OBSERVATIONS OF CHANGE OF POSITION 21 



meant by direction if we draw two straight lines which shall 

 pass at right angles through the point o. Lines A M, A N 

 drawn perpendicularly from A to these lines of reference show 

 by their relative magnitude in what direction A lies with 

 regard to o. It is important to note that our observations 

 do not extend beyond particles, that is, bodies or portions 

 of bodies so small that their dimensions may be neglected. 

 How small such a body need be will depend upon the purpose 

 of the measurements and the accuracy attainable. 



18. Observation of Change of Position. If the position 

 of a particle be observed or measured at different times, 

 and the necessary measurements be not found unchanged, 

 then the particle has undergone a displacement or change 

 of position. The simplest change of this kind which can be 

 observed is the alteration in the linear distance between 

 two particles A and B. If we consider these two bodies 

 entirely by themselves, without reference to any other body, 

 we may represent fully by diagram the amount of displace- 

 ment during any given interval. All that is necessary is to 

 draw a straight line, A B, representing the linear distance 

 between them at the one instant of time, and another line, a b, 

 representing in the same direction the linear distance at the other 

 instant. The difference of the two lines in length taken on 

 the same scale represents the displacement, but only when the 

 straight lines A B and a b remain strictly parallel. As to 

 the exact mode of displacement or condition of the par- 

 ticles during the change, such a plan tells us absolutely 

 nothing ; and as to whether one alone or both together have 

 undergone an absolute displacement, we are unable to decide. 

 We are unable to say in the simplest case of displacement 

 whether A or B has moved. In other words, we are only 

 aware of displacement as a change in a relation of two bodies 

 at least, that is, we can observe relative displacement alone. 

 If we refer to a third body, and make the necessary measure- 

 ments, it is true we gain additional knowledge, but an exten- 

 sion of our measurements to a fourth body might disclose 

 further displacements. A little consideration will make 

 clear the connection between our inability to know any- 



