100 THEORY OF NEWTONIAN FORCES. [PT. 1. CH. 1. 



or the numeric of a certain acceleration varies inversely as the 

 magnitude of the unit of length, and directly as the square of the 

 unit of time. For instance, an acceleration in which a velocity of 

 10 feet per second is gained in 2 seconds is equal to one in which 

 a velocity of 9000 feet per minute is gained in a minute, 



10 ft. = ioft. 9000 ft. 



(2 sec.) 2 4 sec. 2 min. 2 ' 



The unit of acceleration is one centimeter-per-second per second. 



Since force = mass x acceleration, 



r Force l - [Mass]. [Length] _ 

 [(Time)*] - 



The unit of force is one gram-centimeter-per-second-per-second. It 

 is called a dyne. 



All physical equations must be homogeneous in the various 

 units, that is, the dimensions of every term must be the same. 

 This gives us a valuable check on the correctness of our equa- 

 tions. 



54. Absolute Systems. The above system of units, which 

 has for its fundamental units the centimeter, gram, and second, is 

 called the C. G. S. system, and was recommended by a committee of 

 the British Association for the Advancement of Science in 1861. 

 It is sometimes incorrectly spoken of as the absolute system of 

 units. 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 *. 



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

 persons and (or including) engineers, does not belong to the abso- 

 lute 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 



* Gauss. Intensitas vis magneticae terrestris ad mensuram absolutam revocata* 

 Gottingen, 1832. Ges. Werke, v. p. 80. 



