20 Row Hampton St., Pentonville - JI would like an explanation of a short passage in WW's discussion of the conception of fluidity, given in his Thoughts on the Study of Mathematics as Part of a Liberal Education [1835]. On page 30 WW makes a citation… read more
20 Row Hampton St., Pentonville - JI would like an explanation of a short passage in WW's discussion of the conception of fluidity, given in his Thoughts on the Study of Mathematics as Part of a Liberal Education [1835]. On page 30 WW makes a citation which he describes as typical reasoning 'among our mathematicians': ''A fluid is a body, the parts of which are perfectly moveable in all directions; if therefore a force act in any direction upon any particle of it, there must be, acting on the same particle, equal forces in all other directions.'' WW then writes 'Now this is palpably a fallacy. If a particle be kept at rest by forces acting on it, the only consequence which follows from the laws of mechanics is, that it must be acted on by pairs of equal and opposite forces: we cannot hence infer the smallest necessity that the lateral forces should be equal to the vertical ones'.] JI does not know why the citation is inconsistent with WW's reasoning: 'Is not the citation true of a particle of a fluid, although that particle be subjected to the action of any pairs of forces such as you describe, which impress no motion in any direction? Is not the condition of the particle the same as if it was entirely free from the action of any such forces?' JI asks WW: 'Is the citation from any of my papers? If so, have the goodness to specify the passage?' JI suspects that the real reason WW included this in his pamphlet was 'to support the principle which is universally assumed as sufficient for the equilibrium of a homogenous mass fluid at liberty, namely, that a fluid mass is necessarily in equilibrium when every particle is pressed equally by all canals down from it to the upper surface?...That the equilibrium of the mass is a self-evident consequence of the Principle of the canals, or, if you please, of that principle conjoined with perpendicularity of the forces to the upper surface. See Prof. Airy's Tracts, 2nd edit. p.146, 28'. JI wants WW to specify what he intended by this passage.
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