62 FALLING BODIES. 



indicate the velocity with which K was moving when it 

 passed B at the end of the first second. In a similar way 

 the velocity at the end of the second, third, or fourth 

 second may be found. 



124. Results. Whatever the space passed over in the 

 first second by the weights or the ball, it will be found 

 that there is an uniform increase of velocity. Galileo found 

 .that if the plane was so inclined that the ball would roll 

 one foot during the first second, it would roll three feet 

 during the next second, five feet during the third, and so 

 on, the common difference being two feet, or twice the dis- 

 tance traversed in the first second. 



He found that under the circumstances supposed, the 

 ball would have a velocity of two feet at the end of the 

 first second, of four feet at the end of the next, of six feet 

 at the end of the third, and so on, the increase of velocity 

 during the first second being the same as the increase 

 during any subsequent second. 



He found that, under the circumstances supposed, the 

 ball would pass over one foot during one second, four feet 

 during two seconds, and nine feet during three seconds, 

 and so on. Similar results may be obtained with Att- 

 wood's machine. 



125. Table of Results. These results are gener- 

 alized in the following table, in which t represents any 

 given number of seconds: 



etc. etc. . etc. etc. 

 t.. ...2t-l.. ...2t t 2 



