## Corrections

### Chapter 2

**Page 25:**

equation (2.38)_2, last term should read ...g)T***k**;

in (2.41), last term should be Ra T**k**.
**Page 31:**

Exercise 2.3. This is just used as an exercise in scaling, but there
are a couple of omissions, which become more important if the sub-text
is considered. Just above the diagram on page 31, v/v_0 should
obviously be |v|/v_0. On line 2 of page 32, x
should be x_j, and in part (iv) line 3, there should be
"...approximately, if u_t > 0, by".

The point is, that the fast time behaviour represents earthquakes, in
which (we expect) u_t > 0, while in the slow phase,
there is no motion. So the reason to have u_t > 0 in the
fast phase is that this is appropriate in earthquakes. However, it is
*not* appropriate for analysing linear stability, and strictly
the last part requires the friction law with the modulus sign.

In fact, sgn(w) should be interpreted here as -1 <
sgn(w) < 1 if w = 0, to allow for static friction. It is
then easy to analyse the relaxational motion in the phase plane, in
the absence of spatial variation.

See also the chapter 2 notes.

### Chapter 3

**Page 42:**

equation (3.39): minus sign missing, should be ...z^{-1}w^4 -
z^{-1}(\frac{4}{9})w^6...
### Chapter 4

**Page 53:**

line 6, irrotational -> incompressible
Question 5, the displayed formula should have ...- \frac{1}{4}
... (minus not plus). Thanks to Tom Witelski of Duke University and
his students for this.

### Chapter 6

**Page 94:**

The displayed formula in the middle of the page, should have
p_l-p_g=...+a\ddot{a}]-...

### Chapter 10

**Page 150:**

Two lines above (10.20), and page 152, line above (10.26):
the transformation should be t = p\tau/2f.

### Chapter 12

**Page 191:**

Oops; air density is wrong below eq 12.56; correct values:
c_0 = 0.4 x 10^-5, \rho = 0.5 x 10^-3 , which gives T_c = 924 K, rest
is ok, though having \beta \sim \mu seems most natural.
**Page 199:**

Eq. (12.110) The square bracket term in the denominator should be
squared: [1+|w|^2]^2.

Eq. (12.112) q definition should be 2+r\theta'.

**Page 200:**

Exercise 5. \beta >> \delta in line 4.

Exercise 6. Line 5: \theta\sim\beta/\mu and also \theta = \beta\Theta/\mu.

### Chapter 18

**Page 334:**

(18.27) is correct, but the first exponent in (18.28) should be
*n*, not *n-1*. There is a knock on effect in (18.29)
(*n* -> *n+1*, and (18.30) and (18.31), where *n+1* ->
*n+2*. However, (18.32) is correct again.

Back to my
home page.