32 I. KINEMATICS OF A POINT. LAWS OF MOTION. 



An absolute system is any system, irrespective of the magnitudes of 

 the units, by which physical quantities can be specified in terms of 

 the least number of fundamental units, which shall be independent 

 of time or place, and reproducible by copying from standards. A 

 system based on the foot, pound, and minute is just as much an 

 absolute system as the C. G. S. system. The idea of an absolute 

 system is due to Gauss. 1 ) 



The ordinary method of measuring force, used by non- scientific 

 persons and engineers, though very convenient, does not belong 

 to the absolute system of measurements. The unit of force is 

 taken as the weight of, or downward force exerted by the earth 

 upon, the mass of a standard piece of metal, such as the 

 standard pound or kilogram. To measure the force in absolute units, 

 we must know what acceleration the earth's pull would cause this 

 mass to receive, if allowed to fall. As stated above, the attraction 

 according to the Newtonian law exercised by the earth is the same 

 as it would be if the whole mass were concentrated in a very small 

 region at its center. Consequently the more remote a body is from 

 the center the less will be the earth's pull upon it, or its weight. 

 If however we consider a region so small that its dimensions may 

 be neglected in comparison with those of the earth, the force exerted 2 ) 

 upon a given body at any point of the region may be considered as 

 constant, and exerted in a constant direction, called the vertical of 

 the place. Dividing the weight, which is proportional to the mass 

 of the body, by the mass, we find that the acceleration experienced 

 by all bodies at a given place is the same. This was proved exper- 

 imentally by Galileo, to the great astonishment and scandal of the 

 philosophers of the time. (On account of the disturbing action of 

 the air, this statement is exactly true only for bodies falling in 

 vacua.} The value of this acceleration is denoted by g, and its 

 value at the sea -level in latitude 45 is 



= 980.606 . 



Accordingly the force exerted by the earth on a mass of m grams 

 is mg dynes, or the 



weight of a Mogram in latitude 45 = 980,606 dynes. 



Now the value of the acceleration g is not constant, but varies 

 as we go from place to place on the earth's surface, ascend mountains 

 or descend into mines. Accordingly, the weight of a kilogram is 



1) Gauss, Intensitas vis magneticae terrestris ad mensuram dbsolutam revo- 

 cata. Gottingen, 1832. Ges. Werke, V. p. 80. 



2) For the effect of the earth's rotation, see 104. 



