Hassler’s reduction of the mètre, as deduced by Beach at 62° F., 39·36850154, compared with the English reduction of the mètre, 39·37079 inches, gives an excess to the United States Standard of 0·002029 inch.
The following reductions have been given for the United States yard in English inches:
| Report of Sec. of Treas., 1857 | 36·00087 | = 1·00002416 |
| Chambers’ Encyclopædia, 1872 | 36·00087 | |
| “ “ “ | 36·0020892 | = 1·0000580334 |
| Trautwine | 36·0020894 | = 1·000058038 |
| Mathewson, U. S. surveyor | 36·00208944 | = 1·00005804 |
| Hassler and Beach | 36·002092 | = 1·00005811 |
| J. E. Hilgard, Coast Survey | 36·00076 | = 1·000021 |
To Mr. Hassler’s reduction the name of United States inch has been applied; but his reduction is not correct, as he used a rate of expansion for brass deduced by himself of 0·0003783 inch in one yard for 1° F., and later experiments show that the smaller rate of 0·000342, deduced by Airy, is more correct.
By correcting Hassler’s reduction with the later rate of expansion, J. E. Hilgard shows that the difference would be very small, or only 36·0002286 = 1·00000635, or about ⅖ of an inch in a mile.
In Coast Survey report for 1876, J. E. Hilgard calls attention to another difficulty in the matter of extreme accuracy, in the uncertainty with regard to the permanence in the length of a bar, and states that the bronze standard bar No. 11 and the Low Moor iron standard bar No. 57, presented to the United States by Great Britain, are found to have changed their relative length by 0·00025 inch in 25 years; the bronze bar being now relatively shorter by that amount. This subject, he states, is undergoing further investigation.
COMPARISON OF UNITED STATES AND FRENCH STANDARDS.
In 1817 Mr. Hassler examined the French standards in America, for the Coast Survey, using the Troughton bronze standard scale, which is identical with Sir George Schuckburg’s standard, as the reference, with the following results, all being reduced to temperature of 32° F.
| Original Iron Mètre, | 1799 | 39·381022708 | inches. |
| Lenoir Iron Mètre, | Coast Survey | 39·37972015 | “ |
| “ Brass “ | “ | 39·380247972 | “ |
| “ “ “ | Eng. Dept. | 39·38052739 | “ |
| Canivet Iron Toise, | 1768 | 76·74334472 | “ |
| Lenoir “ “ | 76·74192710 | “ |