Nottingham, 9 Feb. 2006.

Dear Arend, Jim and Andy, 

Some comments on Klein and Sommerfeld (1910). 
What I stated as a mere possibility, that Fritz Noether wrote the bicycle 
part, now appears to be so. That the preface is not in Arend's copy, may 
have several reasons. It is possible that it is a reprinted edition, or 
the binder removed the unnumbered pages. Now more about the contents. 

About the date of writing: I think the part was written in the years just 
before publication, although it could go back as far as 1901, as the 
references are concerned. Reference is made to Rankine, Bourlet, Whipple and 
Carvallo. The part is predominantly written in the 'neue Rechtschreibung' 
(new orthography), which was introduced in 1903, although some words are 
written in the old spelling, such as 'Zuthun' on page 865, line 20. 
This does not say anything, because the publisher might change the spelling 
to their house style. They apparently did not agree with some of the new 
rules. Kaiser Wilhelm II did not approve either, so, as a compromise, to this 
day, the Germans write 'Thron'. We should remember that F. Noether was born 
in 1884, which make a late date more probable.  

There are a few typos or slips, although the ultimate equations are correct. 
On Page 875, Eq.(9), there should be s_2 instead of h_2 sin \sigma in the 
third line, or the full expression for s_2. The slip continues in the 
fifth line of Eq.(10) on Page 876. In the same line, in the last term, in 
the expression between ( ), c_1 should be c_2. 
On Page 880, 2nd line of the unnumbered expression, a \sigma is missing. This 
is a mere typo. 
On Page 881, Eq. (15), a cos \sigma should be added to the very last term, 
inside the (). 

Comparisons. On P.866, it is said that 'The equations so obtained agree with 
those of Whipple and Carvallo', and on page 877, footnote **) says: 
'Our equations I,II,III are linear combinations of those obtained by Whipple 
(page 323) as well as those by Carvallo (page 100)', so it seems that at least 
some comparison was made. So Klein and Sommerfeld, with Noether, were the 
first to compare results. 
It appears that Doehring (1953-1955) closely follows the derivation 
given here, but generalizes the model. Even some of the notation is the same. 
It seems very probable that Doehring compared his equations for the special 
case which is treated here, which is easy to do, but that he did not compare 
his results with those of Whipple and Carvallo. 

Best regards, 
Jaap.