PART I. 



GENERAL PRINCIPLES. 



CHAPTER I. 



FOBCE8 IN THE SAME PLANE COMMON POINT OF APPLIOATKW. 



1. Notation, etc. In order that a force may be " given " 01 

 completely determined in its relations to other forces, we must 

 know not only its intensity, but also its direction, and the posi- 

 tion of its point of application. These three being known, the 

 geometrical expression of our knowledge is very simple. We 

 have only to assume a certain length as the unit of force, and 

 then any force is at once given by the length, direction, and 

 position of a straight line. This method of force representa- 

 tion is so obvious, that it is in fact used in mechanics, even 

 where the treatment itself is essentially analytical. 



Unless expressly stated, all the forces with which we have to 

 do, will be considered as lying and acting in the same plane. 

 Graphically then, any force is completely determined by a 

 straight line, the beginning of which represents the point of 

 application, and the length and direction of which give the in- 

 tensity and direction of the force. 



We shall indicate a force in general by the letter P, its point 

 of application by A. When we have several forces we repre- 

 sent the points of application by A t , A 2 , A 3 , etc., and the ends 

 of the corresponding lines by P 1} P 2 , P s , etc. The direction in 

 which a force is supposed to act is thus unmistakably indi- 

 cated. 



When, however, lines representing several forces are laid off 

 one after another, the beginning of each at the end of the pre- 

 ceding, it will be sufficient to put at the beginning of the 

 first, and 1, 2, 3, etc., at the end of each. No confusion can 

 arise, as each force acts and reaches from the point indicated 

 by the figure which is one less than its index, to the point indi- 

 cated by that index. 



When, finally, we designate a force by the two letters or fig- 

 ures which stand at the beginning and end, we shall always 

 indicate by the order in which the letters or figures are written, 



