26 PHYSICAL FORCES AND CHEMICAL BONDS 



its deep contributions to chemistry, which has always worked on the 

 level of energy. 



Newton started from the Galilean principle of inertia (known also as 

 Newton's first law of motion) which asserts that bodies move with con- 

 stant velocity unless a force acts on them. Thus, the observation of a 

 nonconstant velocity (an acceleration) is taken as evidence for the 

 existence of a force on the body. Then Newton's second law provides a 

 recipe for quantitative work by asserting that the acceleration produced 

 by the force is directly proportional to the force. It is also inversely 

 proportional to the mass of the body. These two assertions are combined 

 in the usual statement of the law: 



/ 

 a = — • 

 m 



When an acceleration is then observed, it is studied in as many dif- 

 ferent situations as needed to give us an idea of its general behavior: 

 its dependence on time, distance between bodies, dependence on masses, 

 velocities, etc. By such a study, Newton was able to deduce the expres- 

 sion for the first force ever studied as such: the gravitational force. He 



deduced its formula as 



mim 2 



./grav " 



Gr' 2 



where ?% and m 2 are the masses of the two bodies exerting gravitational 

 forces on each other, r is their separation, and G is the gravitational 

 coefficient which puts / in the proper units. 



The procedure for using this result in a case where a gravitational 

 force is known to be acting is to insert the expression for /, with the 

 proper values of the masses, into the first equation, solving for the ac- 

 celeration, a. From a, by standard mathematical procedures, the position 

 and velocity of the body in question can be determined at all times. For 

 physics, the problem is solved. 



Are there any other forces in nature? How could we recognize them? 

 In a situation in which we can show the gravitational force not to be 

 effective, the observation of an acceleration is evidence for a new force. 



Peasants from the province of Magnesia (Greece) long ago observed 

 that some stones could attract or repel other stones, and two aspects of 

 the situation permit us to deduce the existence of a new force. First, 

 there is both an attraction and a repulsion, whereas with gravitation 

 there is only attraction. Second, these stones exert their effect along a 

 table top, at right angles to the predominant gravitational attraction of 

 the earth. Thus the existence of what we call magnetic force was deduced. 



Next, when a piece of fur is stroked with a piece of amber, both the 

 amber and the fur acquire the capacity to attract pieces of lint, paper, 



