22 ELEMENTS OF LABORATORY WORK 



thing of absolute position and our ignorance of absolute dis- 

 placement. 



19. Further Observations of Position and Displacement. 

 We have now to consider less simple modes of displacement. 

 We have learnt that position, and consequently change of posi- 

 tion, must be measured by reference to something considered as 

 fixed, and further that reference to a single point is not suffi- 

 cient even when we are limited to a given plane. If we 

 consider the surface of the floor, one side and one end of a 

 rectangular room as fixed, while a body within the room is in 

 motion, a simple experiment will illustrate that the position 

 of that body is completely defined at any moment by measur- 

 ing its shortest distance from each of these three surfaces. 

 Instead of these surfaces, the roof, other end, and other side 

 might be used with the same completeness of definition, 

 although the actual measurements might differ. But the same 

 result would not follow if two of the surfaces were parallel. 

 The three surfaces are best at right angles to each other. The 

 body under consideration may now be caused to move in three 

 directions, and in three directions only. It may be displaced 

 with regard to one surface only, its distance from the other 

 two remaining unaltered. It may also be displaced with 

 regard to two surfaces at the same time, and, lastly, it may be 

 displaced with regard to three surfaces simultaneously. These 

 three methods include all the possible kinds of displacement, 

 that is, if measurements be taken at two distinct times of the 

 distances from the three surfaces, either one, two, or three 

 may be found to have altered. By taking a number of con- 

 secutive observations of these distances and marking the 

 positions in some way, we may construct the path of the body. 

 In common occurrences of displacement a series of rough 

 measurements are made from sight, and, by the aid of memory, 

 the path along which the body has moved may be described. 

 But in every possible case of displacement, the limit of 

 knowledge attainable is that given by three linear measure- 

 ments from three plane surfaces at right angles to one another. 

 These measurements may be taken at as short intervals of 

 time as possible, and the more frequently they are made the 



