194 Supplement to the Calculus of Operations. 



virtue of its force; the equilibrium is disturbed through 

 the circumference, as follows : 



The first differential is one. As it in- 

 creased uniformly, its amount would be two 

 in the second time, increased by one as the 

 original genesis, to which add the square 1, 

 making in all four; the sum generated in 

 the third time will be five, to which add four, 

 making nine, etc. The last column will be 

 the squares. 



When a ball is struck, the force from the 

 centre to the circumference is annihilated, 

 the opposite force is equilibrated, and carries 

 the ball away ; thus inertia is explained. 



Take two tubes each about a foot in 

 length, both open at one end, and one open 

 and the other shut at the other end; blowing into each, the 

 open tube will sound twice the intensity of the shut one. 

 The former has a node at the origin and a venter at the 

 extremity ; the latter has a node at both ends, and a venter 

 in the centre. 



Comparing this example with the former one of mo- 

 tion, we find they both agree to make the operator and his 

 instrument the node, and the venter the result of his effort. 

 "We will make this a general rule. 



The sun is a node, and its venter is its extreme border 

 of emanation ; outside of the sun are the other suns of the 

 universe, which have like nodes and venters. Within the 

 sun's jurisdiction, there are many nodes and venters, each 

 planet, etc., being one pair. 



In the case of motion, the operator is a node, and termi- 

 nates at the centre of the ball, which, of coarse, is a node, 

 with venter at the extremity of its motion. 



If we take a piece of iron and a hammer, and strike the 

 iron repeatedly, it produces heat. Or better, take two 

 pieces of hard wood and rub them together until they take 



Xos. 



Diff. 



Sq's. 



1 



2 



3 

 4 

 5 

 6 

 7 

 8 

 9 



10 



1 



3 



4 

 5 

 9 

 7 



1 ft 

 9 

 25 

 11 

 36 

 13 

 49 

 15 

 64 

 17 

 81 

 19 



1 



4 



9 



16 



25 

 36 

 49 

 64 

 81 

 100 



