drawn tho plans, then draw * y, 

 tho ground line, parallel to one side of tho square ; draw a m and 

 b 1; draw the lines ci and fk, continuing them above xy equal 

 to tho height of tho frustrum 2*8 inches ; join im,kl, and t k; 

 mikl will be the elevation. The pupil will observe that other 

 elevations can bo drawn from the sitne plan, opposite any 

 other side, when required for working purposes a common 

 practice in drawing extra elevations for building construction ; 

 in those cases all that is necessary is to arrange the ground line 

 or axis of the planes opposite the side of which the elevation is 

 required. Fig. 18 is the same subject as Fig. 17 : * y is placed 

 parallel to one of tho diagonals of the plan, consequently two faces 

 of the frustrum are seen, a' and b', shown in the plan as a and b. 



LESSONS IN FRENCH. XX. XV If. 



SECTION LXXXI.-THE DEMONSTRATIVE PRONOUN CS 

 ( 103). 



1. The pronoun ce answers to the English pronoun it, used 

 before the verb to be, or a verb followed by to be, when the 

 Utter is itself followed by a personal, a demonstrative, or a 

 possessive pronoun. In this case, the English personal pro- 

 nouns are expressed : I by moi, thou by toi, 7e by ltd, she by 

 elle, we by nous, you by vous, they (m.) by eax, they (f.) by 

 elles. 



The verb is used in the singular, except before personal pro- 

 nouns of the third person plural, and before possessive and 

 demonstrative pronouns in the plural. In the interrogative 

 form, however, the verb remains in the singular even before 

 personal pronouns of the third person plural. 

 C'est moi, c'est lui, c'est elle. ft u I, it u hi, it u tht. 



Ce sout elles qui parlent. It i thcj vho tptak. 



Ce peuvent 4tre lea miens. Thty may be rain*. 



Est-ce eux t Est-ce elles t 1$ it thty I 



Sont-ce ceux quo vous conniunsez t Art thty (AoM you know f 

 Non, ce ne Bont pas ceux quo je A'o, thty art not thott I know. 



conuais. 



2. If tho relative prononn qui and another verb follow *tre, 

 thie second verb must agree in number and person with tho 

 pronoun preceding the relative : 



C'est vous qui avez fait cek. It i* you who hart dont that. 



CYst iious qui avous declare* oette It it vt vho taM (on that Ur. 

 ooie. 



3. Ce is also the equivalent of the English prononn it, used 

 impersonally with tho verb to be, when the latter is not followed 

 by an adjective* [103 (5)] : 



Co fut en Allemaguo qu'il troura If ir<u t'n Germany (hot lU/omd hu 

 sou ami. /rinL 



4. Celui qui, celle qui, ceux qui, m., celles qui, f., are 



* Etre, used impersonal!/, snd not followed by any of the 

 mentioned above and in Sect. 82, has for subject 11: 



II cat vrai que je 1'ui dit. II it trut that I hart tatid U. 



11 eat difficile do le croire. It u difficvU to Mint U. 



