5, 6] DISPLACEMENT. 7 



quantities. We shall proceed in the next Chapter to discuss the 

 geometry of vectors, and shall take up the proper development 

 of our subject in the following Chapter. 



6. Note on the determination of frames of reference. To determine 

 a frame of reference we require to be able to mark a point, a line through 

 that point, and a plane through that line. Suppose to be the point, OA 

 a line through the point, AOB a plane through the line. We can draw 

 on the plane a line at right angles to OA meeting it in 0, and we can 

 erect at a perpendicular to the plane. The three lines so determined can 

 be a frame of reference. 



In practice we cannot mark a point but only a small part of a body, for 

 example we may take as origin a place on the Earth's surface ; then at the 

 place we can always determine a particular line, the vertical at the place, and, 

 at right angles to it, we have a particular plane, the horizontal plane at the 

 place ; on this plane we may mark the line which points to the North, or in 

 any other direction determined with reference to the points of the compass, 

 we have then a frame of reference. Again we might draw from the place 

 lines in the directions of any three visible stars, these would form a frame of 

 reference. Or again we might take as origin the centre of the Sun, and as 

 lines of reference three lines going out from thence to three stars. The choice 

 of a suitable frame of reference, like tfie choice of the time-measuring process, 

 is in our power, and it is manifest that some motions which we wish to 

 describe will be more simply describable when the choice is made in one 

 way than when it is made in another. We shall return to this matter in 

 Chapter XIII. 



