Sir Joseph Whitworth gives 1/40000 of an inch as the smallest length that can be measured with certainty, with an ultimate possibility of 1/1000000 of an inch; but imperceptible variations of temperature affect these infinitesimal lengths to such an extent that he believes the limit can only be reached at a standard temperature of 85° F., to avoid the effect of heat of the body.
It appears to me that comparisons should be made of double yards and mètres with the old French toise, as the limit of exactness would be thereby doubled.
Another great defect in statements of relative values is the omission of necessary facts—the material of which the bars or standards are made, the temperature at which comparison was made, and the standard temperatures used as to the final reduction, with the coefficient of expansion adopted.
Again, bars of different metals appear in time to sensibly change their relative length.
ENGLISH STANDARDS OF LENGTH.
The first establishment of a uniform standard appears to have been made in 1101 by Henry I., who is said to have fixed the ulna (now the yard) at the length of his arm; but nothing definite was done till 1736, when the Royal Society took steps toward securing a general standard, and in 1742 they had a standard yard made by Graham from a comparison of various yards and ells of Henry VII. and Elizabeth, that were kept in the Exchequer.
Two copies of the Royal Society standard yard were made by Bird in 1758 for a committee of Parliament, one of which was marked “standard of 1758,” and the other 1760. But no exact legal standard was yet established, as shown by comparisons in 1802 of the various standard measures in use which Pictet, of Geneva, made with an accurate scale by Troughton, using means exact to the ten thousandth part of an inch, with the following results at the temperature of 62° F.:
| Troughton Scale | 36·00000 | inches. | ||
| Parliamentary | Standard | (1758, Bird) | 36·00023 | “ |
| Royal Society | “ | (1760, “ ) | 35·99955 | “ |
| “ | “ | (Graham) | 36·00130 | “ |
| Exchequer | “ | 35·99330 | “ | |
| Tower | “ | 36·00400 | “ | |
| Gen. Roy | “ | (Trig. Survey) | 36·00036 | “ |
Parliament finally undertook to reform the measures of England, and appointed a commission in 1818, under whose authority Capt. Kater compared the standard yards then in use with the following results, as referred to the Indian Survey standard: