Arthur S. C. Wurtele, an assistant engineer on the New York Central & Hudson River Railroad, opens his 1882 investigation by noting that a standard measure of length appears simple—merely a bar of metal—but quickly reveals a tangle of scientific reductions. He observes that every author assumes the right to use his own judgment about which reduction is most exact, producing a confusing difference in apparently exact figures. Wurtele aims to indicate the cause of this confusion by presenting the roots of the figures used as statements of length, rather than offering a single authoritative table.

The Problem of Conflicting Reductions

Wurtele identifies a central defect in existing comparisons: the omission of necessary facts such as the material of the bars, the temperature at which comparison was made, and the standard temperatures used. He argues that comparisons should be made of double yards and metres with the old French toise, as the limit of exactness would be doubled. The text includes a long table of different reductions of the metre in inches, ranging from 39.368 (Phoenixville Hand-book) to 39.3828 (Wollaston and Playfair, 1814), demonstrating the wide spread of values. Wurtele notes that the legal value in England is 39.37079 inches, but the latest reduction by Clarke in 1866 gives 39.37043 inches, which he considers probably the most exact.

Temperature and the Limits of Precision

Wurtele cites Sir Joseph Whitworth's claim that the smallest length measurable with certainty is 1/40000 of an inch, with an ultimate possibility of 1/1000000 of an inch. However, imperceptible variations of temperature affect these infinitesimal lengths to such an extent that Whitworth believes the limit can only be reached at a standard temperature of 85° F., to avoid the effect of heat from the body. Wurtele suggests that it would be preferable to give comparisons at the same temperature in connection with the corrected result, so that international comparisons of scientific measurements may not be vitiated by accidental variations.

Historical Comparisons and Their Discrepancies

The text recounts a series of historical comparisons between English and French standards. When the metre standard was established in France in 1799, it was compared with Sir George Schuckburg's standard yard by Captain Kater, yielding a metre equal to 39.37079 inches. Later comparisons by Wollaston and Playfair in 1814 gave 39.3828 inches, while the French Academy of Sciences deduced 39.3824 inches at 32° F., which reduced to 62° F. would be 39.3711 inches. Wurtele also presents a table of different reductions of the French toise into English feet, with values ranging from 6.3945925921 feet (Kater, 1799) to 6.39625 feet (Nystrom).

Wurtele's Methodological Approach

Wurtele's method is to give the figures of actually observed comparisons and reductions, rather than selecting a single authoritative value. He examines authorities including Kelly's Universal Cambist, Maunder's Weights and Measures, Encyclopaedia Britannica, Smithsonian Reports, and Coast Survey Reports. He notes that the only concise and clear statement he found was J. E. Hilgard's 1876 report to the Coast Survey on standards, which he was gratified to find coincides with his own deductions. The text thus serves as a compendium of conflicting data, with Wurtele acting as a compiler who highlights the sources of confusion rather than resolving them.

Readers should approach Wurtele's tables as a record of historical disagreement rather than a definitive reference. The author's own preference for Clarke's 1866 reduction is stated, but the work's value lies in its documentation of the many values in circulation. Those interested in the history of metrology will find a snapshot of late-19th-century confusion, while engineers may note the practical challenge of reconciling standards across nations.