Assuming the Russian observations to be the best, as they probably are, it will be seen that a troy pound deduced according to the method prescribed by the Act, would be 2·829 grains too heavy; while, if the Austrian observations had been accepted as the best, the troy pound would have been 4.707 grains too heavy. On the other hand, it was possible to recover the weight of the lost standard in air to within a fraction of 0.001 grain, by means of the troy pounds which had been compared with it, and could be easily brought together for recomparison. Seeing, then, that the error of one of these two methods of restoring the lost standard, is at least 2829 times as large as the error of the other method, the Committee could not hesitate to recommend the adoption of the latter.

A Committee was appointed by a Treasury Minute of June 20, 1843, to carry out the recommendations contained in the Report referred to above. The evidence for ascertaining the weight of the lost standard, placed at the service of this Committee, consisted of the following weights: -The brass troy pounds of the Exchequer Office; the brass troy pounds from the cities of London, Edinburgh and Dublin; the platinum troy pound and the two brass troy pounds then in the possession of Professor Schumacher; the platinum troy pound of the Royal Society; the troy pound used by the late Mr. Robinson of Devonshire Street, purchased by the Committee; four troy pounds made in 1758, two of which were formerly in the possession of Mr. Bingley of the Royal Mint, one the property of Messrs. Vandome and Titford, and one the property of the Bank of England.

The troy pounds of the Exchequer, and of the cities of London, Edinburgh and Dublin had been compared with the lost standard by Captain Kater in 1824. The three troy pounds in the custody of Professor Schumacher, and the troy pound of the Royal Society, were compared with the lost standard with extraordinary care in 1829 by the late Captain v. Nehus. The troy pounds bearing the date 1758 were constructed, along with the lost standard, by Mr. Harris, Assay Master of the Mint. These were referred to at the suggestion of Professor Schumacher, in the hope of arriving at a knowledge of the volume of the lost standard, which, unfortunately, had never been determined by weighing it in water. For, as long

as the volume of the lost standard remains unknown, the weight of the air displaced by it, and, consequently, its absolute weight, is uncertain within limits far exceeding the errors of weighing.

Let U denote the lost standard; Ex, L, Ed, D, RM the troy pounds of the Exchequer, the cities of London, Edinburgh, Dublin, and the Royal Mint, respectively; Sb, K two brass troy pounds, Sp a platinum troy pound, all in the custody of Professor Schumacher; RS the platinum troy pound of the Royal Society. Let A prefixed to the symbol by which any weight is designated denote the ratio of the density of the weight at the freezing-point to the maximum density of water; t the temperature of the air in degrees of Fahrenheit's scale; the height of the mercury in the barometer in inches reduced to the freezing-point. The symbol placed between the symbols of two weights will be used to denote that they appear to

be equal when weighed in air. The two weights in this case will not be equal unless their volumes are equal. When the weighings have been made in air of given density, or have been reduced to what they would have been in air of given density; or, when the volumes of the weights, the temperatures and pressures of the air being unknown, we are compelled to assume that their volumes are equal, the symbol may be substituted for ✩.

=

By the observations of Captain Kater (Philosophical Transactions, 1826),

Ex U+0.0010

=

By the observations of Captain v. Nehus in 1829

10-log A Sp=8-67392, 10-log A RS=8.67392,

10-log▲ Sb=9.08471, 10-log A K=909724.

These weights were afterwards compared with each other with a balance of extreme delicacy procured from Mr. Barrow. In its con

struction it nearly resembled the balances of the late Mr. T. C. Robinson. The beam is made sufficiently strong to carry a kilogramme in each pan. Instead of having an index pointing downwards, as is usual in balances of this description, a thin slip of ivory is affixed to one end of the beam, a little more than half an inch long, divided into spaces of about 0.01 inch each. This scale is viewed through a compound microscope having a single horizontal wire in the focus of the eye-piece. A screen was interposed between the observer and the front of the balance-case, having a very small opening opposite to the eye-piece of the microscope.

In making a large number of comparisons, the weights compared are exposed to the risk of being injured by wear. In order to obviate this danger, two light pans were used of very nearly equal weight, each of which has a loop of wire forming an arch, the ends of which are attached to the pan at opposite extremities of a diameter of the pan. To the upper point of the loop of wire is affixed an iron hook. Each pan is suspended by a wire of suitable length bent into a hook at either end, from the ring attached to the agate plane resting on the knife-edge at either end of the balance.

Calling the weights of the pans X and Y, and the weights to be compared P and Q, P was placed in X and Q in Y, and P+X compared with Q+Yn times; then P was placed in Y and Q in X, and P+Y compared n times with Q+X. The weights were thus exposed to the wear of two ordinary comparisons only in the course of 2n comparisons. The mean of the 2n comparisons gives the difference between P and Q unaffected by the very small, but unknown difference between X and Y. This contrivance was found to be especially useful when either of the weights to be compared consisted of several parts.

In using the method of double-weighing, the counterpoise was placed in the left-hand pan of the balance, and the detached pan X containing the weight P, and the detached pan Y containing the weight Q, were alternately suspended from the right-hand end of the beam, and the positions of equilibrium deduced in each case from the extreme positions of the beam at the beginning of each of three consecutive oscillations (usually twenty times). The weights were then

interchanged, and the pan Y containing the weight P, and the pan X containing the weight Q, suspended alternately from the right-hand end of the beam the same number of times.

In weighing by Gauss's method, in which the two weights to be compared as suspended from the right and left-hand ends of the beam respectively, and are then interchanged, it was desirable to be able to transfer the pans and the weights contained in them from one end of the beam to the other, without opening the doors of the balance-case, and thus avoid sudden changes of temperature of air in the balance-case, and consequent production of currents of air. In order to effect this, a slender brass tube 38 inches long was made to pass freely through two holes in the ends of the balance-case, which is nearly 23 inches long, near the top of the case and half-way between the balance and the front of the case. To the middle of the tube is attached a depending loop of wire. Suppose that by sliding the tube the loop is brought near to the right-hand end of the beam, and the pan with a weight in it transferred from the end of the beam to the wire loop by a brass rod having a hook at the end, which is inserted through a hole in the right-hand end of the balance-case. By sliding the tube in the opposite direction, the loop with the pan and weight suspended from it, is brought near to the left-hand end of the beam, to which it is transferred by a brass rod having a hook at the end, passing through a hole in the left-hand end of the balance-case. A similar tube halfway between the balance and the back of the case, serves to transfer the other pan and weight from one end of the beam to the other. In this manner any number of comparisons may be made without opening the balance-case, except in the middle of the series, for the purpose of changing the pans.

A sufficient number of preliminary comparisons of Sp, RS, Sb, K, Ex, L, Ed having been made in 1844, the results were reduced, when the material of one weight was platinum and that of the other brass, to what they would have been in air (t=65·66, b=29·75), or, of the mean density of the air during the comparisons of Sp and RS with U in 1829. Using U, Sp, RS, &c. to denote the apparent weights of U, RS, &c. in air (t=65'66, b=29.75), it was found that

In the interval between 1829 and 1844, the difference between the two platinum troy pounds Sp and RS had undergone no very sensible relative change. If, as appears probable, Sp and RS have undergone no sensible absolute change, Sb has gained 0.0046 grain, and K has lost 0-0061 grain. On the same supposition it appears

RM 0.0068

5

RM-U+0.0021 (1829) RM-U+0·0089

With the single exception of K, all the brass weights have become heavier since they were compared with U, in consequence probably of the oxidation of their surfaces, while U, which was made in 1758, was protected from further change by the coat of oxide already formed. One of these weights, Sb, appeared to have been protected by gilding, though imperfectly, since parts of its surface were slightly tarnished. Ex and L were brighter than Ed and D. K, though it had become lighter, was much tarnished. The discordances presented by the different weighings of K appear to have greatly perplexed both Professor Schumacher and Captain Kater, and were probably the cause of the numerous and accurate comparisons of the several troy pounds placed at the disposal of the Committee with the lost standard, on which alone depends the possibility of restoring it with sufficient accuracy. Previous to the comparison of K in 1844, a small fragment of wood, like a grain of coarse sawdust, was found adhering so firmly to its under surface, that it was detached with some difficulty. It appears probable that the changes of the weight