118 SEC. 4. KINEMATICS, STATICS, AND DYNAMICS. 



proportioned to the traction as the length of the inclined plane is to the 

 height. 



For example, if the length be 80 and the height 40, then 20 grammes in the 

 burden scale will be balanced by 10 grammes in the traction scale. 



2. Jf the string runs horizontal, then the burden is proportioned to the 

 traction as the base of the inclined plane to the height. 



For example, if the basis be 40 and the height 40, then 4 grammes in the 

 burden scale will be balanced by 20 grammes in the traction scale. 



In order to make the difference in the two cases intelligible, such positions 

 in the inclined plane are advantageous in which the three distances are indi- 

 cated by round figures, such as height, 20 ; length, 29 ; base, 21. The weight 

 20 in the traction scale balances then with the string in horizontal position, 

 the weight 21 ; and with the string parallel the weight 29 will be equipoised. 

 With the height 30 and the base 40 the length will be 50, and 30 grammes in 

 the traction scale will balance 50 grammes in the burden scale with parallel 

 motion, whilst the burden at a horizontal motion will amount to only 40 

 grammes. 



528d. Parallelogram of Forces, constructed by Professor 

 Dr. Bertram. Ferdinand JSrnccke, Berlin. 



Apparatus for demonstrating the theorem of the parallelogram of forces. 



If two adjacent sides of a parallelogram represent in magnitude and direc- 

 tion two forces acting at a point, the diagonal through the point will represent 

 their resultant in magnitude and direction. 



This theorem is illustrated by the apparatus. The angular point of the 

 parallelogram is the (white) peg, over which a ring has been placed, on 

 which are fastened the three cords ; the magnitude of the forces is deter- 

 mined by the weight in the scales, the direction passes along the three rails, 

 of which the one, AB, which is stationary, vertically upright ; the second 

 AC, and likewise the third, AE, movable around the peg A, always moves in 

 the elongated diagonal of the parallelogram BADF. The greatest of the 

 forces is always taken in the direction of AB, and determined as equal to 

 100, and those of the two others is read on the graduations of the lines BG 

 and AF. 



If, for example, the parallelogram is placed so that the lines AB are equal 

 to 100, BF=70, AF = 80, the ring in that case will poise freely without 

 coming into contact with the peg, if the weights in the scales amount respec- 

 tively to 100, 70, 80 grammes ; of course must the equilibrium of the scale 

 weights be adjusted previously by tare weight. 



528e. Centrifugal Apparatus, complete. 



Ferdinand Ernecke, Berlin. 



529. Drawing. Experimental demonstration of the theory 

 of the parallelogram of forces or velocities, used by the exhibitor 

 since 1835. Professor Daniel Colladon, Geneva. 



Two small pulleys are placed at some distance from each other on the edge 

 of a table. On the opposite edge, held by the hand, is a small ball of the 

 size of a musket ball, to which are attached, by one of their extremities, two 

 helicoidal springs of fine brass wire ; the other extremity of these two springs 

 is drawn parallel to the plane of the table by cords passing over the pulleys, 

 and themselves stretched by the weights P and P'. The table being sprinkled 

 with lycopodium, two lines are traced upon it, marking in direction and in- 

 tensity the tensions of the two springs which draw the ball, which are equal 

 to the weights P and P'. On discharging the ball it traces on the table a 

 straight line, which is in the direction of the diagonal of the parallelogram of 

 the forces P and P' of the two springs. 



