The Recumbent Stones Circles (hereafter RSCs) of north-east Scotland are a distinctive class of stone circle, dating to *c.* 2500–2000 BC (Figure 1). Unlike other stone circles, they are characterised by the presence of a huge recumbent stone enclosed by two tall stones known as flankers. Typically, the rest of the circle stones are then graded, shortening in height away from the flankers, and in many instances there are internal cairns (RCAHMS 2007: 59). A recent re-examination of their remains proposes that an extent population of 71 circles still exists (Welfare 2011).

Bradley (2005) has presented a chronology that can be used as a model for the construction of these circles. Firstly, there was a pyre, then a platform cairn and finally the recumbent and its circle stones. Thus, a RSC was the final result of staged processes of construction but, importantly, the final appearance of the circle was probably anticipated from the outset (Welfare 2011: 69).

Experimental archaeology provides an insight into how these circles could have been planned. Indeed, testing a hypothesis to show how stone circles were laid out by eye, Barnatt and Moir (1984) concluded that the true-circle geometry of the RSCs was the only explanation that could be offered. That is, peg and rope techniques must have been used. My survey work amongst the RSCs indicates that not only were the builders designing their circles using ropes but the dimensions of the lengths of ropes contained 'units of measurement'. In this paper I present the photographic results of six examples.

As it has been observed that the outer faces of the recumbent and its enclosing flankers tend to be more regular and flatter than their opposite inner faces (RCAHMS 2007: 62) I, sought my 'unit of measurement' by measuring the outer edge to outer edge of these stones. I then checked whether or not this measurement had been repeated for setting out the positions of the other circle stones by measuring the distances between their outer edges, inner edges and combinations such as inner edge to outer edge or vice versa. To avoid problems associated with disturbance I only measured those stones known to stand within (or fallen very close to) their original stone holes and used Welfare's (2011) stone numbering classification.

*Easter Aquhorthies (NJ 7323 2080)*

The layout is that of a true-circle and the circle retains its full complement of two flankers, recumbent plus nine circle stones. My survey shows the eastern quadrant of the circle stones to have been laid out more formally than the western side. Analysis of the survey data shows the unit of measurement employed here to be 21½ feet or 6.5m (Figure 2). The measurement can be found from stones 1 & 12; 12 & 11; 11 & 10; 10 & 9; 9 & 8; 6 & 7.

*Loanhead of Daviot (NJ 7476 2885)*

A true-circle albeit restored. Survey shows the eastern quadrant of the circle stones was laid out more formally than the western side. Analysis shows the unit of measurement employed here to be 20½ feet or 6.25m (Figure 3). The measurement can be found from stones 3 & 4; 4 & 5; 5 & 6; 6 & 7; 7 & 8; 8 & 9; 9 & 10; 1 & 11; 10 & 11.

*Castle Fraser (NJ 7150 1254)*

A restored circle with one missing stone. The inclusion of this RSC gives an opportunity to report a variation on the use of the unit of measurement. Here the measurements for the placement of the circle stones are proportional to the unit of measurement. Analysis shows the width of the flankers and recumbent to be 15 feet or 4.5m (Figure 4). The unit of measurement appears to be half 15 feet, i.e. 7½ feet (2.3m). The measurement used for the placement of the stones was 22½ feet or 6.9m (i.e. 7½ feet x 3 = 22½ feet or 2.3m x 3 = 6.9m). The measurement can be found at those stones still standing, i.e. 3 & 4; 4 & 5; 5 & 6.

*Cothiemuir Wood (NJ 6170 1980)*

A slightly flattened circle with a number of fallen and missing stones. Analysis shows the width of the flankers and recumbent to be 20½ feet or 6.25m (Figure 5).The measurement can be found from stones 3 & 4; 8 & 7.

*Nine Stanes (NO 7232 9122)*

This circle is included because it allows me to show not only what happens with flattened circles but also the situation where a flanker has fallen (flanker no. 3 still lying close to its stone-hole). Here it is possible to work out the circle's unit of measurement, i.e. 14¾ feet or 4.5m (Figure 6). This measurement can be found from stones 11 & 10; 7 & 6; 6 & 5; 5 & 4. The geometrical impact of a flattened-circle means that the distance between those stones nearest the flankers (along the flattened-edge) will equal a measure proportional to the unit of measurement e.g. the distance between no.1 and no. 11 is 18½ feet (5.6m), which represents 14¾ feet x 1¼.

*Sunhoney (NJ 7159 0570)*

A true-circle with a full complement of stones. Analysis shows the unit of measurement here to be 26 feet or 7.9m (Figure 7). The measurement can be found from stones 1& 12; 12 & 11; 11 & 10; 10 & 9. Like Easter Aquhorthies and Loanhead of Daviot, the eastern quadrant of this circle seems to have been laid out more formally than the western side.

My fieldwork suggests that the builders of RSCs were using a common method of determining a unit of measurement for the laying out of the final stone setting. It is also not unreasonable to propose that they were capable of understanding a rudimentary form of mathematics whereby the lengths of rope used for setting-out possessed units of measurement. Certainly, lengths of ropes can explain how the sizes of the recumbent, flankers and circle stones were determined even before the circle was built. Indeed, it is feasible to propose that these units were determined from the dimensions of the respective internal cairn that stood before the RSC. The extant Loanhead of Daviot (Figure 3) provides a good example. The diameter of the cairn is 51 ¼ feet (or 16.6m) which is 2½ times the 20½ feet unit used for setting out the recumbent, flankers and circle stones. Thus, laying out ropes across the earlier cairn allowed the RSC builders to determine not only the proportional dimensions of the later stone circle but also position the standing stones. In this sense, complex designs materialise from rudimentary methods.

Experimental archaeology gives us a way of exploring these magnificent stone circles without disturbing them. With a tape measure or length of rope and enough time and enthusiasm it should be possible to find many more examples of potential units of measurement at other RSCs.

- BARNATT, J. & G. MOIR. 1984. Stone circles and megalithic mathematics.
*Proceedings of the Prehistoric Society*50: 197–216. - BRADLEY, R. 2005.
*The Moon and the bonfire:**an investigation of three stone circles in north-east Scotland.*Edinburgh: Society of Antiquaries of Scotland. - RCAHMS. 2007.
*In the shadow of Bennachie: a field archaeology of Donside, Aberdeenshire*. Edinburgh: Society of Antiquaries of Scotland & Royal Commission on the Ancient and Historical Monuments of Scotland. - WELFARE, A. 2011.
*Great crowns of stone: the recumbent stone circles of Scotland*. Edinburgh: Royal Commission on the Ancient and Historical Monuments of Scotland.

*Author for correspondence

**John Hill**

School of Archaeology, Classics and Egyptology, University of Liverpool, Liverpool L69 7WZ, UK (Email: johnhill.ma@googlemail.com)