Mr. J. J. Waterston on the Theory of Sound. 487 



influence the result. Also the ■ repulsive action is necessarily 

 assumed to be limited to adjacent particles, not extending through 

 the interstices of these to the particles beyond (for such is the 

 extraordinary and improbable hypoAesis required to deduce 

 Mariotte's law from a static repulsive force) . This may be sup- 

 posed subject to modification durin'g yibratoiy action. 



But the hypothesis upon which the- mathematical demonstra- 

 tion rests is open to three grounds of objection : — 1. It does 

 not take account of the condition of the front of a pulse when 

 the particles from a condition of rest enter into the cycle of 

 motion defined by the theory. 2. The force of repulsion be- 

 tween two adjacent particles required by the theory is extrava- 

 gantly large. 3. The other physical properties of gases are not 

 deducible from the hypothesis. 



To these may be added, that the dynamical theory of heat has 

 suggested another hypothesis which is free from these objections, 

 and which therefore claims a preference according to Newton's 

 first " rule of reasoning in philosophy," viz. " We are to admit 

 no more causes of natural things than such as are both true and 

 sufficient to explain their appearances. To this purpose the 

 philosophers say that Nature does nothing in vain, and more is 

 in vain when less will serve ; for Nature is pleased with simplicity, 

 and affects not the pomp of superfluous causes." 



1. The theory does not take account of the condition of the 

 front of the pulse, or rather of the front of the first of the series 

 of pulses of which a sound consists. This is apparent if we con- 

 sider that a particle is represented by the theory as at rest at 

 each extremity of its oscillation, and at those points the accele- 

 rative force is at its maximum, and is derived from the difference 

 between the lengths of the lineolse that issue from the particle 

 in front and in rear. The front lineola cannot differ from the 

 mean length so long as the front particle is at rest unaffected by 

 the advancing pulse. The rear lineola is less than the mean 

 length by a certain small amount a. If the front particle were 

 in action in a pulse cycle, the length of the front lineola would 

 be greater than the mean length of a lineola by the same amount 

 a, so that the accelerative force at each extremity of the oscilla- 

 tion of a particle is represented by 2« ; and unless it were so, 

 the condition required to sustain the beautiful relation of velo- 

 city and propelling force would be wanting. But at the front 

 of the first pulse the lineola does not differ from the mean length, 

 80 that the accelerative force is represented by a, and this is only 

 one-half the amount required by the theory to begin the oscilla- 

 tion. In truth, the demonstration only applies to a pulse having 

 similar ])ulse8 operating on both sides. 



2. The force of repulsion between two adjacent particles re- 



