52 



THE POPULAR EDUCATOR. 



THE 

 ACTIVE. 



Principal Tenses. 



8ing. 



2. 



3. 

 Dual. 1. 



2. 



3. 



1. 



2. 



3. 



-All. 



-ffi. 



-Tl. 



Historical T- 

 -v. 

 -*. 



TERMINATIONS. 



MIDDLE. 



Principal T. Historical T. 

 -/wu. -A"?"- 



-TOI. 



-ro. 



-JUC00C. 



PZu. 



/J.V. 



re. 



-TJJ'TOl. 



By studying these terminations now, and by reverting to 

 them afterwards, the student will be materially assisted ; but 

 he must make himself thoroughly master of all the paradigms 

 before he attempts to set a step in advance. 

 VOCABULARY. 



befit, suit, agree ] sent active, to be- 

 with. The infini- i hold ; ttmv 6pa.v, 

 tive is in the text literally, it is to 

 used as a noun, 

 and may be ren- 

 dered in harmony. 



po, -os, rj, a mar- 

 ket. 



Airopos, -a, -or, im- 

 passable ; TO 

 orropa, straits, ex- 

 tremities. Ob- 

 serve that ttpctt, 

 with the preposi- 

 tion tin, signifies to 

 be in the power of. 



Apiffrov, -ov, TO, 

 Breakfast ; fifj.tv 

 apiffTov <TTI, we 

 have breakfast. 

 Eivai, with a dative 

 of the person, has 

 the force of to 

 have; the pronoun 

 must be put in 

 the dative, the 

 person being pre- 

 served : thus tan 

 pot is I have ; trn 

 ffoi, thou hast, etc. 



'Apfj.oTreti', to fit, 



you 



see, that 

 may see. 



Upiauai, I purchase ; 

 irpiaffOai, infini- 

 tive present mid- 

 dle, to purchase; 



OVK 7JV TTptGLffuCtl, 



literally, was not 

 to purchase, that 

 is, could not be 

 purchased. 



Suy/coAfeo, I call to- 

 gether, convoke ; 

 6 ffvyKa\<av, con- 

 vener. 



Tots, -ftos, T), a rank 

 or file of soldiers. 



$epo>, I bear. 



QuTfia, -os, TJ, plant- 

 ing, care. 



'fipa, -os, ij, an hour 

 (Latin,7iora),time. 



agricultural ; 

 hence the name 

 Qeorgics, given to 

 Virgil's didactic 

 poem on agricul- 

 ture. 



Ai/u>, I go down, 

 enter ; irpo OUVTOS 

 ;\J<N/, before sun- 

 set. 



EmAeiirai, I leave, 

 lack ; ftrt\tTre , se- 

 cond aorist active, 

 failed. 



0eA.cc, I desire, I will. 



Nt/coco, I conquer. 



'Opaco, I see, behold ; 

 0paj/,infimtive pre- 



EXERCISE 72. GREEK-ENGLISH. 



1. 'H TO|IS f\v eKaTov avopes. 2. Hi> TTJS clpas u.iKpov vpo SVVTOS 

 rj\iov. 3. Of VOV.QI fapicu fiffi Ttav au.apTta\tav. 4. TOUTOIS 6a.va.ros 

 tffTiv i) w a - 5. 'O ffiros tire\fiff, /cat irptaffOai OVK rjv. 6. Fo'Tiy 

 6pav TO opos. 7. 'H Ayr)ffi\aov aptrr] irapaSfj^/xa nv. 8. 'Hv.iv 

 apiffrov OVK tffTiv. 9. E-yeo fffou.ai 6 <rvyKa\a>v. 10. OUTOS effTiv & 

 VIKO>V, 11. Eyco fj-ia. TOVTUV etfj.1. 12. Bafft\<us vov.iei vu.a.s O.VTOV 

 fivat. 13. EcrTii' ovv TTJS yewpyiKris Tex*''? 5 V r<av SfvSpcev <pvTeia. 

 14. EffTtv OUTOIS ayopa. 15. E^ TOJS oirop-'is rffifv. 16. 'O Kupos 

 tv rovrois i\v. 17. Eir( trot tcrTot rovra 18. Ou /uiKpoc ayadov 

 TCO apu.oTTfiv irpoffeffTiv. 19. Tr? /3ia irpaffiffiv t-)(Qpai KOI KivSvvoi. 

 20. TTJ eiriu.f\fia. iffpifivai TU>V <pt\cav 6e\o>. 21. Uapr/v A.yf(n\aos 

 5ci?po (btpuv. 22. Kvpy iropTjcroj' CK Tl\oirovvriffov I'Tjes. 



EXERCISE 73. ENGLISH-GREEK. 



1. This is in my power. 2. The laws are in your power. 3. 

 It is in your power (that is, it depends on you) to purchase corn. 

 4. It was in the power of the enemies to be present. 5. It is 

 in the power of good boys to excel. 6. It will be in my power 

 to approach the city. 7. Punishments belong (Trpoo-eivoi) to sin- 

 ners. 8. Thy care of thy friends is an example to all. 9. The 

 ships have come to the king. 



MECHANICS. XVII. 



STATICAL FORCES. 



WE must now look at two propositions which are often very 

 useful, and we shall then be able to trace the application of 

 what has been said to a few common cases. 



When a body is kept at rejt by the action of any number of 

 forces uDon it, if we resolve these forces along any two directions 

 at right angles to one another, their resolved parts in each direc- 

 tion must neutralise each other. If they did not, some motion 

 must ensue. In a similar way we can often find whether any 



number of forces will produce equilibrium, and if not, what their 

 resultant will be. This mode of solving the question is some- 

 times more convenient than the polygon of forces. 



Suppose three forces, represented by A B, A c, and A D (Fig. 84), 

 act on A. Fix on any two lines E F and G H at right angles to 

 one another, and both passing through A. From B, C, and D 

 drop perpendiculars on E F and G H. This may be done with a 

 square. Now A B is the diagonal of the parallelogram K A N B, 

 and thus is the resultant of two forces which are represented by 

 A N and A K. We may therefore resolve it into those two, and, 



rig. 84. 



instead of A B acting on A, we shall have the two forces A N 

 acting along E F, and A K acting along H G. 



In the same way resolve A c and A D into A L and A M, and 

 A o and A P respectively. 



We have thus resolved all our forces into others acting in 

 the directions we fixed upon. Three of these, AN, AM, and 

 A o, act along E F ; and if A N equals the sum of the other two, 

 these will cancel one another, and so of the forces along G H. 

 If there are any residues in either case we mark off distances 

 from A to represent them, and complete the parallelogram, the 

 diagonal of which will be the resultant. 



The other proposition is as follows : If a body be kept at 

 rest by the action of three forces, their lines of action must, 

 unless the forces be parallel, pass through one point. For if not, 

 since two of them pass through the point in which they meet 

 (and they must meet, not being parallel), the body will turn till 

 this point comes into the line of action of the third. If in Fig. 

 85 two of the forces act through B, and the third through A in 

 the direction A c, the body will evidently turn till B, A, and c are 

 in one straight line. The cases when the forces are parallel 

 have all been considered except the one when equal and parallel 

 forces act in opposite directions, and we have what is termed a 

 couple. Let A c and B D represent two such forces. In any 

 other case, if forces act on a body, a single resultant can be 

 found, but here no one force that can be applied will produce 

 equilibrium. The motion, however, which these forces tend to 

 produce, is not one of progression 

 through space, but merely one of 

 rotation round a point midway 

 between A and B. This tendency 

 to rotation increases with the 

 distance A B, and is clearly 

 equal to the sum of the forces 

 multiplied by half that distance. 



Fig. 85. 



The only way to overcome these forces is to introduce another 

 couple having an equal tendency to turn the body in the con- 

 trary direction. 



EXAMPLES. 



1. A lever of the first kind, 8 feet long, weighs 10 pounds. What 

 weight will a power of 10 pounds raise, the fulcrum being 15 inches 

 from the end? 



2. In the first system of pulleys there are four blocks, each weighing 

 2 pounds. If one-fifth of the power be lost by friction, what weight 

 will 15 pounds support ? 



3. If friction be reckoned at 9 pounds per ton, what power will be 

 required to draw a train weighing 20 tons up an incline of I in 100 ? 



4. What strain must a horse poll with, to draw a load of 27 cwt. 

 up an incline of 1 foot in 70, the co-efficient of friction being fa ? 



* 



