62 MOTION OF FALLING BODIES. ACCELERATION. 



is also shown in that column that the space may be 

 found more simply by multiplying the number of 

 seconds during which the body has been in motion by 

 itself and by 0*5, that is by the space passed over 

 during the first second, or by half the increase of ve- 

 locity in each second. The product of a number mul- 

 tiplied by itself is the square of that number, thus 25 is 

 the square of 5 ; again, the increase of velocity in each 

 second, if the motion is uniformly accelerated, is briefly 

 called the acceleration:, the above fact may therefore be 

 stated thus: 



The magnitude of the space traversed by a uniformly 

 accelerated body during a given time from the beginning of 

 the motion 'is found by multiplying half the acceleration 

 by the square of the time. 



Thus in 7 seconds the space traversed by the weighl 

 would be 7 x 7 x 0-5 = 24' decim 5. If the perforate 

 brass plate, after the weights specified in the beginning 

 of this article have been attached, be fixed at the fo< 

 of the scale, it will be found that the weight passes 

 exactly opposite to the divisions corresponding to O5, 

 2, 4*5, 8, 12*5 decimetres after 1, 2, 3, 4, 5 seconds 

 respectively, provided that the motion commenced 

 exactly at the beat of the pendulum. That the numbers 

 given in the table represent the correct velocities ac- 

 quired at the end of the first, second, etc. second may 

 be tested thus : the perforated brass plate is succes- 

 sively suspended opposite to the division at which the 

 descending weight arrives after 1, 2, etc. seconds. The 

 extra weight sets the whole into uniformly accelerated 

 motion ; but when the descending weight passes through 

 the brass plate, the extra weight is retained upon it, and 



