Erik Moltke´s book "Runes and thier Origins - Denmark and Elsewhere"
includes every runic inscription known until the time of publication
within the borders of modern Denmark, both in the older 24-letter
alphabet and in the younger 16-letter alphbet. In the section about
the earlier inscriptions in the 16-letter alphabet, we see several
different ways of representing long and short O. Some examples:

1. þurmutR. niåut kubls. OI. Þórmundr. Njót kumbls.

2. þiauþui risti stin þånsi aft uþinkaur. niut kums ual. iak sata
runa rit. OI. Þjóðvé reisti stein þenna eftir Óðinkár. Njót kumbls
vel. Ek setta rúna rit.

3. kurmR kunugR karþi kubl þusi aft þurui kunu sina tanmarkar but.
OI. Gormr konungr görði kumbl þessi eftir konu sína Danmarkar bót.

4. haraltR kunugR baþ kaurua þausi aft kurm faþur sin auk aft þåurui
muþur sina. sa haraltR ias sår uan tanmaurk ala auk nuruiak tani
karþi kristnå. OI. Haraldr konungr bað körva þessi eftir Gorm föður
sinn ok Þórvé móður sína, sá Haraldr er sér vann Danmörk alla ok
Norveg ok Dani görði kristna.

How shall be find our way out of this mess? Here is the solution:

The Ó in þurmutR (#1 above) is from Proto-Norse U (þunaramunduz).
Draw a basic U-rune. This = U. Now place one dot to the LEFT of the
U-rune close beside the vertical line. This dot should be 1/4 of the
way down from the TOP of the vertical line (where it meets the bar
betweem which the runes are written). This character = O by the A-
mutation of U by A in a following syllable, as in 'orð' (from early
Proto-Norse 'wurða', later 'worða'). You have now learned how to
write every O by A-mutation of U. Now place one dot to the RIGHT
above the arm extending to the right on the U-rune (which should
begin about 1/3 of the way down the vertical line). This character =
Ó from original U. The combination of these 2 dots will represent
every instance of Ó from Proto-Norse U, just as the 1st alone will
represent every instance of O from Proto-Norse U. The placement of
the 2nd dot to the RIGHT and ABOVE the arm extending to the right is
part of a theme in that its placement makes U into Ú, Y into Ý, and
(here) O into Ó. Remember, it is the dot to the LEFT of the vertical
line which symbolizes O from U by A-mutation. In 'þórmundr' the Ó is
from loss of N after O (þonaramunduz), which makes it not only a
long vowel, but a nasal. Now add a 3rd dot the the LEFT of the
vertical line and 1/4 of the way from the BOTTOM of the vertical
line. You should now have 2 dots to the LEFT of the vertical line,
one 1/4 of the way from the top and another 1/4 of the way from the
bottom. This dot nasalizes characters based on the U-rune. You have
now learned how to write the following characters from Proto-Norse
U: U,Ú,O,Ó and any nasal variant. What if the change was þunaraz -
þúnaraz - þóaraR - þóarR - þórR instead of þunaraz - þonaraz -
þóaraZ - þóarR - þórR? The answer is: it does not matter whether A
mutated U before or after N disappeared. The dot for nasalization of
U is always the same - thus, we are only debating which of the other
2 dots was written first (the one creating O from U and the one
which turns U into Ú or O into Ó). What about the lost A-sounds in
Proto-Norse 'þunaraz/þonaraz'? Our system of vowel representation is
not concerned with representing lost vowels in secondary syllables,
but only with the derivations and mutations of vowels in the primary
syllables. Also, we are not representing vowel CHANGES in the many
inflectional endings. Lost vowel from syncope and vowel changes in
inflectional endings will only be represented in an academic variant
of standard written Rúniska designed to represent ALL changes from
Proto-Norse in writting. Thus, we will be writting 'þurR', as in the
earliest written Norse of the Viking Age.

The way Ó/O is written in 'þiauþui'(#2 above) will be rejected (with
one rare exception to be discussed later). This is because A+U will
be used as the base for any diphthong combining characters based on
the runes Ár and ÚrR. The O in "þiauþui"(=OI þjóðvé) is from Proto-
Norse U (þeuð-) and will thus be represented by the ÚrR-rune, as on
other old inscriptions. For Old Icelandic, we will be using the Ó
character we learned above. Does your dialect have O instead? Then
we will be writting the O character we learned above. In either
case, our spelling will be 'þiuþ-'(for 'þ', see a later entry about
consonants).

The Ó in 'uþinkaur' (#2 above) is from Proto-Norse O/Ó. Thus, while
we may sympathize with our Viking Age writer, we cannot adopt his
choice of spelling for a system of accurate representation of Norse
vowel-sounds as O/Ó is not here derived from Proto-Norse U/Ú. In our
conservative system of spelling, the diphthong ÅU will represent the
O from natural Proto-Norse O and ÅÚ will represent Ó from natural
Proto-Norse Ó. As pointed out by Moltke, this spelling for O/Ó was
clearly in use during this period as well (see 'þåurui' in #4 above)
This unique glyph (Å+U) will represent O/Ó from Proto-Norse O/Ó. It
does not matter that the O/Ó in 'þåurui' is really from Proto-Norse
U in this particular case. What matters is that our forbearers have
represented O/Ó in two different ways on these old stones (that is,
excluding the 3rd way AU - which we will discuss later). This is all
that we need to reprent both O and Ó, including their mutations (Ö
with a line thru it and OE) and their nasalizations. To write OE,
the mutation of Ó, write Å and U (with on dot ABOVE the cross-line
creating Ú and a second BELOW it between the lines creating Ý). To
write Ö (with a line thru it = Danish Ö #1 - mutation of O), write
the same diphthing, but do not include the 2nd dot below the cross-
line - thus creating Y. Under normal conditions, these punctuations
of the U-rune will create Ú,Y,Ý from U; however, in conjuction with
the Åss-rune, the same punctuations will create Ó,Ö,OE from O (which
is represented by basic ÅU). This ancient spelling innovation has
solved the problem of how to represent O/Ó from two different basic
vowels in Proto-Norse. Although our Viking Age ancestors may not
have understood our reasoning behind retaining both of their ways of
spelling O/Ó or decision to spell the same sounds in two differnt
ways, they would no doubt have approved had we explained it to them.
In case you are wondering, how are we going to represent Ö (with a
line thru it - mutation of O - Danish Ö #1) and OE (mutation of Ó)
if they are not from natural Proto-Norse O/Ó (as just explained),
but from Proto-Norse U/Ú (as explained above)? This is the answer:
by the same punctuation which turns U into Ú,Y,Ý and O (from natural
O/Ó - written ÅU) into Ó,Ö,OE. Remember, it is only the dot to the
LEFT of the vertical line of the U-rune which indicated O from Proto-
Norse U by mutation from a following A - the dots to the RIGHT of
the vertical line follow the same pattern of variations. Also, for
either O/Ó it will be a lower dot to the LEFT which indicates the
nasalization. Thus, we will be writing 'åúþin-' (we will discuss the
termination later when dealing with consonants, loss of W and other
topics). We have now learned how to spell the names of 2 friendly
powers. The 3rd, OI. 'Sól' will employ the 3rd and final spelling of
O/Ó, which we will discuss in my next post. This one is getting too
long for my taste. We will also discuss other issues which come up
in the texts above (#'s 1-4). We have now learned how to write O,Ó,Ö
(=Danish Ö #1, not #2 or Ö form U-mutation of A - which were both
discussed under the Ár-rune), and OE. The rare spelling for O/Ó
found in the next post (about Sól) will conclude our section on O/Ó.
Please let me know if you have any questions.

Regards,
Konrad.