Note 20 — Chapter IV · Carving out the Universe

This is near enough, but not absolutely accurate. Exact mathematical analysis shews that the weight of the minimum condensation M is given by

M = ( √⅓πκ)³ C³ ,

———

(√γ)³ √ρ

where C, γ, ρ, κ are the molecular velocity, gravitation constant, initial density, and ratio of specific heats, whereas the weight from which molecules moving with velocity C just fail to escape is given by

M = 3 C³ ,

—— ———

4π (√γ)³ √ρ

With κ = 1⅔ the minimum weight of condensation is 9·7 times the weight which is just adequate to retain the molecules.