54 



THE POPULAR EDUCATOR. 



This principle is said to have been discovered by Archimedes 

 in the following manner : Hiero, the King of Syracuse, had 

 some gold which he wished made into a crown ; so, having 

 weighed it, he handed it to a jeweller of the day for that pur- 

 pose. When it was returned he found the weight was correct, 

 but had a suspicion that some of the gold had been kept back 

 and its place supplied by baser metal. He accordingly re- 

 quested Archimedes to try and discover whether or not it was 

 so. For a long time he puzzled his brain, trying to devise some 

 plan for solving the problem. At last, when taking a bath, he 

 noticed that his body displaced a bulk of the water, and was 

 buoyed up by its pressure. From this the idea struck him, and 

 he rushed out exclaiming, " I have found it ! I have found it ! " 



EXAMPLES. 



1. In an hydraulic press the diameter of the small piston is three- 

 quarters of an inch, and that of the large one 9 inches. The lever ia 

 2 feet long, and the piston is attached 4 inches from the end. What 

 power must I apply to compress any substance with a force o 

 20 tons ? 



2. What is the pressure on the sides and what on the bottom of a 

 vessel 10 feet by 6, filled with water to a depth of 4 feet 6 inches ? 



3. A canal is 9 feet wide, and the water rises against a lock-gate to 

 the height of 12 feet 6 inches. Bequired the pressure on the gate. 



4. Two pistons are fitted into a vessel. One has an area of 4 square 

 inches, the other is 7 inches in diameter. What force must be exerted 

 on the small one to produce a pressure of 380 pounds on the other ? 

 (The area of a circle is 31th times the square of the radius.) 



5. A canal is 6 feet deep, but the bank slopes so that the length ot 

 it from the surface to the bottom is 6 feet. What pressure does a 

 portion of the bank 12 yards long sustain ? 



6. The pressure on a surface 3 inches long and 2 inches wide, 

 immersed in a vessel of water, is 3 pounds. If it be sunk 3 feet deeper, 

 What will the pressure be ? 



LESSONS IN GREEK. XXXY. 



CONTRACTED PUEE VEKBS. 



IN order to obtain a perfect acquaintance with those verbs, we 

 must still take up the forms in detail, and first 



THE PRESENT AND IMPERFECT ACTIVE OF CONTRACTED 

 VERBS IN aw. 



VOCABULARY. 



QUESTIONS ON THE ENSUING EXERCISE. 



What is f^airartacriv made up of ? What mood, tense, and 

 person is it ? What class of verbs does it belong to ? 



Why is i)\iKias in the genitive case ? Go through the noun 

 that is, decline it. 



Give the tense to which 6pa belongs in all its parts first 

 uncontracted, then contracted. 



What part of the verb is 5p<n P 



Wkat is the root of yo-rpaTrrfv ? What augment has the 

 form? 



Explain the formation of crvveKvica. 



What part of the verb is aya-iraey ? Go through the tense. 



EXERCISM 97. GREEK-ENGLISH. 



1. rioAAaKis yvcafj.r]v t^airarfaffLv <5ecu. 2. MTJ ere i/iKarca /cepSos. 

 3. Epw TTJS ctperrjs. 4. FIoAAaKis viica /cat tcaitos avSpa ayaQov. 5. 

 Of ayadot epcaffi TTJS aperrjs. 6. IIoAAot avdpcairoi fv TTJ TTJS ^Ai/cias 

 UK/J.TI TeAeuTcotnj'. 7. H fficaira, TJ Ae-ye a/Afivova.. 8. Ava.yK.rj tern 

 iravras avdpuirovs TeAeurav. 9. Nous opa, /cat vovs aitovei. 10. 

 0a/5aAws, <a ffTpariatrai, op/j.cofj.ff tin TOVS Tro\efj.iovs. 11. Tlpiv 

 ufv irfivyv iroAAoi ecrdiovffi, irpiv 5e Si^/riv irivovaw. 12. Oun fff'n 



rois /XT; Spcaffi crvfj.fj.axos "rv^jn- 13. TiepiK\.r)s ijcrTpairrev, t&potira., 

 ffvveKUKa. TI\V 'EAAaSa. 14. Ei0e iravres iratSes TOI/S yoveas 

 aycnrcpev. 



EXERCISE 98. ENGLISH-GREEK. 



1. Thou deceivest. 2. He deceives. 3. He was deceiving. 

 4. You two deceive. 5. They deceive. 6. They were conquer- 

 ing. 7. We were conquering. 8. The general conquers all his 

 enemies. 9. I am hungry. 10. We are thirsty. 11. They are 

 hungry. 12. The allies are hungry. 13. It lightens. 14. It 

 thunders. 15. Thou didst put the city in confusion. 16. Good 

 children love their parents. 17. The boy loves his mother. 18. 

 Thou lovest all men. 19. They see thee. 



THE PRESENT AND IMPERFECT ACTIVE OF CONTRACTED 

 VERBS IN ew. 



VOCABULARY. 



EXERCISE 99. GREEK-ENGLISH. 



1. AvTjp iroj/rjpos Sinrruxei, KO.V fVTvxy. 2. Bios KpariffTos (sc. 

 o"Ti) av 6v[j.ov Kparris. 3. 'Siyav yuaAAoi/ 77 AaAeiV irpeirei. 4. 'O 

 rt av TroiTjre, vo/K^ere bpav Qeov. 5. <J>iAos <pt\cii av^LVovwv ai/Tip 



TTOVfl. G. Ot avOpUTTOl Ql>7]TOl fj.ri (ppOVOVVTWl' VTTfp OtOVS. 7. 'O 



juaAiffTa tvrv-)(_<av yurj /j.eya (ppovfirta. 8. OvSeTror' a6v/j.eit> TOV 

 Kanias irpaTTOVTa 8e<, ra f)f\Tico 5e TrpoffSoKav aet. 9. Tai TTOVOVVTI 

 eos o"uAAa/x$apet. 10. AiKaioavitrtv aiTKeire *cai fpyy /cat \oyy. 



REMARKS. 



Kav, a contraction of /cat av or /cat tav, means even tliough. 

 Of avBpooiroi, etc., let not mortal men aspire above the gods. 

 KOKCOS irpaTTtiv ia to be in bad circumstances, to be ill off, to 

 be in an unhappy condition. 



EXERCISE 100. ENGLISH-GREEK. 



1. He is unfortunate. 2. They are fortunate. 3. They are 

 fortunate, but they are not happy. 4. You are unfortunate. 5. 

 Conquer your spirit. 6. Friends work together with (dat.) 

 friends. 7. Let not a mortal man think (carry his aims) above 

 the gods. 8. They become dispirited when they are unfortunate. 

 9. Thou art dispirited. 10. He is dispirited. 11. The boy 

 neglected his body. 12. A wise man praises those who (TOVS 

 with pros, part.) practise justice. 



THE PRESENT AND IMPERFECT ACTIVE OF CONTRACTED 

 VERBS IN 00). 



VOCABULARY. 



