Let Fig. 3 represent a ball revolving about its center _O_, in the direction indicated by the arrows, but the ball, as a whole, not moving in any direction. Let _BB_, _BB_, be lines at right angles to each other. Let the resistance of the atmosphere be represented by lines _AB_, _AB_, _AB_, _AB_, and _AB′_, _AB′_, _AB′_, _AB′_, running in a direction opposite to the revolution of the ball. The lines _AB_, _AB_, _AB_, _AB_ are already perpendicular to _BB_, _BB_, and need not be changed. But the lines _AB′_, _AB′_, _AB′_, _AB′_ must be resolved into components perpendicular to _BB_, _BB_. This has been done in one case, the components being _CB′_ and _DB′_. But the force _CB′_ acting on the point _B_ is equivalent to the force _EF_ acting on _BB_, and the force _DB_ is equivalent to the force _GH_ acting on the other _BB_. [Illustration: Fig. 3] In a similar manner all the other forces, _A′B′_ may be resolved into forces perpendicular to the lines _BB_, _BB_. [Illustration: Fig. 4] If, in Fig. 3, all the forces acting on each of the lines _OB_, be represented by a single line, we have as the result the four equal lines _AB_, _CD_, _EF_, _GH_, Fig. 4 representing the total force acting on the ball. Now, suppose the ball to move in the direction indicated by the large arrow, Fig. 5, then the resistance on the side _B_ would increase, that on the side _F_ would decrease, hence _AB_ would increase, while _EF_ decreased proportionately. Again, the air in front of the ball at _H_ is condensed, that in the rear at _D_ is rarefied, hence the resistance at _H_ is increased, that at _D_ being lessened, and _GH_ is increased, while _CD_ is lessened. [Illustration: Fig. 5] Set off on _AB_, _AK_ equal to _EF_; _AK_ will balance _EF_, and we have only the force _KB_ acting on the line _BF_. Making _GL_ equal, _CD_, in the same manner, we have only the force _LH_ acting the line _HD_. Now, the force represented by the line _BK_ can not do any work in the directions _BF_ or _FB_, and therefore merely slows the ball. But the force _LH_, although it can not do any work in the directions _HD_ or _DH_, can do work in the direction _LH_, and causes the ball to follow the curve _HM_. Of course, all the forces, _AB_, _CD_, _EF_, _GH_, tend to stop the rotation of the ball, but the forces _KB_ and _LH_ are the only ones which change the motion of the ball as a whole. F. H. C. * * * * * The following verses were written by a young poet of eleven, who began making rhymes at the rather early age of three. CONSOLATION. BY ETHEL S. K. PACKARD. The waves of the coming tide Crept gently along the beach, With musical, silv’ry plash, As if they broke into speech.