410 NOTES. 



force is exactly contrary, being in the direction C Q, ; hence, the differ- 

 ence of the two is the force called gravitation, which makes bodies fall 

 to the surface of the earth. At any point, m, not at the equator, the 

 direction of gravity is m b, perpendicular to the surface ; but the centri- 

 fugal force acts perpendicularly to N S, the axis of rotation. Now the 

 effect of the centrifugal force is the same as if it were two forces, one of 

 which, acting in the direction b m, diminishes the force of gravity ; and 

 another which, acting in the direction m t, tangent to the surface at m, 

 urges the particles toward Q, and tends to swell out the earth at the 

 equator. 



NOTE 118, p. 44. Homogeneous mass. A quantity of matter, every- 

 where of the same density. 



NOTE 119, p. 44. Ellipsoid of revolution. A solid formed by the revo- 

 lution of an ellipse about its axis. If the ellipse revolve about its minor 

 axis Q, D, fig. 6, the ellipsoid will be oblate, or flattened at the poles like 

 an orange. If the revolution be about the greater axis A P, the ellipsoid 

 will be prolate, like an egg. 



NOTE 120, p. 44. Concentric elliptical strata. Strata, or layers, having 

 an elliptical form and the same center. 



NOTE 121, p. 45. On the whole, be. The line N Q S q, fig. 1, repre- 

 sents the ellipse in question, its major axis being Q, q. its minor axis N S. 



NOTE 122, p. 45. Increase in the length of the radii, Src. The radii 

 gradually increase from the polar radius C N, fig. 30, which is least, to 

 the equatorial radius C Q., which is greatest. There is also an increase 

 in the lengths of the arcs corresponding to the same number of degrees 

 from the equator to the poles, for the angle N C r, being equal to q Cd, 

 the elliptical arc N r is less than q d. 



NOTE 123, pp. 45, 259. Cosine of latitude. The angles mCa,mCb, fig. 

 4, being the latitudes of the points a, b, &c., the cosines are C q, C r, &c. 



NOTE 124, p. 46. An arc of the meridian. Let N Q S g, fig. 30, be the 

 meridian, and m n the arc to be measured. Then if Z' m, Z n, be verti- 

 cals, or lines perpendicular to the surface of the earth, at the extremities 

 of the arc m n they will meet in p. Q,an,Q,b m, are the latitudes of the 

 points m and n, and their difference is the angle mpn. Since the lati- 

 tudes are equal to the height of the pole of the equinoctial above the 

 horizon of the places m and ?t, the angle mpn may be found by observa- 

 tion. When the distance m n is measured in feet or fathoms, and divided 

 by the number of degrees and parts of a degree contained in the angle 

 mpn, the length of an arc of one degree is obtained. 



NOTE 125, p. 46. Ji scries of triangles. Let M M', fig. 31, be the 



Fig.M. 



meridian of any place. A line, A B, is measured with rods, on level 

 ground, of any number of fathoms, C being some point seen from both 

 ends of it. As two of the angles of the triangle ABC can be measured, 

 the lengths of the sides A C, B C, can be computed ; and if the angle 

 m A B, which the base A B makes with the meridian, be measured, the 

 length of the sides B m, A /, may be obtained by computation, so that 



