MECHANICS. 



m'enverri-vou P IB. Jo TOU* envorrai le moilleur quo j'aie ; pronez 

 garde de le taohor. 1'J. I'OUHOZ-VOUH quo iVtudiuut ui>|>rauna tout cola 

 par ccuurP 20. Je ue croia pa qu'il l'ui>]>i< nuu. 21. PenMC-voua 



,-uiie ? 22. Ja oroi* qu'il vioudru biuuUit. J.J. I'uiicez-vouii <]ue 

 M. Totro piiru cuuipte tur moi ? -1. Jo lais qu'il cotupte iur vou*. 

 a i..- . ..ii i.!< t-il pus sur moi P 26. Jo pease qu'il compto 

 HUT votro n p..itiur rentrera-t-il bioutot P 28. J'otpero 



qu'il no tardera pan loug-teinp*. 29. No voulez.roua pa* mo priter 

 votre panipluie '< 'M. Jo vous le preterai aoo plaiiir. 31. Mun fr.'-re 



ildeboutf '-' 1 1 no veut pat 'oMeoir. 33. Dt%iruz-vouM quo 

 jo m'ossoiu 't 31. Jo desire quo vou restiez debout. 35. Ja ddsire 



IjU'jl VI 



EXERCISE 145 (Vol. II., page 202). 



1. Would you with me to buy a coat half worn out P 2. I wish 



that you should buy a nw one. 3. Did they wish that sick soldier to 



to his post P 4. They wished that he might repair to bin 



regiment. 5. Would it bo uecossary for me to dwell on the sea-shore 'f 



11. It would bo necessary, for the recovery of your health, that you 

 should n-i'iiir to Switzerland. 7. Do you not thiuk Unit this child 

 resembles his mother P 8. I do uot think (that) he resembles her. 9. 

 Whom does ho resemble P 10. Ho resembles his eldest sister. 11. 

 Would you couseut to your daughter's marriage with that druukurd ? 



12. Would you have us die with want ? 13. I feared lest those ladies 

 might die with the cold. 14. Will you not fire at that hare ? 15. I 

 would fire at that woodcock, if my guu were loaded. 16. How muuy 

 shots would you have me fire ? 17. If you had powder, I would have 

 you fire at that partridge. 18. Do you wish me to cast a glance upon 

 that letter ? 19. I would have you read it. 20. What would you 

 have me do P 21. I would have you pay attention to your studies. 

 J_'. Would it be necessary for me to go out ? 23. It would be neces- 

 sary for you to remain at home. 21. What would you that I should 

 do to that horso ? lio. I would have you strike it with the whip. 



EXERCISE 146 (Vol. II., page 202). 



1. Quo voudii -/.-voiis que je fisse? 2. Je voudrais que vons jetas- 

 siez un coup d'ueil sur cette lettre. 3. Voudriez-vous que je doniiasse 

 des coups de baton a ce chien ? 4. Je voudrais quo vous donnassiez 

 des coups de fouet a ce cheval. 5. Exigeriez-vous que nous revins- 

 sions a cinq heures ? 6. J'exigerais que vous revinssiez de bonne 

 heure. 7. Pensez-vous que votre frere ressemble a M. votre pore ? 8. 

 Je ne pense pas qu'il ressemble a mon pere ? 9. A. qui peusez-vous 

 qu'il ressemble ? 10. Je crois qu'il ressemble a ma mere. 11. Com- 

 bien de coups (de fusil, Ac.) avez-vous tire's ? 12. J'ai tir cinq coups 

 sur cette Wcasse. 13. Ne voudriez-vous pas quo je tirosso sur cette 

 perdriz ? 14. Je voudrais que vous tirassiez sur cette perdrix, si votro 

 fusil ^tait charge". 15. Ou faudrait-il que je demeurasse ? 16. II 

 faudrait que vous demeurassiez au bord de la mer. 17. Voudriez-vous 

 que je mourusse de foim ? 18. Je ne voudrais pas que vous inourus- 

 siez de faim. 19. Voudriez-vous que votre frere mourut de froid ? 

 20. Je ne voudrais pas qu'il niourut de froid ou do misere. 21. Que 

 youdriez-vous que fit M. votre flls ? 22. Je voudrais qu'il opprit ses 

 lecons. 23. Voudriez-vous qu'il apprit Vallemand ? 24. Je voudrais 

 qu'il aprit 1'allenmnd et 1'espagnol. 25. Avez-vous tird sur ce lievre ? 

 26. Je n'ai pas tire 1 sur ce lievre. 27. Faudrait-il que je sortisse ? 28. 

 II faudrait que vous sortissiez. 29. Faudrait-il que je rcstosse ici ? 

 30. II faudrait que voas allassiez a I'^glise. 31. Que dtteiriez-vous ? 

 32. Je voulais que vous m'ccrivissiez. 33. Vouliez-vous que j'ache- 

 tasse un habit a demi-usd ? 34. Je voulais que vous achetassiez uu 

 bon chapeau. 



are bineoted by the arrow perpendicular to them, is another 

 instance, the arrow being the axis of ymmt-try. Whererer 





MECHANICS. VII. 



AXIS OF SYMMETRY STABLE AND UNSTABLE EQUILIBRIUM. 

 AXIS OF SYMMETRY. 



THERE is a large number of cases in which, though we may not 

 be able actually to find the centre of gravity, we can say it is 

 on some line in reference to which the body is symmetrically 

 formed. In an egg, for example, the line joining the round and 

 pointed ends is an axis of symmetry. If we make cross sec- 

 tions of it perpendicular to this line, they will be all circles 

 through the centres of which the line will pass. The elliptic 

 oval at a, Fig. 33,* and the cylinder at c, and the right cone 

 at d, are instances. The cubical box at e is another, in which 

 the cross section is a square, the line joining the meetings of 

 the diagonals on the upper and lower faces being a symmetrical 

 axis. The oval board at b, also, in which all the dotted lines 



It will be noticed that some of the figures which have been em- 

 ployed in Lesson VI. in Mechanics have been introduced a second 

 time in the present lesson. This has been done to spare the reader 

 the trouble and annoyance of bavin? to turn from one page to another 

 when reference has been made in the course of a lesson to any figure 

 which has been used before as a means of illustrating the text. When- 

 ever, therefore, any figure is given a second time, it must be under- 

 stood that this is the reason for its repetition. 



a 



Fig. 



two such axes exist, of course the centre of gravity is their 

 point of intersection ; but if there be one only, aa in the 

 /\ portion of the ring in Fig. 34, the posi- 



tion of the centre on it most be ascer- 

 tained by other means. 



STABLE AND UNSTABLE EQUILIBRIUM. 



In the last lesson, I showed yon that 

 when a body rests in equilibrium on a 

 horizontal plane, the perpendicular from 

 the centre of gravity falls within its base. 

 Fig. 34. Thig condition being satisfied, it will not 



upset of itself, but may be overturned from without by a force 

 acting sideways. What are the conditions on which depend 

 the ease, or the difficulty, with which it can be so upset ? Let 

 three cylinders, a, b, c, Fig. 35, be taken in illustration ; the 

 first of broad base and small height, the other two of equal 

 heights and bases, the 

 latter narrow in each. 

 Suppose that a force, say 

 of one pound, represented 

 by the dotted arrow 

 pointing to the right, is 

 applied transversely to 

 each, and let the weights 

 of the bodies be repre- 

 sented by arrows pointing 

 downwards on the ver- 

 tical lines in which their 

 centres of gravity lie. 

 Now, the resultant in 

 each cylinder of these 

 two forces, represented F . 35 



by the arrows slanting to 



the right, is the upsetting force. If this arrow strikes the 

 ground outside the base of any cylinder, it will overturn ; if 

 uithin, it will remain standing as before. 



1. Now, taking any one of the cylinders, say a, it is evident 

 that the transverse force remaining the same, and the height 

 at which it is applied the same, the greater its weight is the 

 longer will the arrow o P be, and therefore the more will the 

 resultant o R slope downwards towards o p, tending to fall 

 within the base. Therefore, everything else being the same, 

 the greater the weight of the body the less easily is it upset, 

 that is, the more stable it is. 



2. Again supposing the weights of the two cylinders, a, c, to 

 be equal, but the base of the former greater than that of the 

 latter, if equal transverse forces be applied to both at eqnal 

 heights, then o R being also equal in both and equally inclined 

 to o P, the resultant will tend more to fall within the base 11 

 than in b, that is, everything else being the same, the broader 

 the base the greater the stability. 



3. Further, if, as in 6 and c, the bases and weights being the 

 same, and the transverse force applied to each cylinder being 

 still one pound, the force is applied higher up in one cylinder 

 than in the other, then the resultant is more likely to meet 1 

 ground within the base in the latter than in the former ; that 

 is, the lower doirn the transverse force is applied, everything 

 else being the same, the greater the stability. 



