Clarke's comparisons

Alexander Ross Clarke (1828 – 1914) was active in geodesy in the last half of the 19ᵗʰ century. With the encouragement of the Director of the Ordnance Survey, Henry James, he carried out a series of comparisons of national standards. Knowledge of the relative sizes of the standards was necessary to connect the national geodetic surveys, which had been made in various differing units, such as yard, meter, toise and klafter.

The selections that follow are taken from his book, Geodesy (Oxford: Clarendon Press, 1880).

Page 146: the standards

The unit of length, in which by far the greater part of the geodetical measurements in Europe are expressed, is the Toise of Peru, a measure, 'à bouts,' of which fortunately there exist two copies (compared with the original and certified by Arago), one made for Struve in 1821, and a second for Bessel in 1823; it has moreover a third representative in Borda's Rod, No. 1. The Standards of Belgium and Prussia are copies of the toise of Bessel; and the Russian Standard, which is two toises in length, is measured from the toise of Struve. The Standard of the Ordnance Survey is ten feet in length and in section a rectangle of an inch and a half in breadth by two and a half in depth, supported on rollers at ¼ and ¾ of its length. The ends of the bar are cut away to half its depth, so that the dots marking the measure of ten feet are in the neutral axis.

Page 151: the Southampton facility

At the Ordnance Survey Office, Southampton, is a building specially constructed for comparisons of standards. The inner room, measuring 20 feet by 11, with thick double walls, is half sunk below the level of the ground, and is roofed with 9 inches of concrete. An outer building entirely encloses and protects the room from external changes of temperature; so that diurnal variations are not sensible in the interior. Along one wall of the room are three massive stone piers on deep foundations of brickwork; the upper surfaces of these stones (which are 41 feet above the flooring on which the observer stands) carry the heavy cast-iron blocks which-projecting some seven inches to the front over the stones--hold in vertical positions the micrometer microscopes under which the bars are brought for comparison. Each micrometer microscope is furnished with an affixed level for making its axis vertical; one division of the micrometer is somewhat less than the millionth of a yard.

It is a most essential point in the construction that the foundations which carry the stone piers—the supports of the bars under observation—and the flooring on which the observer stands, are separate; thus, no movement made by the observer communicates any motion either to the bars or to the microscopes.

The illumination of the disks (on the bar) which bear the lines or dots indicating the measure, is effected by the light of a candle placed some ten inches behind each microscope: the light of the candle passes through a large lens which forms an image of the flame on the disk, giving abundant illumination with a minimum of heat.

When two bars are to be compared they are placed generally in the same box side by side and close together; each bar rests immediately on rollers to which a fine vertical movement can be communicated. The first adjustment is to level one of the bars and bring the microscopes over the terminal dots; the microscopes are then made truly vertical, brought perfectly to focus, with the collimation axis closely over the dots. It is usual to arrange a pair of bars at least twenty-four hours before any comparisons are made, so that a steady equality of temperature may have been obtained. The bars are visited for the purpose of comparison three or four times a day; all adjustments are frequently put out and renewed, and the bars themselves are made to interchange places so as to avoid constant error, the possibility of which requires to be ever kept in mind. The observations made at one visit and constituting 'a comparison' are these:— (1) The thermometers in the bars are read; (2) the bar A being under the microscopes the lines or dots at either end are bisected and the micrometer read; (3) the second bar B is brought under the microscopes and read i (4) B is thrown out of focus, brought back again, and read again i (5) A is observed a second time after renewed focussing; (6) the thermometers are read again.

As no artificial temperature is used, it is the practice to compare bars when the temperature is near 62°, which is the standard temperature for standards of length in this country, and again when it is much lower, so as to eliminate the differences of expansion.

Page 155: comparison of standards

In order that the triangulation of the continental countries of Europe might be put in connection with the triangulation of England, the Government of this country, at the suggestion of General Sir Henry James, then Director of the Ordnance Survey, invited the Governments of Russia, Prussia, Belgium, Spain, Austria, and also the United States of America to send their standards to Southampton to be compared. The invitation in each case was complied with, and an account of the comparisons, which are of the highest importance to Geodesy, will be found in two papers in the Philosophical Transactions for 1866* and 1873: fuller details are given in the work entitled Comparison of the Standards of Length of England, France, &c., by Col. Clarke, R.E.

The following are some of the principal results of these comparisons, the Old English capitals [replaced by bold caps Y, T, M, K-ed.] representing the true lengths of the Yard, Toise, Metre, and Klafter :—

Name of Standard Stand.
Length in
Belgian Toise 61.25 T − 0.00100 l 2.13150851
Prussian Toise " T − 0.00099 l 2.13150911
Russian Double Toise " 2T − 0.00560 l 4.26300798
Spanish 4 Metre Bar " 4M + 0.40710 mm 4.37493562
Platinum Metre, Royal Soc. 32.0 M − 0.01759 mm 1.09360478
Pulkowa copy of Klafter 61.25 K − 0.00029 l 2.07403658
Milan copy² K1. 3 " K − 0.00580 l 2.07401462
Milan copy, KI.II " K − 0.00000 l 2.07402990

1. The 'line' represents the 864th part of the Toise, or of the Klafter.

2. The Milan copy of the Klafter of Vienna has two measures of the Klafter laid off on it, one on its upper surface defined by dots 1, 3. the other on its under surface by dots marked by Roman numerals I. II.

The first three lines in this table afford, from many thousands of observations, three entirely independent values of the toise. The greatest divergence of anyone of the three values from their mean is but half a millionth of a toise. Then the toise being known, the length of the metre follows by means of the definition 443296 T = 864000 M. A further check on this value of the metre is afforded by the Spanish bar, of which the length, as taken from Borda's rod No. 1, is 4.0004071 M. According to the observations at Southampton the Spanish bar is 4·0004052 M, a difference of only half a millionth of the length.

The final results are these :

T = 2·13151116 Y,

M = 1·09362311 Y,

K = 2·07403483 Y



*The first paper was read on 13 December 1866, but it was not published until the following year. (Philosophical Transactions of the Royal Society of London, vol. 157 (1867), pages 161-180). It discusses standards from England, France, Belgium, Prussia, Russia, India, and Australia. The second paper (Phil. Trans., vol. 163 (1873), pages 445-469) discussed comparison with standards from Austria, Spain, America, the Cape of Good Hope, and a second Russian Standard. Both papers are readily available in the online database JSTOR. Copies of Clarke's book, Comparisons of the Standards of Length of England, France, Belgium, Prussia, Russia, India, Australia, Made at the Ordnance Survey Office, Southampton (London: HMSO, 1866) are less easily found.

It is important to notice that Clarke's conversion factor between the yard and meter was calculated from his examination of toises, since those were the standards for the geodetic surveys with which he was concerned. It was not based on the 1799 Mètre des Archives. The International Prototype of the Meter did not even exist prior to the 1880's.

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