OF THE PROPERTIES OF MATTER. 13 



seven the fourth, nine the fifth, and so on in proportion. 

 And thus it appears, that the spaces described in suc- 

 cessive equal parts of time, by an uniformly accele- 

 rated motion, are always as the odd numbers, 1, 3, 5, 7, 

 9, &c. and consequently, the whole spaces are as the 

 squares of the times, or of the last acquired velocities. 

 For, the continued addition of the odd numbers yields 

 the squares of all numbers from unity upwards. Thus, 

 1 is the first odd number, and the square of 1 is 1 ; 3 is 

 (.he second odd number, and this added to 1 makes 4, 

 the square of 2 ; 5 is the third odd number, which 

 added to 4 makes 9, the square of 3 ; and so on for 

 ever. Since, therefore, the times and velocities proceed 

 evenly and constantly as 1, 2, 3, 4, &c. but the spaces 

 described by each in equal times, are as 1, 3, 5, 7, Sec. it 

 is evident that the space described 



In one minute will be .... Irrsquare of 1 



In 2 minutes l+3=4=square of 2 



In 3 minutes .... l+3+5=lrrsquare of 3 



In 4 minutes . l+3+5+7=16=square of 4, &C. 1 * 



N. B. The character + signifies more, and = equal. The de- 



As heavy bodies are uniformly accelerated by the sc ^ n(1 . ln s 

 * J velocity 



power of gravity in their descent, it is plain that they will give 

 must be uniformly retarded by the same power in their of P equal 



Xote 10. A very beautiful illustration of the doctrine of accelerated ^ 

 motion may be furnished by a reference to a geometrical figure. 



The perpendicular row of figures in 

 the triangle represent equal portions 

 of time, during which, the body may 

 be supposed to fall from the highest 

 point. The smaller triangles repre- 

 sent the number of feet the body 

 would pass through in any given 

 period from one to four seconds. In 

 the first we find it would have passed 3\ 

 through but one foot, in the second 

 through three feet, in the third through 

 five feet, and in the last through seven 

 feet. 



