Researches in the Theory and Calculus of Operations, 263 



entire history, of the universe : every change is motion. 

 Three kinds of movement in a solid hody have passed in 

 review, respectively distinguished both by the conditions 

 infixed upon the body acted upon, and the manner in which 

 the action is applied to it. 1° "When free, and strongly im 

 pulsed, the body moves in toto; 2° When fixed on one side, 

 renewed impulsions produce condensation of the substance, 

 attended with calorific vibration; and 3° When the body is 

 fixed in place, but with opposite surfaces free, gentle friction 

 applied to one surface develops electric force on the other. 

 We have now to allude to the case in which the body acted 

 upon is slender in form and fixed in particular points. It 

 may be a thin membrane stretched like the head of a drum, 

 which gives out sonorous vibrations when beaten; or it may 

 be a stretched string like that of a violin, which yields mu- 

 sical tones varying with the, distance between the fixed 

 points which determine its tension ; or it may be a cylin- 

 drical column of air, as in the tube of a flute. When one 

 aperture of the tube is suitably breathed upon, the funda- 

 mental tone is produced : the accumulated emanating central 

 force is destroyed by the breathing impulsion, liberating 

 the opposing emanation at the other extremity of the tube ; 

 and at this instant, the whole column of air constitutes one 

 full wave with nodes at the extremities and the venter at 

 the centre as in A (fig.12). When the operator increases the 

 breathing force rightly, the octave of the fundamental tone 

 is heard; the stronger compression develops a new node at 

 the centre, with a venter midway on each side of it as in B. 

 In the instrumental flute, other different tones are obtained 

 by piercing the sides of the tube, giving rise to as many 

 different nodes and venters. In stringed instruments, such 

 nodes are made by stops and frets, etc. 



A metallic rod is forcibly struck at its extremity a in the 

 direction ab (fig. 13); the accumulated emanation oa is de- 

 stroyed, ob is liberated, and the rod moves bodily; a and b 



