A confusion of “natural” expressions of map scale

Here’s some thoroughly unenlightening testimony given in 1824 to a parliamentary committee:

[committee] On what scale do you propose that the surveys containing the field should be described? — [answer] I should suppose about an inch to 40 perches.

How much will that be to a mile? — It comes very nearly to about the scale of the property surveys in this country.

Are you aware on what scale the ordinary property surveys are drawn? — I believe about 40 perches to an inch. I should think it would require a scale of that size. (Spring Rice 1824, 17)

A wonderful example of utterly useless piffle!

But it is piffle that helps us understand how the early nineteenth-century gentry in Britain conceived the verbal expression of the relationship of the map or plan to the territory, at a time of profound developments in surveying and mapping (for background, see Edney 2019, chapter 5).

The parliamentary committee, chaired by an Anglo-Irish landowner, Thomas Spring Rice (1790–1866), was the “Select Committee appointed to consider of the best mode of apportioning more equally the local Burthens collected in Ireland, and to provide for a general Survey and Valuation of that part of the United Kingdom.” Its goal was to recommend the best way to go about reconfiguring the various land taxes so that they were actually proportional to the area and quality of the land being taxed. A key part of the committee’s work addressed the nature of the necessary field survey, to which end it questioned a number of landowners, engineers, and map makers. This particular witness was Richard Keane (1780–1855), another Anglo-Irish landowner and a militia officer—lieutenant colonel, no less—from County Waterford.

Not surprisingly, in the face of such unenlightening twaddle, the committee pressed Keane to be more specific. After getting Keane to restate his proposed three-part survey, the committee asked,

Then on what scale do you propose the last part [surveys of fields] to be effected? — Not being accustomed to mix French measures with British measures, I am not exactly at once prepared to say.

What would be the French measure? — Four centimetres to one hundred metres.

Can you give the Committee any information with regard to the proceedings which have taken place in France, with respect to the cadastre, or land valuation? — Yes; I have known something of it for the last two years.

Will you have the goodness to state to the Committee, what you know of it? — The French cadastre, which is composed of the acreage partition, and of the correct delineation of each proprietorship, has been organized by the establishment of a school of geography, and the creation of a central and general agency of contributions. …

On what scale are those maps of the French cadastre taken? — Four centimetres for one hundred metres. (Spring Rice 1824, 17–18)

The sudden tangent to bring in “French measures” is decidedly odd. Neither Keane nor the committee had yet mentioned the contemporary French cadastre. My sense is that Keane had been selected as a witness because he had some knowledge of the French cadastre, that he had been briefed to talk about the French cadastre, and he jumped the gun in getting to that topic, rather than letting the committee lead him to the subject, as it does a couple of questions later. A poor witness, indeed.

Keane’s testimony is revealing because of how he insisted on talking about property and cadastral plans as being drawn at y units of personal measure to z units of world measure, and how he was unwilling, perhaps even unable, to convert the specifically agricultural measure (perch, also known as the rod or pole) into itinerary measure (miles). He even extended this practice to recast the plans of the French cadastre as 4cm to 100m. And why not give the scale of the French plans in a more direct way, as 1cm to 25m? I think it was because “4cm” is more akin to the personal measure of an inch (being 1.6 inches) than is 1cm (0.4 inches).

The customary formula of y units of personal measure to z units of world measure explicitly references the use of maps. It is a functional formula. It relates the personal measures that one uses as an extension of one’s body for measuring small things—inches as opposed to feet or ells, used for larger things, like furniture—to the functional measures relevant to what is being mapped beyond one’s body, whether agricultural land (perches/poles/rods, chains, furlongs) or itinerary or distance measures (miles, leagues). Thus, one inch to 40 perches (agricultural) or one inch to one mile (itinerary). The customary formula refers directly to how the maps are used, as a stand-in for the earth that is sized to the body and that can be gauged and measured using personal measures.

By comparison with the numerical ratio (1:x) developed by French engineers soon after 1800, formulas of y units of personal measure to z units of world measure came to be called “natural” scales as opposed to the “rational” scales of 1:x (“rational” as in “ratio”). After 1850, however, once British engineers began had adopted the numerical ratio, then “natural scale” became the numerical equivalent of the customary formula, as 1:63,360 (one inch = 63,360 inches, or one mile), in contrast to “rational scales” with rounded denominators (as 1:25,000).

Customary formulas were not always understandable, though. Keane’s “1 inch to 40 perches” was plainly meaningful to him, but it was not to the committee members who were pushing for a more standardized understanding of an extensive survey covering geographical areas; they accordingly wanted to understand the property surveys in terms of the itinerary measures used to express geographical distances. They asked for a conversion of one inch to 40 perches into so many inches to one mile.

Fortunately, for the committee members, another witness was able to make the conversion, but not with great clarity. This witness was the Anglo-Irish engineer and geologist Richard Griffith (1784–1878), who would soon be appointed to direct the surveys of Irish property boundaries. His response to the committee further reveals the complexities introduced by the varying lengths of measures:

For the purpose of laying down the boundaries of townlands, what scale should you propose for a new survey to be carried on? — On a scale of six inches to an English mile; the usual scale for making territorial [i.e., property] surveys in Ireland; where only the farms are laid down, is 40 perches Irish to an inch, which is equal to eight inches to an Irish mile, and the difference between eight inches to an Irish mile, and six inches to an English one, is as 21 to 22. (Spring Rice 1824, 44)

As the surveyor Patrick Kelly further testified, Irish land surveyors generally used “plantation measure”—a chain of 14 Irish yards, i.e., two Irish poles/perches of 21 feet each—whereas English surveyors used the four-pole chain of 22 English yards (i.e., the Gunter’s chain of 66 feet) (Spring Rice 1824, 84). Note that both sets of measures were enshrined in law, one in Ireland, the other in England, so both might properly and unhelpfully referred to as “statute measure.” Acknowledging the variety of measures, the Scottish surveyor William Bald (ca. 1789–1857) proposed a system for surveying and valuing Irish properties that called for surveying lands at 12 Irish perch to one inch and that the calculated areas of each property should be provided in English, Scottish, and Irish acres (Spring Rice 1824, 60). (I’m away from my library right now, so I don’t know if there was any difference between Irish and English inches that also needed to be taken into account. 😊)

All of this testimony entailed exactly the kind of comparisons for which the French engineers had created the numerical ratio in the first place. It would have been so much easier, to present-day minds at least, to resolve Keane’s Irish property plans as being at 1:10,080 (see also Prunty 2004, 323), the French cadastre as being at 1:2,500, and the committee’s own favored scale of six inches to the mile as 1:10,560.

Not that the committee members thought in such Francophilic terms. Their final report did mention a numerical ratio, according to the testimony of the Anglo-Irish civil engineer William Edgeworth about the ongoing Bavarian cadastral and topographical survey:

What is the scale of the survey? — One 5,000dth part of the real size.

That is 12 inches to a mile? — Thereabouts. (Spring Rice 1824, 103)

In the final report, the customary formula was given first in the description of the Bavarian survey:

The map is laid down on a scale of 12 inches to the mile, or 1/5000 part of the real size. (Spring Rice 1824, 5)

Returning to the Keane’s reluctance or inability to convert perches to miles, it was perhaps too much for the committee to ask him to do so on the fly. It is nonetheless plain that Keane had not previously thought about making such a conversion. Why should he have done so? Property plans are one kind of work, territorial maps another. Expressions of their respective scales are not commensurate.

At the same time, it is evident from the committee’s proceedings that its members were trying to relate these and other mapping modes together so as to form a single whole. In doing so, they sought to determine for each map and survey the customary formula of y inches to one mile.

This was not a new concern. It had been the impetus in part behind the Bavarian survey and it had been debated at length by French officials who sought to make a single, all-purpose survey of France after 1815. In Bavaria and France, the deliberation had been assisted by the use of numerical scales, but the British in 1824 remained wedded to the customary formulas relevant to different mapping modes.

Eventually, British engineers embraced the numerical ratio, calling it the “representative fraction,” although, as noted, the British remained committed to “natural” scales until the needs of NATO and inter-European economic cooperation led the Ordnance Survey in the 1970s to forego the old one-inch series (at 1:63,360) in favor of the nicely “rational” and metrical 1:50,000. But note that even then, the OS labeled its new map series with the customary formula of 2cm to 1km.

[The blog roll image is a detail of Co. Wexford sheet 37, of the six-inch survey of Ireland, printed in 1841; for a complete set of such maps, see maps.nls.uk. Select OS maps and six-inch series.

References

Edney, Matthew H. 2019. Cartography: The Ideal and Its History. Chicago: University of Chicago Press.

Prunty, Jacinta. 2004. Maps and Map-Making in Local History. Dublin: Four Courts Press.

Spring Rice, Thomas, chair. 1824. “Report from the Select Committee on the Survey and Valuation of Ireland [The Select Committee appointed to consider of the best mode of apportioning more equally the local Burthens collected in Ireland, and to provide for a general Survey and Valuation of that part of the United Kingdom].” House of Commons Papers 8, no. 445.