APPENDIX. 295 



of its vibrations gradually, until it settles again in its origi- 

 nal position A B. According to the laws of pendulums, 

 those of equal length move in equal times, though they pass 

 through difterent arcs, or portions of a circle. If the pen- 

 dulums AB, fig. 18. and C D, fig. 19. be equal, the time of 

 passing through EF is equal to that of passing through G H. 

 Thus the vibration of the string AB, fig. 17. is considered 

 as a double pendulum, vibrating from the points A and B, 

 the respective vibrations of which, from the greatest to the 

 least, are performed in the same time : this is the reason 

 why a musical string has the same tone from the beginning 

 of the vibrations to the end. 



LESSON 8L 



Optics. Rejicction and Refraction of Light. If L G^ 

 fig. 29. Engr. III. be a reflecting surface, as a looking glass, 

 then B C is the incideiit ray, and C E is the reflected ray. 

 The line F C is a perpendicular to the reflecting surface 

 L G. The angle of incidence is that which is contained 

 between B C and C F, and the angle of reflection is that 

 contained between E C and C F : and the angle of incidence 

 is equal to the angle of reflection, that is, the angle B C F 

 is equal to the angle E C F. (It is usual to call every angle 

 by three letters, and that at the angular point must be always 

 the middle letter of the three.) 



Let B C, fig. 29. be a ray of light passing out of air into 

 water or glass L G at the point C, the ray B C, instead of 

 proceeding along C H, will be bent, or refracted towards the 

 perpendicular C K, as along C I. But if C I be supposed to 

 be a ray of light passing out of glass or water into air, that 

 is, out of a denser into a rarer medium, it will not proceed 

 in the direction of the line C x, but in the direction C B, 

 farther from the perpendicular F C than C x, [Note. On 

 the subject of optics the instructer should be particular in 

 giving his pupils a correct idea of angles, parallel lines, &c.] 



LESSON 32. 



Lenses. Fig. 3Q. A is a plano-convex lens, B plano- 

 concave, C double convex, D double concave, E a meniscus. 

 F G is the axis of all the five lenses. 



Fig. 36. A candle at C diverges rays of light towardi ar» 



