with the height ascended by a body projected vertically upwards with a velocity of 30 feet per second?

10. A rifle is pointed horizontally, with its barrel 5 feet above a lake. When discharged, the ball is found to strike the water 400 feet off. Find approximately the velocity of the ball.

11. A balloon is carried along at a height of 100 feet from the ground with a velocity of 40 miles an hour; a stone is dropped from it. Find the time before the stone reaches the ground, and the distance from the point where it reaches the ground to the point vertically below the point where it left the balloon.

12. What is the average velocity of a point executing a simple harmonic motion for the time occupied in moving from the one to the other extremity of its range, its maximum velocity being 5 feet per second?

13. A particle is describing simple harmonic motion in a period of 1/10 of a second, and with an amplitude of 4 centimetres. Find the acceleration of the particle when at the extremity of its range. Find also the velocity of the particle when passing through the middle of its range.

CHAPTER FOURTH.

DYNAMICAL.

SECTION XXII.-MASS.

ART. 124.-Mass and Weight. By the mass of a body is meant the quantity of matter in it. Mass is the intrinsic property of a body; whereas weight is an accidental property depending on the presence of another body in the neighbourhood. These two ideas of mass and weight are confounded in the popular mind, and are not clearly discriminated in many text-books. A clear perception of the distinction greatly facilitates the application of arithmetic in the case of many problems.

Mass is a fundamental idea, and the general unit of mass is appropriately denoted by M.

ART. 125.-Imperial Standard of Mass. In the Imperial system the Standard of Mass is a cylinder of platinum, constructed in 1844, and now in the custody of the Warden of the Standards. It is denominated the "Imperial Pound Avoirdupois." The previous standard of mass, which was lost along with the standard of length, was a Pound Troy. The provision which had been made for its restoration was that one cubic inch of distilled water at 62° Fahr., the barometer standing at 30 inches, weighed 252-458 grains. This provision, however, was repealed on the recommendation of a scientific committee, and the new standard

was constructed from authentic copies of the old, the size of the standard being at the same time changed to the pound avoirdupois. Four parliamentary copies of the new standard pound were

prepared, and deposited along with those of the yard. A fifth copy has been prepared to be used instead of the imperial pound in all ordinary comparisons.

According to the Weights and Measures Act, the comparison of any other mass with the standard of mass is to be done by weighing in vacuo.

ART. 126.-Derived Units of Mass. The other units of mass in the Imperial system which have a special name (see table appended), such as the ton, ounce, grain, are defined as a multiple or a sub-multiple of the pound. The avoirdupois denominations form the principal legal system; the ounce troy and its decimal

derivatives form the legal system for weighing bullion, and may be used in the sale of precious articles. For the retail trade in drugs, apothecaries' denominations may be used.

Local standard weights are constructed by the Standards Department, and distributed along with the local standard measures. The figure represents the form of the modern local standard avoirdupois weights.

ART. 127.-Metric Standard of Mass. In the Metric system the kilogramme was originally defined as the mass of a cubic decimetre of distilled water at the temperature of its maximum

density (about 4° C.). Distilled water is very suitable for a standard substance on account of its being obtainable everywhere in a state of purity, its homogeneity, and the invariability of its density at a given temperature. By weighing and measurement the mass contained in a cubic decimetre of water at its standard state was found, and a piece of platinum was constructed to represent that mass. The piece of platinum is called the kilogramme. des archives; it, or rather

a

standard kilogramme subsequently constructed, is now the ultimate standard for the kilogramme in the same way as a piece of platinum is the ultimate standard for the pound. In the Standards Department there is a standard kilogramme of platinum, which is similar to the kilogramme des archives.

The gramme is the one-thousandth part of the kilogramme, and therefore the mass of a cubic centimetre of water at its temperature of maximum density.

In the C.G.S. system the gramme is chosen for the unit of