24 Transactions. 
competent authorities, are in reality grave-yards), and lastly the 
grave-stone, with its sculptured cross, the style of which brings 
it up to a comparatively modern date. 
Another point is the relation and bearings of these ancient 
structures to the natural features of the ground. It cannot be 
mere chance that every one of them is quite close to a stream. 
There is abundance of ground less well watered on either side. 
The moat at Kirkclaugh is washed by a stream ; the two stand- 
ing stones at High Auchenlarie stood between two streams, as 
also the stone circle close at hand; while on the Laggan Burn, 
within 400 yards of it, we find the three distinctive remains of 
Cairn, cup-marked, stone, and grave. 
In the same way, too, Cairnholy and its numerous other 
remains are close on the banks of what is now Kirkdale Burn, 
and the cairn and circles on the north slopes of Cairn Harrow 
are also near another running stream—the Cauldside Burn. 
Lastly, the measurements of distances both as to large spaces 
and small:seem to me to indicate some system. As I once before 
pointed out, all the dimensions in detail of the 7’umu/i and Stone 
Circle at Cauldside are in multiples of 9 and 3; and, I think, 
you will find that the same law holds good with regard to most, if 
not to all, the dimensions of these other circles, cairns, sculptured 
stones, and grave at present described. I do not for a moment 
wish to be misunderstood to the effect that I advocate the build- 
ing of a merely fanciful theory of numbers in connection with 
this subject, but rather simply to draw attention to the fact that 
certain numbers do certainly occur in these dimensions with a 
frequency that cannot be the result of a happy accident. When 
there is so little systematic or regular in a subject as yet so 
slightly worked out, I think a reasonable endeavour to place any 
clue in the hands of those who are much more competent than 
the present writer to investigate the whole subject of Petroglyphs 
is our plain duty as observers. There is still a vast deal to be 
done—to be observed, drawn, described, and properly recorded 
in our annals; for as time goes on and steam ploughs become 
commoner, the very face of the earth undergoes a change which 
often causes the heart of the Archeologist to sink within him ; 
and, once lost, the very sites of such a colony as I have attempted 
to picture to-night, fade away into the past and are forgotten, 
