RATES 129 



observers by speeding past their posts, but, because 

 the machines were slowed down in the intervening 

 distance, the actual figures indicated compliance with 

 the law. The average speed was only necessarily the 

 actual instantaneous speed at each observation post in 

 case the car traversed the entire distance at a uniform 

 rate. By shortening the distance for which the car is 

 timed a result more nearly approximating the actual 

 speed at either post is obtained, but this is because 

 in the correspondingly reduced time only a negligible 

 change in speed can occur, and hence the observer is 

 dealing with an essentially uniform speed throughout 

 the measured distance. 



The general method which is indicated for obtain- 

 ing the actual, that is, instantaneous, speed at any 

 point on the path of a moving body is as follows : 

 Establish an observation station at the point in ques- 

 tion and a second station as near as possible 1 to the 

 first. Observe the time required for the body to 

 traverse this distance and find the ratio of the distance 

 to the time. 



We recognize that this method requires that we shall 

 go the limit in reducing the separation of the two 

 stations. Now, our observations are separated not 

 only in space but also in time, and it is usual to empha- 



1 Of course, in practice other sources of error than the change in 

 velocity must be taken into account. The first source of error occurs 

 in the observation of the coincidences of the moving body with 

 the two reference points, and the second is found in the measure- 

 ments of the distance and the corresponding time interval. What- 

 ever means we may employ we only approximate the magnitude, 

 and hence in exactness we should always express each measured 

 magnitude as a definite amount, plus or minus a limiting error. 



K 



