NOTE S. 



NOTE 1^ page 2. Diameter. A straight line passing through the cen- 

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

 of a circle or sphere. In fig. 1, q (J, N S, are diameters. 



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

 leach the laws of number and quantity ; mechanics treat of the equi- 

 librium 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 swing- 

 ing of the pendulum of a clock, or waves in water. The tides are oscil- 

 lations 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. Sen- 

 sible 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 ultimate 

 atoms into which matte r is believed to be divisible. Their form is un- 

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



NOTE 7, p. 4. J hollow sphere. A hollow ball^ like a bomb-shell. A 

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

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

 through the center 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 center with the sphere as the circles QEqd and Q. N q 3. The 

 circle A B is a lesser circle of the sphere. 



NOTE 8, p. 4. Concentric hollow spheres. Shells, or hollow spheres, 

 having the same center, like the coats of an onion. 



NOTE 9, p. 4. Spheroid. A solid body, which sometimes has the shape 



Fi<r. I. 



