MOTION OF FALLING BODIES. 



61 



during the whole of the first second, but does not 

 acquire this velocity until the end of it. The weight 

 had no velocity at the beginning of the first second, but 

 it increases its velocity uniformly during the second, 

 and it is l decim at the end of this time; the weight will 

 therefore pass over the same space which it would have 

 traversed had it moved with a mean velocity of O decira> 5, 

 this being the mean of and 1 ; the weight will hence 

 pas? over O decim '5 in the first second. At the end of the 

 first second, or, what is the same, at the beginning of the 

 second second, the velocity of the weight is l decim ^ at the 

 end of the second second 2 decim , the mean velocity durino* 

 the second second is therefore l decim -5 7 and this is also 

 the space passed over during the second second. If 

 this calculation were continued in the same manner, 

 we should obtain the following table: 



The length of the whole space passed over during a 

 certain time is found by summing the spaces traversed 

 in the single seconds : this is done in column V, but it 



