2 MR CLERK MAXWELL ON 



geometrical as regards the position and direction of the forces, but arithmetical 

 as regards then magnitude. 



But, by assuming that a line of a certain length shall represent a force of a 

 certain magnitude, we may represent every force completely by a line. This 

 is done in Elementary Statics, where we are told to draw a line from the point 

 of application of the force in the direction in which the force acts, and to cut off' 

 as many units of length from the line as there are units of force in the force, and 

 finally to mark the end of the line with an arrow-head, to show that it is a force and 

 not a piece of the frame, and that it acts in that direction and not the opposite. 



By proceeding in this way, we should get a system of arrow-headed forces 

 superposed on the skeleton of the frame, two equal and opposite arrows for 

 every piece of the frame. 



To test the equilibrium of these forces at any point of concourse, we should 

 proceed by the construction of the parallelogram of forces, beginning -with two 

 of the forces acting at the point, completing the parallelogram, and drawing the 

 diagonal, and combining this with the third force in the same way, till, when all 

 the forces had been combined, the resultant disappeared. We should thus have 

 to draw three new lines, one of which is an arrow, in taking in each force after 

 the first, leaving at last not only a great number of useless lines, but a number 

 of new arrows, not belonging to the system of forces, and only confusing to 

 any one wishing to verify the process. 



To simplify this process, we are told to construct the Polygon of Forces, by 

 drawing in succession lines parallel and proportional to the different forces, each 

 line beginning at the extremity of the last. If the forces acting at the point 

 are in equilibrium, the polygon formed in this way will be a closed one. 



Here we have for the first time a true Diagram of Forces, in which every 

 force is not only represented in magnitude and direction by a straight line, but 

 the equilibrium of the forces is manifest by inspection, for we have only to 

 examine whether the polygon is closed or not. To secure this advantage, how- 

 ever, we have given up the attempt to indicate the position of the force, for the 

 sides of the polygon do not pass through one point as the forces do. We must, 

 therefore, give up the plan of representing the frame and its forces in one 

 diagram, and draw one diagram of the frame and a separate diagram of the 

 forces. By this method we shall not only avoid confusion, but we shall greatly 

 simplify mechanical calculations, by reducing them to operations with the 

 parallel ruler, in which no useless lines are drawn, but every line represents an 

 actual force. 



A Diagram of Forces is a figure, every line of which represents in magnitude 

 and direction the force acting along a piece of the frame. 



To express the relation between the diagram of the frame and the diagram 

 of forces, the lines of the frame should each be indicated by a symbol, and the 



