NOTES. 



NOTE 1 , page 2. Diameter. A straight line passing through the centre, 

 and terminated both ways by the sides or surface of a figure, such as of 

 a circle or sphere. In fig. 1, q Q, N S, are diameters. 



NOTE 2, p. 2. Mathematical and mechanical sciences. Mathematics 

 teach the laws of number and quantity ; mechanics treat of the equili- 

 brium and motion of bodies. 



NOTE 3, p. 2. Analysis is a series of reasoning conducted by signs or 

 symbols of the quantities whose relations form the subject of inquiry. 



NOTE 4, p. 3. Oscillations are movements to and fro, like the swinging 

 of the pendulum of a clock, or waves in water. The tides are oscillations 

 of the sea. 



NOTE 5, p. 3. Gravitation. Gravity is the reciprocal attraction of 

 matter on matter ; gravitation is the difference between gravity and the 

 centrifugal force induced by the velocity of rotation or revolution. Sensible 

 gravity, or weight, is a particular instance of gravitation. It is the force 

 which causes substances to fall to the surface of the earth, and which 

 retains the celestial bodies in their orbits. Its intensity increases as the 

 squares of the distance decrease. 



NOTE 6, p. 4. Particles of matter are the indefinitely small or ulti- 

 mate atoms into which matter is believed to be divisible. Their form is 

 unknown ; but, though too small to be visible, they must have magnitude. 



NOTE 7, p. 4. A hollow sphere. A hollow ball, like a lomb-shell. 

 A sphere is a ball or solid body, such, that all lines drawn from its centre 

 to its surface are equal. They are called radii, and every line passing 

 through the centre and terminated both ways by the surface is a diameter, 

 which is consequently equal to twice the radius. In fig. 3, Q q or N S 



is a diameter, and C Q, 

 C N are radii. A great 

 circle of the sphere has 

 the same centre with the 

 sphere as the circles Q E 

 qd and Q N q S. The 

 circle A B is a lesser circle 

 of the sphere. 



. NOTE 8, p. 4. Con- 

 centric hollow spheres. 

 Shells, or hollow spheres, 

 having the same centre, 

 like the coats of an onion. 



NOTE 9, p. 4. Sphe- 

 roid. A solid body , wh ich 

 sometimes has the shape 

 of an orange, as in fig. 1 ; 



Fig. 1. 



