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



528c. Inclined Plane, constructed by Professor Dr. Bertram, 

 Councillor of the Board of Education. Ferdinand Ernecke, Berlin. 



The inclined plane is represented by tv?o parallel iron rods, which can be 

 placed at any angle with the horizontal bar. 



Three distances can be measured as follows : 



1. The length of the inclined plane, that is to say, the distance from the 

 joint to the perpendicular iron support bar, which maintains the plane in its 

 proper position. 



2. The base, that is to say, the horizontal distance from the joint to the 

 support bar ; this is read on the horizontal pedestal. 



3. The height, that is to say, the perpendicular from the terminal point of 

 the first distance to a horizontal line drawn through the joint ; this is read 

 on the support bar, the zero point of which is situated on a level with the 

 joint. 



The weight on the inclined plane can be balanced in two different ways : 

 either parallel to the inclined plane, or in a horizontal direction. The 

 carriage of the roller can be turned, and the pulling string can, therefore, 

 be placed parallel to the inclined planes or horizontally. The double division 

 on the slotted support bar serves for observing the horizontal position of the 

 string. 



At every experiment the weight carriage, that is, the two-wheeled axle 

 with its scale, is balanced with the scale which is suspended on the string. 

 This is effected by tare weights. Then the weight and the power of traction, 

 that is to say, the weights which are balancing each other in the weight scale 

 and the traction scale, are adjusted by means of the measured distances. 



1. If the string remains parallel to the inclined plane, then the weight is 

 to the traction in the proportion of the length of the inclined plane to the 

 height. 



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

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



2. If the string remains horizontal, then the weight is to the traction in 

 the proportion of the base of the inclined plane to the height. 



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

 weight 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 numbers, such as height, 20 ; length, 29 ; base, 21. The weight 

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

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

 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 weight scale with a parallel 

 direction, whilst the weight required in a horizontal direction will amount to 

 40 grammes. 



52 Sd. Parallelogram of Forces, constructed by Professor 

 Bertram. Ferdinand Ernecke, 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 weights in the pans, the directions pass along the three rails 

 of which the one, AB, which is fixed, vertically ; the second AC, and the 



