262 



THE POPULAR EDUCATOR. 



Having thus correctly measured all the lines, the next step will 

 be to " plot ' ' them, that is, to lay them down upon paper in exact 

 proportion to their length. This is done by means of a, plotting 

 scale, which is a straight rule, usually twelve inches long, made 

 of ivory or boxwood, and bevelled on both edges, the edges 

 being exceedingly accurately divided into equal parts byfine lines, 

 each inch being distinguished by a longer line. The inch is sub- 

 divided into shorter lines, 2, 3, 4, etc., in each, at equal distances. 

 These secondary divisions represent chains, and each of these 

 divisions is again divided into ten equal parts, which being the 

 tenth part of a chain will represent ten links. An approximation 

 of intermediate numbers is made by the eye. Suppose a scale in 

 which each inch is divided into four equal divisions ; this scale 

 would be marked "40," and would, if used to plot a survey with, 

 make the scale of the plan so plotted = 4 chains to the inch. 



In using this scale, draw with a very finely-pointed pencil a 

 straight line, and commencing at a point (A, for instance), lay the 

 scale evenly along the line, letting the zero, or first line, coincide 

 exactly with that point. Then, referring to the Field Book, note 

 the figures inserted successively in the ruled column, and make 

 fine marks on the line corresponding to the distances indicated by 

 these figures. 



We subjoin the most elementary form of Field Book, and 

 show what it implies when plotted, 

 to . 



D294 



622 

 496 



270 



490 B 



Commence at 1 A . and range north-west. 

 We have here a straight line A c, measuring altogether 6'22 

 chains ; at 2'70 chains a perpendicular is set off to the right, 4'90 

 chains long, terminating at B. Further on the line, at 4'96 

 chains, another perpendicular is 

 set off on the opposite or left- 

 hand side to D, measuring 2 - 94 

 chains. What will be the form 

 of the field so measured, and what 

 its area ? Supposing this page 

 stands due north and south, the 

 line A c will lie as shown in Fig. 6, 

 and the points of divergence of the perpendiculars as indicated. 

 Then the area will be 



622 X 



490 + 294 



= 243,824 links = 2 acres 1 rood 30 poles. 



To -ensure correctness in the measurement, the lengths of the 

 four sides A B, B c, C D, and D A may be found both by calcula- 

 tion and the chain. Of course both should agree. 

 Further examples will follow in our next lesson. 



KEY TO EXERCISES IN LESSONS IN MENSURATION. IV. 



EXERCISE 16. 



1. About 251. | 2. About 6 acres, 2 roods. | 3. 1931-3 sq. yds. 

 4- Nearly 2 roods, 25 poles. | 5. About 2 acres 2 roods, 31^ poles. 



EXERCISE 17. 

 1. Ncarl/ 33. | 2. Nearly 161'2. | 3. 4C075. 



EXERCISE 18. 



1. : ;-06S5. I 2. -7854. | 3. 18 ft. 142 in. (sq. measure). 



4. 2 ft. 5A in. | 5. Nearly 78 yds. 1 ft. 7 in. 



EXERCISE 19. 

 1, 18ffc.l42in. (square measure). 2. 1 acre. 



EXERCISE 20. 

 1. 2-86488. | 2. 1 acre. | 3. About T069. 



EXERCISE 21. 

 1.50 feet. | 2. Nearly 5125. | 3. 1 acre, 2roods, 11-14 poles. 



EXERCISE 22. 



1. 71. 2. 28416. 



EXERCISE 23. EXERCISE 26. 



\. 311-23. | 2. 226-1448. 

 EXERCISE 24. 

 1. About 28-274. 

 EXERCISE 25. 

 L About 8i'82. 



1. 15 cub. ft., 1080 cub. inches. 



EXERCISE 27. 

 1. 540 cubic inches. 



EXERCISE 28. 

 . 259,332,888,183 cubic miles. 



LESSON'S IN SPANISH. IX. 



CONJUGATION OF THE AUXILIARY VERBS. 



As the auxiliary verbs are required to form the compound censes 

 of every other verb, we first give the conjugation of the 

 auxiliary haber, to have. 



INFINITIVE MOOD. 



SIMPLE TENSES. 



Present. Habe"r, to have. 



Present Gerund. Habieado, having. 



Past Participle. Habido, had. 



COMPOUND TENSES. 



Past. Habe'r habido, to have ha&. 

 Past Gerund. Habie'ndo habido, 

 liaving had. 



INDICATIVE MOOD. 



Present. 

 Sing. Yo he, I have. 



Tu has. 



Elba. 

 Plur. Nosotros be"mos. 



Vosotros habeis. 



Ellos ban. 



Imperfect. 

 Sing. Yo liabia, I had. 



Tu hablas. 



El habia. 

 Plur. Nosotros habiamos. 



Vosotros habiais. 



Ellos habian. 



Perfect Definite. 

 Sing. Yo hube, I had. 



Tu hubiste. 



El hubo. 

 Plur. Nosotros hubimos. 



Vosotros hubisteis. 



Ellos hubieron. 



.First Future. 

 Sing. Yo habre, I shall or will have. 



Tu habras. 



El liabi-ii. 

 Plur. Nosjtros habre'mos. 



Vosotros habrdis. 



Ellos habran. 



Pei-fact Indefinite. 

 Sing. Yo be habido, I have had. 



Tu has habido. 



El ha habido. 

 Plur. Nosotros hemos habido. 



Vosotros habeas habido. 



Ellos han habido. 



first Pluperfect. 

 Sing. Yo habia habido, I had had. 



Tu habias habido. 



El habia habido. 

 Plur. Nosotros habiamos habido. 



Vosotros habiais habido. 



Ellos habian habido. 



Second Pluperfect. 

 Sing. Yo hube habido, I had had. 



Tu hubiste habido. 



El hubo habido. 

 Plur. Nosotros hubimos habido. 



Vosotros hubisteis habido. 



Ellos hubieron habido. 



Second Future. 

 Sing. Yo habre habido, I shall or witt 



Tti habras habido. [have had. 



El habra habido. 

 Plur. Nosotros habrdmos habido. 



Vosotros habreis habido. 



Ellos habrau habido. 



IMPERATIVE MOOD. 

 Sing. Ha tii, have thou. 



Haya 61, let him have, or may he have. 

 Plur. Hayamos nosotros, let us liave, or may we have. 



Habdd vosotros, have you. 



Hayan ellos, let tlwm have, or may t7iey have. 



Present. 

 Sing. Yo haya, I may have. 



Tu hayas. 



El haya. 

 Plur. Nosotros hayamos. 



Vosotros hayais. 



Ellos hayan. 



Imperfect. 



Sing. Yohubidra, habria, or hubie'se, 

 I would, should, or might 

 have. 

 Tu hubie'ras, habrias, or 



hubidses. 

 El hubiera, habria, or 



hubie'se. 

 Plur. Nosotros hubidrainos, habria- 



mos, or hubiesemos. 

 Vosotros hubie'rais, habriais, 



or hubidseis. 



Ellos hubieran, habrian, or 

 hubie"sen. 



First Future. 



SUBJUNCTIVE MOOD. 



Perfect Indefinite. 



Sing. Yo haya habido, I may havo 

 Tu hayas habido. [had 



El haya habido. 



Plur. Nosotros hayamos habido. 

 Vosotros hayais haUJo. 

 Ellos hayan habido. 



Pluperfect. 



Sing. Yo hubie'ra, habria, or liubie'se 

 habido, I would, should, or 

 might have had. 

 Tu hubie'ras, habrias, or 



hubie"ses habido. 

 El hubiera, habria, or hubidsc 



habido. 



Plur. Nosotros hubieramos, habria 

 mos, or hubie'semos habido. 

 Vosotros hubierais, habriais, 



or hubieseis habido. 

 Ellos hubieran, habrian, ot 

 hubiesen habido. 



Second Future. 



Sing. Si yo hubidre, if I should 

 have. 



Si tii hubi^res. 



Si 61 hubiere. 

 Plur. Si nosotros hubidremos. 



Si vosotros hubi^reis. 

 Si ellos hubie"ren. 



Sing. Si yo hubiere habido, if I 



should have had. 

 Si tii hubie'res habidc. 

 Si el hubiere habido. 

 Plur. Si nosotros hubieremos 



habido. 



Si vosotros hubi<?reis habido. 

 Si ellos hubieren habido. 



By examining the above conjugation, it will be seen that, 

 after having learnt the simple tenses, the compound ones ara 



