17, 18] II. IMPORTANT PARTICULAR MOTIONS OF A MATERIAL POINT. 33 



not an invariable, or absolute standard of force. At the center of 

 the earth, a kilogram would weigh nothing. Its mass is, however, 

 invariable. 



The ordinary method of comparing masses by means of the 

 balance is in reality a comparison of two forces, the weights of the 

 bodies. As these are proportional to the masses, the method becomes 

 one for the comparison of masses, being a statical one, as distinguished 

 from the kinetic method of 13. If, however, we should make use 

 of a balance with arms so long that the two masses compared were 

 situated in regions for which the values of g were different, equality 

 of weights would not connote equality of masses. An instrument 

 which shows the variable weight of a body as it changes locality is 

 found in the spring -balance, another in the pendulum. 



The value of g at points on the earth in latitude A and h centi- 

 meters above the sea -level, is given by the formula, originally given 

 by Clairaut 1 ), 



g = 980.62 - 2.6 cos 2 1 - 0.000003 h. 



For further information with regard to units, the reader may consult 

 Everett's The C. G. S. System of Units. 



CHAPTER H. 



IMPORTANT PARTICULAR MOTIONS 

 OF A MATERIAL POINT. 



18. Constant Accelerations. Let us examine the motion of 

 a particle experiencing a constant vertical downward acceleration g. 

 If the axis of Z be taken vertically upward, we have for the equations 

 of motion, 



Integrating with respect to t we have 



where V X9 V y , V z are constants representing the component velocities 

 at the time t = 0. 



Integrating again, 



3) x -x = V x t, y-y, = V y t, - * = - gt* + V,t, 



1) Everett, The C. G. S. System of Units, Chap. VI. The above constants 

 are adopted by Helmert. 



WEBSTER, Dynamics. 3 



