observations were made, and the results of these comparisons were calculated as follows:

ACTUAL DIFFERENCES in parts of an Inch between the three STANDARD YARDS Nos. 2, 3, and 5.

The results (c) finally adopted being obtained by combining the three separate results (a) and allowing for their probable error (+0000012 inch) as follows, the three sets of comparisons being made independently of each other, so that any error committed in one set did not affect the other set:

Here A1, A2, A3, represent the three yard measures ; a1, a2, as their differences: e1, e2, eg their probable errors.

All comparisons are referred to a temperature of 62° F. for the yard, and 0° C. for the metre, therefore the actual temperature at the time of observation has to be taken, and a correction made if the temperature is not exactly 62° F., or 0° C.

Examples of co-efficients of linear expansion as applied to the corrections for temperature:

In the work of dividing or graduating a liuear standard a "Dividing-Machine" is employed, and the graduations can only be accurately made when a screw of great precision is used, so set as to give equal divisions of the scale. The graduation of the Imperial standard was carried out by a machine designed by Messrs. Troughton and Simms. In the production of "diffraction gratings" used in optical research as in the measurements of wave-lengths of light, the highest precision has been obtained in the use of the dividing machine; rulings of 20,000 lines to the inch being

FIG. 18.-BALANCE ROOM, JEWEL TOWER.

cut by a diamond on speculum metal, only visible of course with a microscope of high power. The unit of a wavelength is the ten-millionth of a millimetre.

For scientific work balances of great precision are Balances used, and the use and theory of such balances has been of prewell explained by several authors, as—

HARTIG, Dr.--" Theorie der gleicharmigen Waagen,
Polyt Centralblatt," 1859.

66

JEVONS, Prof. Article "Balance" in Watt's 'Dictionary of Chemistry."

DITTMAR, Prof. Wm., F.R.S.-Article "Balance"
in 9th edition of the "Encyclopædia Britannica."

MAREK, W. J.-" Formules, Constantes et Tables,
Travaux et Mémoires du Bureau International des
Poids et Mesures," Tome III.

THIESEN, Dr. M.-" Études sur la Balance, Travaux
et Mémoires du Bureau International des Poids et
Mesures," Tome V..

WALKER, JAMES, M.A.-"The Theory and Use of a
Physical Balance." Oxford, 1887.

STEWART, BALFOUR, F.R.S., and GEE, W. W. H.—
"Lessons in Elementary Practical Physics." London,
1889. Vol. I., Chapter III.

The balances of precision used at the Standards Office are kept in the basement of the Jewel Tower (see page 123), and are placed on slate shelves or on pedestal tables, as shown in Figure 18; they will "turn" with

No. 1. 300 lbs. avoir. in each pan will turn with 1 grain
No. 2. 50 lbs.

cision.

0.2