To explain our philosopher's inten tions more fully, let us admit the suppo sition, that the length of a pendulum vi brating seconds in the latitude of London is 39.2 inches ; the length of one vibrat ing 42 times in a minute amounts to 80 inches ; by the same unerring rule, ano ther vibrating 84 times in a minute must be 20 inches : the difference resulting from these data is 60 inches and his pro posed standard measure. Pursuing his experiments to the very acme of perfec tion, he found the variation in the length of the two pendulums to be 59.892 inches, instead of 60, arising from an er ror in the assumed length of the second's pendulum.
It is generally admitted, that .Me. Whitehurst has succeeded in his design:, and demonstrated to the learned how an invariable standard may at any time be found for the same latitude. Besides this discovery, the world is indebted to him for the accurate ascertaining of a fact of very considerable importance in natu ral philosophy. A person who wrote with ability oft this point observes, with respect to the fact just mentioned, " The difference between the lengths of the rods of two pendulums, whose vibrations are known, is a datum from which may be derived the true lengths of pendulums, the spaces through which heavy bodies fall in a given time, with many other par ticulars relative to the doctrine of gravi tation, the figure of the earth," he. Mr. Whitehurst perceived from this experi ment, that the length of a second's pendu lum, vibrating in a circular arc of 3° 20', is very nearly 39.119 ; but performing the same motion in the arc of a cycloid, the result would be 39.136 inches ; conse quently, weighty substances will descend in the first second after they are detached from their support nearly 16.094 fact, or 16.14 inch.
Dr. Young, to whom we acknowledge ourselves indebted for many of the follow ing particulars, has given an excellent compressed table of measures and stand ards, in his recent valuable work, " A Course of Lectures on Natural Philoso phy," &c. from which we find, that the Euglish yard is said to have been derived from the length of the arm of Henry I. in the year 1101 ; that Graham asserts the length of the pendulum vibrating seconds accurately is equal to 39.13 inches ; that Bird's parliamentary standard is admitted to be of the greatest authority, and that it agrees nearly with the scales of Shuck burgh and Pictet, made by Troughton. The standard of the Royal Society by Graham exceeds that of Bird's in length about 1000th part of an inch, but it is not quite uniform throughout its length. The
standard in the Exchequer is about .0075 inch shorter than the yard of the Royal Society. General Roy used a scale of Sisson, divided by Bird, and found it to agree exactly with the Tower standard on the Royal Society's scale. Sir George Shuckburgh, adopting. Troughton's scales for the standard, found the original 'row er standard 36.004 ; the yard E. on the Royal Society's scale by Graham 36.0013 inches ; the yard Exchequer of the same scale 35.9933 ; Roy's scale 36.00036 ; the Royal Society's scale by Bird 35.99955 ; Bird's parliamentary standard of 1758, 36.00023. The English have employed and adjusted their standards at the tem. perature of 62° of Fahrenheit's thermo meter, and the French at the freezing point of water. The French metre is 39.37100 English inches, and the ten mil lionth part of the quadrant of the meri dian. The same measure contains 36.9413 French inches, or three feet 11.296 lines. Hence, says the Doctor, the French toise of 72 inches is equal to 76.736 English inches. One of Lalande's standards mea sured by Dr. Maskelyne was 76.732, the other 76.736. In latitude 45°, a pen dulum of the length of a metre would perform in a vacuum 86116.5 vibrations in a day. The length of the second pen dulum is 993827 at Paris.
The French National Institute of Sci ences and Arts have turned their atten tion to this subject, and in the month of Nivose, in the year 1801, a member read a report from a committee, founded on the comparison of the standard metre of the Institute with the English foot. And M. Pictet, professor of natural philosophy at Geneva, exhibited to, the class, in the month of Vendemiaire, a collection of the most interesting objects, which lie had collected in England, relating to arts and sciences. One of the number was a stan dard of the English linear measure, which was of brass, 49 inches in length, and neatly divided by engraved lines into tenths of an inch. This standard was made for the exhibitor by Troughton, a resident in London, who has deservedly acquired the reputation of dividing instru ments with the utmost accuracy,. which was compared with another made by the same artist for Sir George Shuckburgh, when it was ascertained, satisfactorily; that the variations between them did not amount to more than the difference between the divisions of each ; in other words, the variation was almost imper ceptible. Arguing from this ' circum stance, the standard may be considered. as identical with that described by Sir George Shuckburgh in the Philosophical Transactions for 1798.