Supposed 'No wobble' alignments

Apparent alignments for Lunar Limb without Δ at a  Standstill :-  Possible explanations

There are a number of examples where there is an apparent alignment for  ± ε ± ι ± s ± Δ and for  ± ε ± ι ± s, from the same observing position.  i.e. alignments for both a limb with ‘wobble’ and for a limb with no ‘wobble’.  (In the references below, the Thoms' give fourteen examples and two more were found in the present investigation).      An alignment for no Δ does not appear to serve a useful purpose. The moon is not in a unique position as it is for  ± Δ.  It can be marked on paper but not observed in practise.  At  successive lunations at such a time the maximum declination reached is changing relatively rapidly; typically by 8’ per lunation and so the only way of  'observing'  the no wobble position would be by calculating when it would occur from the preceding 'wobble position and knowing the value of Δ.     So such an alignment even if it were set up would apparently give no information not more easily found from observing the ‘wobble’ itself.

Thom considered that the probable explanation was that the mean of two successive but opposite ‘wobbles’ was found.  I.e. marking the position left and right of the O.P. for the relevant limb of the moon at the alignment at successive + Δ and – Δ  about 86 days apart and then taking the mean.  He considered  that this would be more accurate than a single observation for a limb with ‘wobble’ (Thom & Thom 1980, p S84; A.S Thom in Ruggles and Whittle 1981, p45 ).

Sites where this occurs seem to be more  common than chance would account for, so there must be a logical explanation.   While the Thom idea is technically possible, an alternative is offered:-

As a Lunar Standstill (Z) approaches it would be useful to know what the likely nature of it would be. E.g. will it be two nearly equal maxima with a single minima ( A ) or the opposite as at  (B)?     (These are of course the two extreme possibilities.)

Consider A, the double maximum, and in particular the region marked to the left.   This is, as it must be, one ‘wobble period’ (or ‘eclipse period’ *Note ) before the next maximum. I.e. about 173 days.  And it is 1 ½ such periods before the actual Standstill Maximum (or about 260 days).   The ‘deficit’ of the marked peak is important:-

i.e. by chance it is very close to the value of  Δ or about 9’.

(*Note The term 'Eclipse Period'  is used as being entirely equivalent to and shorter than ‘half an eclipse year.  Furthermore it is the eclipse period as eclipses can only occur within an approximately 20 day period centred on the maximum of the 'wobble'.  (Thom 1971, ))

If however the situation is as in B (which is the other extreme position)then we have :-

 

i.e. The deficit is much less (or much more at a full eclipse year earlier).

What does this mean in practice?

Consider Ballinaby in Islay where there is an alignment  in the north for the upper limb plus 'wobble' at the Major Standstill (+ε+ι+s+Δ) and, from the same OP, apparently for the upper limb without 'wobble' (+ε+ι+s).  (Thom 1978, p169; Thom & Thom 1980, p S81; A.S. Thom in Ruggles & Whittle 1981, pp54-57).           Let us suppose that situation A is occurring.  Then an explanation of why the apparent alignment for no Δ could be for +Δ when the moon was near, but not at, the major standstill follows:-

 

 

One of the sites investigated is Achara in Duror.  (M7/1, LN1, 9866 5455).

The measurements give :-

In addition to an alignment for the upper limb -Δ  ( +ε+ι+s-Δ), There is what appears to be an alignment for the lower limb with no 'wobble'.

The explanation diagram is a little more complicated than the previous case, but the principle is the same:-

Discussion

In principle all of the 16 presently known examples of this type can be explained using the same ideas.

If the earlier arguments are correct that a limb without 'wobble' could not be measured (at least not directly), we are left with three possible explanations:-

• Thom's explanation above, that each limb was observed at two succeeding + , -Δ, (and therefore some distance either side of the stone) and the mean taken.
• That by measuring the top of the 'wobbles' as the standstill was approaching, it would give an indication of the nature of the forthcoming standstill.
• If lunar eclipse prediction was the purpose of the observations then observing the time (day) of the top of any 'wobble' would be equally suitable.