CUP editors and typesetters have shown almost infinite patience and allowed me many proof readings, but after a while, staring at the same words, the experience resembles the occasions when you repeat the same word over and over again—the word becomes meaningless, nonsensical. So errors remain, and I will list these here as I find them, or even better when readers let me know of errors they have found.

• comment: page 11, note that the fractional change in density, ∆ρ/ρ, is the compressibility times the change in pressure. The compressibility of water is about 4.6×10⁻¹⁰ Pa⁻¹ at 20°C; so while the absolute pressure changes by a factor of one hundred, the density increases by only about 0.5% (this is assuming constant temperature so it's only a very rough estimate). This is why we assert here and throughout the book that liquids are effectively incompressible. Complete incompressibility is an artificial construct: solids are as incompressible as liquids, but their bulk modulus is not infinite!
  

• erratum: page 49, footnote 17: before the integral sign should appear the fraction 1/∆τ
  

  comments: It is notable that div applied to a rank-two tensor is ambiguous. If I used the common convention in fluid mechanics that the indices on the Cauchy stress tensor are reversed then the differentiation implied in the divergence is taken with respect to the first, not the second, index. The same applies to the formula in the footnote: the indices j and n would need to be exchanged; albeit in that expression no explicit differentiation is indicated, and the form is valid in any orthogonal coordinate system.
  

  The convention that the first index of the Cauchy stress tensor refers to the direction of the traction vector and the second, the normal to the element of area over which it acts, seems to be most common in solid mechanics. Certainly that's how Professors Eshelby and Bilby taught it. Then the equilibrium condition reads,
  

  σ_ij,j + f_i = 0 which looks elegant. The comma notation is taken from general relativity and according to google's AI it was first used by Einstein and Grossmann in 1913; however I cannot find it in that paper. It's not used in Eddington's book (or rather he just leaves out the comma, or colon for covariant derivative, which is totally confusing). Einstein introduces it in the 1950s appendix to his book, and Dirac has it in his excellent little book, using comma and colon. So I don't know who started it. Mathematicians including William Prager prefer an explicit differential operator, in which case the equilibrium condition in our convention reads,
  ∂_jσ_ij + f_i = 0 which is a little less elegant, since we like our indices which are to be summed to be contiguous. Maybe that's why Prager uses the reverse convention that interchanges the roles of the two indices. This convention seems to be universal in fluid mechanics. There is no right way, but I do deprecate the convention that the sign of the Cauchy stress is reversed in fluid mechanics, which desecration seems to have been perpetrated by Bird, Stewart and Lightfoot.
  

  It was Professor Bilby who first showed me how to get the Navier-Stokes equations from the condition of elastic equilibrium of an isotropic solid. Indeed I found my old undergraduate notes and it appears that he actually did reverse the order of the indices when he made the passage into fluid mechanics. I don't imagine that he intended to confuse the students and maybe he had fused two sets of lecture notes. My choice has been to start with the solid mechanics convention and stick to it!
  

• erratum: page 72: There is mass, m, missing in the formula for angular momentum: L = mr×v
  

• erratum: page 125, figure caption: after (e) the less than sign should be a greater than sign.
  

• erratum: page 178, first sentence in section 6.7: the upper case gothic "B" should be lower case gothic "b" with superscript v.
  

• erratum: page 223: equation (7.7.11) is not Darken's relation. From the equation above (7.7.10) you see that the fraction in (7.7.11) is trivially one. To get Darken's relation you need to use (7.7.6a) for D_A; then you easily find:
  
  D_A / D_A^•
  = 1 +
  d  ln γ_A / d  ln  x_A
  
  This is Darken's thermodynamic relation. The ratio of intrinsic to tracer diffusivity is equal to one if the solution is ideal, Henrian or Raoultian.