= Solution
Write the proposed <Jeans mass> as $M_J=K v^aG^bP^c$, with dimensionless $K$. The dimensions of <speed>, the <gravitational constant> and <pressure> are
$$
[v]=\mathsf L\mathsf T^{-1},\qquad [G]=\mathsf L^3\mathsf M^{-1}\mathsf T^{-2},\qquad [P]=\mathsf M\mathsf L^{-1}\mathsf T^{-2}.
$$
Equating the exponents of <mass>, length and time gives
$$
-b+c=1,\qquad a+3b-c=0,\qquad -a-2b-2c=0.
$$
Thus $a=4$, $b=-3/2$ and $c=-1/2$, so the <pressure-confined Jeans mass> scales as
$$
\boxed{M_J=K\frac{v^4}{G^{3/2}P^{1/2}}.}
$$
A larger <speed of sound> gives stronger support against <gravitational collapse>; stronger confinement at fixed <speed of sound> lowers the characteristic unstable <mass>. \b[<Dimensional analysis> determines the scaling, not $K$], which requires a particular cloud model and instability criterion.
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