Elements of Mechanics. II.

1. Define a uniformly accelerating force.

Prove the relation between the time of motion and the space described by described by a body falling from rest in vacuo under the influence of such a force.

2. A ball projected vertically upwards in vacuo is moving with a velocity of 128.8 feet per second when it has attained to the height of 322 feet. Find (1) the whole height and (2) the whole time of its ascent. [932.2 feet per second.]

3. Describe Atwood's machine. Find the value of g which results from the following data. The masses attached to the ends of the string which passes over the middle wheel are 16 and 16.25 ounces; the larger mass descends from rest through 36 inches in 5 seconds; and the rotation of the system of wheels has the same effect on the motion of translation as if the total mass moved was greater by 1.25 ounce.

4. A heavy body is projected obliquely in vacuo with a given velocity. Determine for what angle of elevation the horizontal range is greatest.

5. A brass ball, weighing 459.998 grains, was suspended by a counterpoised hair from the pan of a balance. The apparent weights of the ball in distilled water and in a saturated solution of common salt were 406.08 and 394-795 grains respectively. Find, to three places of decimals, the specific gravities of (1) the brass ball, (2) the solution of salt.

[Turn over.

6. Explain the principle of the hydrostatic bellows.

If the internal diameter of the moveable board or piston be one foot and the apparatus be filled with mercury, find what weight must be placed on the board in order to force the mercury to stand 14 inches higher in the smaller than in the larger cylinder.

[The weight of a column of mercury 30 inches high and one square inch in section is to be taken as 15 lbs. and 22 approximately.]

σ = 7

7. Investigate a general expression for the pressure exerted by a heavy liquid at rest upon a surface immersed in it.

8. Quote experiments in proof that the mercury in the tube of a barometer is sustained by the pressure of the atmosphere.

9. Explain why the ordinary kinds of air pump cannot produce complete exhaustion of the receiver.

Describe the most effective air pump with which you are acquainted.

10. Describe and explain the mode of action of (1) the cup of Tantalus, (2) the fountain of Hero.

Elements of Chemistry. I.

1. Describe the construction of a balance, pointing out the conditions upon the fulfilment of which its accuracy and sensibility depend.

2. What is meant by an experimental science? Give examples of (1) a synthetical, (2) an analytical experiment in chemistry.

3. Give some account of the discovery of oxygen, and explain the importance of this discovery in the history of chemistry.

4. What is ozone? What account can be given of the fact that two or more substances of the same elementary composition may have different properties?

5. Express in equations the various reactions known to you in which hydrogen is formed.

6. Water consists of 2 parts by weight of hydrogen and 16 parts by weight of oxygen, and its chemical symbol is therefore H2O.' By what other considerations besides that here named has the formula of water been determined?

7. What is meant by the temperature of any object, and how is this quality measured? How are the centigrade thermometric scale and that of Fahrenheit related to one another?

8. Give an account of the changes which take place when ice at-10°C. is converted into steam at 120°C., and of the quantities of heat required to effect each of the successive changes of state and of temperature.

9. By what methods may nitrogen gas be obtained?

10. How has the analysis of air been effected most accurately? What is its composition, and its density relatively to that of hydrogen?

Elements of Chemistry. II.

1. Describe the native forms of carbon. How is charcoal made, and what are its chief properties?

2. What volume of oxygen can be obtained from one volume of each of the following gases: carbon monoxide, carbon dioxide, nitrous oxide, nitric oxide, chlorine trioxide?

3. How is hydrogen chloride prepared? What are its properties, and how can chlorine be obtained from it?

4. Describe the preparation of silicon fluoride and the action of this gas upon water.

5. Give an account of some classification of the metals, specifying the principal members of each class.

6. Describe briefly the principal operations constituting the manufacture of sodium carbonate, and state and express in equations the chemical changes which occur.

7. What is the chemical nature of the following substances: glass, marble, ruby, agate, steel, brass, chrome yellow, orpiment, vermillion, prussian blue?

8. What are the principal ores of the metals, lead, tin, zinc, and copper?

9. Describe the construction of a blast-furnace, the materials with which it is charged, and the changes which occur as these materials descend from the top to the bottom. Compare the weight of the air blown into the furnace with that of the solid charge.

10. Give examples of the formation of metals by the action of a galvanic current or of other metals upon the solutions of their salts.