PLEASE NOTE: Since html does not deal easily with formula those who have browsers which can deal with such things will be better off using DVI PS or LATEX

Here is
a list of corrections and additions
for the first reprinting. I should like to thank
Robin Chapman of Exeter (first mistake spotted),
Professor Cassels, Dr Garling, Dr Osborne,
Professor Barenblatt,
and Prof J. Taylor (all of Cambridge),
Harold N. Ward (University of Virginia),
Adam Atkinson, Paul Shallhorn and Pat Henry
for spotting various problems and
*for telling me about them*.
I would particularly like to thank
Douglas Quadling and Dr Francis Clarke
(Swansea) for long lists of useful comments.

*Side note on page 54*

Some bats have a mechanism for making themselves temporarily deaf when emitting sound bursts. (See [260], a book evidently written by a man who has never seen a bat he did not love.) They use high frequency sound because their prey is small.

*Side note on page 190*

According to Arnol'd in [264], Kolmogorov started as a student of history. His first paper, written when he was seventeen, concerned the mediaeval tax records in Novgorod. After he had presented his conclusions to a seminar he asked the historian in charge whether he agreed with them. `Young man,' the professor said, `in history we need at least five proofs for any conclusion.' Next day, Kolmogorov switched to mathematics.

*Side note on page 221*

When we talked about oxygen absorption we assumed that the area for absorption A was related to the volume V of an animal in the same way as the surface area of a sphere is related to its volume so that A is proprtional to V to the power 2/3. But we noted on page 218 that lungs look very `fractal'. If the surface of the lung has `Richardson number' different from the surface of a sphere then we would have A is proportional to V to the power beta with beta not equal to 2/3 and the slope of the mouse-elephant curve becomes easier to explain. (See pages 342-5 of [261].)

*Side note on page 392*

However, most of those whose opinions I respect reject Penrose's views on the nature of human thought `not because they are crazy, but because they are not crazy enough'.

*Side note on page 501*

(Added in second printing.)
If you wish to write complex formulae,
I strongly recommend Grätzer's
*Math Into LaTeX* [263].

*Side note on page 505*

Hacker lore says that two heads are faster than one
and three heads slightly faster than two. Thereafter,
adding manpower to a software project actually makes it slower.
The only way to speed up a project is to use cleverer
people. Hence the *three Knuth rule*. If three
Knuths working together cannot do it, it cannot be done.

*Page 53, line before (i) add*

(The restrictions on theta-subscript1 are rather arbitrary, but some restrictions are needed.)

*Page 53, near middle of written matter.*

Replace angle BCX by angle ACX.

*Page 53, 4 lines up.*

Replace a=AX cos theta_{1} by AX=a sin theta_{1}.

*Page 53, last displayed formula should read.*

a sin theta_{1}=2r sin theta_{1}-theta_{2} over 2

*Page 59 middle. Replace*

for 1 leq i leq n$ and guess that that a_{m+1} will be close to

T_{n}(a_{m-n+1},a_{m-n+2},dots ,a_{m})=P(n)

*by*
for 0 leq i leq n-1
and guess that that a_{m+1} will be close to}

T_{n-1}(a_{m-n},a_{m-n+1},dots ,a_{m})=P(n)

* Page 79, line 2*

replace k=b=1 by k=c=1

replace b(t)=1-r(t) by b(t)=1+r(t)

* Page 79, first displayed formula*

replace r'(t)=-(1-r(t))r(t) by

r'(t)=-(1+r(t))r(t)

*Page 79, second displayed formula*
replace
r(t) over 1-r(t)=r(0) over 1-r(0) e^{-t} by

r(t) over 1+r(t)=r(0) over 1+r(0) e^{-t}

* Page 79, end of first para replace*

r(t) tends to 0 for all t>0.

*by*

r(t) tends to 0 as t tends to infinity.

*Page 120*

In the 2nd displayed formula replace tau=gl^{-1}t^{-2} by tau=gl^{-1}t^{2}. As a consequence, in the 4th, 5th and 6th formula g/l should be replaced by l/g. Finally in line -7 replace `varies inversely with' by `is proportional to".

*Page 121, REPLACE side note as follows*

According to materials scientists, when molten glass cools it remains a liquid but one whose coefficient of viscosity increases as the temperature decreases. Thus we can blow glass at high temperatures, mold it at lower temperatures and so on. However, the demonstration of liquid properties for glass at room temperature lies at the very edge of modern experimental technique.

*Page 126, add at end of first side note*

The treatment of dimension I have given follows the traditional pattern in glossing over certain points. In [261] Barenblatt takes a more modern approach and shows that, if we think a little harder, we can understand a lot more.

*Page 133, bottom line*

Replace `wave front' by `shock front'.

*Page 143, Page 143, first equation after 7.1*

should not read (x,y,z,t)=(ct',0,0,t) but should read (x,y,z,t) =(ct,0,0,t).

* Page 166. In BOTH Figure 8.2(a) and Figure 8.2(b)*

Replace squareroot2 on x-axis by 1/squareroot2.

*Pages 167 to 171.*

A factor of 1/2 is missing in many of the formulae. The correct factor may, of course, be found by setting f=1. Alternatively: wherever ))b/N appears replace with ))b/(2N); on page 168 lines 7, 8 and 9 replace f(rb/N)b/N by f(rb/N))b/(2N); page 171, second displayed formula, replace h by h/2.

* Pages 175 and 176*

Replace l/g by g/l wherever it occurs.

*Page 177, 3/4 down*

Replace `collected paper with' by `collected papers) with' and `velocity?)' by `velocity?'.

*Page 186, top third TWICE*

Replace K(t) by Kt.

*Page 187, one third down*

Replace `not much bigger than l' by `not much bigger than l^{2}'.

*Page 264, Figure (e)*

Replace 3 on top path by 2. Replace 1 on almost vertical path by 0.

*Page 264, Figure 11.5*

Label on edge XY replace 10p+10 by p+10

*Page 274, last line but one of Exercise 11.2.6*

Replace 10p+10 by p+10.

*Page 278 line 19*

Extra space between ) [and] are

*Page 290 line -5 replace*

for all integer r with R geq 1.

by

for all integers r with r geq 1.

*Page 291, last displayed formula*

Replace pi by its square root.

*Pages 331, 391, 392*

The correct possesive form is Hodges'.

*Page 331, 3/4 way down. Replace*

A is encoded by SA, B by SB and so on.

by

A is encoded by S(A), B by S(B) and so on.

* Page 364, 1/4 way down*

Replace `Feynmann' by `Feynman'.

* Page 403 First part of proof*

There are three places where the power 1-uN should be replaced by (1-u)N. It is not made clear where the condition 0 leq u leq 1 comes in (observe that u/(1-u) leq 1). I have rewritten the proof slightly to make this clearer.

*Page 419, First line Exercise 17.4 (ii)*

Replace chi(0)<0 by chi(0)>0.

*Page 419, Second line Exercise 17.4 (ii)*

Replace chi(t)<0 by chi(t)>0.

*Page 420, line 19*

Replace `nth generation' by `n+1st generation'.

*Page 428, last line of (i)*

Replace `K=L-1/4' by `K=1/4-L'.

*Page 428, first line of (ii)*

Replace `K=-1/4' by `K=1/4'.

*Page 428, displayed formula in (iii)*

Remove the factor of 1/2.

*Page 428, last displayed formula*

Replace `L-1/4, by `1/4-L'.

*Page 440.Replace first displayed formula in (ii) by*

dI/dS=dI/dt dt/dS= (beta SI-gamma I)/-beta SI=-1+gamma/beta S}

*Page 442, third displayed formula up should read*

J=2S_{0}(S_{0}/(rho-1).

*Page 442, second displayed formula up should read*

S_{0}(S_{0}/(rho-1)=(1+nu/rho)

* Page 443, line 10*

Replace `Claude' by `Claud'.

* Page Page 490, line 10*

Replace Adam's [by] Adams'.

* Page 517, line 5 ending with 37-8*

Add `Batchelor's paper was [262].'

* Page 528*

Additional Bibliography

[260] J. D. Altringham. *Bats, Biology and Behaviour.*
OUP, Oxford, 1996

[261] G. I. Barenblatt. *Scaling, Self-similarity and
Intermediate Asymptotics.*
CUP, Cambridge, 1996

[262] G. K. Batchelor. Kolmogoroff's theory of locally isotropic turbulence. Proceedings of the Cambridge Philosophical Society, 43:533-59, 1947.

[263] G. A. Grätzer. *Math into LaTeX.*
Birkhäuser, Boston, 1996.

[264] S. H. Lui. An interview with Vladimir Arnol'd. Notices of the AMS, 44(3):432-8, April 1997.

*Page 531, add page reference*

historians, killjoy, routed, 104, 153, 190

*Page 531, under Knuth K. E., add item*

three Knuth rule, 505

*Page 531, replace*

lungs, as surfaces of nearly infinite area, 218

by

lungs, as fractals, 218, 221

*Page 531, under menagerie, mathematical, add item*

bats, 54

Now go onto corrections not in first reprint

or return to the main Pleasures of Counting home page

or to my main home page.