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18. What are the advantages of employing the number 10 as the base for logarithms? Having given the logarithms of a number to the base e, show how to find the logarithms of the same number to the base 10.
Given log 10 71968 = 4·8571394; diff. for 1=60: find the value of 0719686 to seven places of decimals.
Set to Candidates for the Admiralty, who selected Algebra as a Subject of Examination.
1. Divide 4 b3 + (4 c − a b) x3 — (4 d + a c) x + ad by 4 x
4. Show that the product of two quantities equals that of their greatest common measure and least common multiple.
Find the greatest common measure of
35 203 +47 202 + 13 x + 1 and 42 x + 41 x3 — 9 x2 — 9 x - 1.
5. Solve the following equations:
6. A and B have the same annual income, and occupy lodgings for 30 weeks, the former at 14s., the latter at 21s. per week, all other expenses being exactly the same for both: B exceeds his income by as much as A comes short of his, and finds that he has spent one tenth too much: Required the annual income and the whole expenditure of each.
7. Find the sum of the following series :
8. Write down the expansion of (3x-4y), and by means of the binomial theorem approximate to 3√31.
9. What are the advantages of employing the number 10 as the base for logarithms? Having given the logarithms of a number to the
base e, show how to find the logarithms of the same number to the base 10.
Given log 10 71968 = 4.8571394; diff. for 1=60: find the value of 80719686 to seven places of decimals.
11. Insert four harmonic means between 2 and 12.
12. Find what number r out of n things must be taken together so that the number of combinations formed may be the greatest possible.
13. When does one quantity vary directly as another, and when inversely as another?
Given that y varies as the sum of two quantities, one of which varies as a directly, the other as a inversely; and that when x=1, y = 4, when x = = 2, y = 6: Find the relation between x and y. 14. In what scale of notation is sixteen-hundred-and-sixty-four ten-thousandth's of unity represented by '0404?
Prepared for an Examination of Candidates for the Colonial
1. Define the terms anticlinal, synclinal, unconformable, strike, and dip. 2. State the reasons for the division of rocks into igneous and sedimentary. What are metamorphic rocks?
3. What are the constituent minerals of granite, basalt, greenstone, gneiss, trachyte?
4. Describe the divisions of the wealden formation, and give a sketch of its distribution in England, and the reasons for looking on it as a freshwater deposit.
5. Where are the points of division placed by geologists to separate the hypozoic, the paleozoic, the mesozoic, and the cainozoic strata? Exemplify the principles on which these divisions have been founded.
6. Coal has been accounted for sometimes as the result of drift, by water, of masses of vegetable matter; sometimes as an accumu lation of such matter by growth in situ. What hypotheses do these views involve, and what circumstances lend probability to each view?
7. Give an accurate description of the stigmaria and the sigillaria, and of the facts that prove their mutual relation, with the most characteristic mode of their occurrence in the strata.
8. Describe the mountain limestone formation. How is it distributed over the world?
9. By what observations and arguments does the geologist seek to determine the period of elevation of a mountain chain? Illustrate this
by some example.
10. Show that, by the amount and by the characters of the distribution of organic remains in one and the same rock in different localities, we may predicate facts concerning its oceanic and littoral deposition, pointing to the limits of the sea in which it was formed. Give illustrations of this.
11. Give a description of the most important characteristics common to the trilobites, and give the history of their distribution in time. 12. What are the usual characters of a mineral vein ?
How far is its
wealth found to depend on the rock it traverses ?
13. Describe the structure of the ammonite, and give an account of the distribution of its species in time.
14. Trace the changes in the character of the zoology during the oolitic period, as illustrated by the reptilia and the cephalopoda.
15. Describe some of the fossils characteristic of the chalk.
16. Give a sketch of the geology of the Malvern Hills.
Prepared for an Examination of Candidates for the Colonial Office.
1. Define the term element. What elements are gascous, what are liquids, under the ordinary conditions of the globe? What changes do these undergo by considerable alteration of such conditions? 2. State the law of multiple proportions; and illustrate it by means of the oxides (1) of nitrogen (2) of manganese.
3. Give the chemical names of, and write in formula, alum, common salt, green vitriol, calomel, corrosive sublimate, and chloride of lime. 4. The equivalent of aluminium is 137. How much per cent of oxygen, of sulphur, and of aluminium is contained in the anhydrous norinal (or neutral) sulphate of alumina ?
5. Of what gases does the atmosphere consist? Give any accurate method of effecting its analysis; and state the results of this analysis.
6. Explain the changes resulting from the action (1) of hydrochloric acid, (2) of strong nitric acid, (3) of very dilute nitric acid, on gold,
iron, tin, and zinc respectively; and state any facts regarding the modification of the result by the purity or the alloying of any of these metals.
7. Define the terms temperature, specific heat, and latent heat, and the term volume as applied to a gas.
8. What law has been asserted connecting the specific heats of the several elements? How far is it universal?
9. What is meant by the theoretical density of carbon vapour? Within what limits is its determination true, and on what assumptions is that determination based?
10. Describe the oxides (1) of carbon, (2) of iron; and give a complete account of the most important oxides of chlorine.
11. Phosphoric acid is tribasic.
Give illustrations of each type of its salts. It undergoes modifications by the action of heat. Under what circumstances, and what types of salts result?
12. What is meant by the empiric as distinguished from the rational formula of a substance? Illustrate each by means of acetic acid. 13. Describe the chemical changes involved in the process called the vinous fermentation.
14. The analyst employs sulphuretted hydrogen to separate metals from each other. Into what groups does he thus divide them, and what principles are involved in the separation?
15. A solution contains lead, tin, nickel, iron, zinc, magnesia, potash, with hydrochloric and nitric acids. Give in detail the process of analysing (qualitatively) such a solution.
16. Give a series of illustrations, (1) from minerals, (2) from the products of the laboratory, of isomorphism, dimorphism, allotropism, and isomerism.
Set to Candidates for the Office of the Committee of Council on Education.
IN THIS EXAMINATION NATURAL SCIENCE IS NOT PRESCRIBED, BUT MAY BE SELECTED BY ANY CANDIDATE WHO HAS MADE IT HIS ESPECIAL STUDY," WITH THE VIEW OF DISPLAYING HIS INDUSTRY AND INTELLIGENCE.
1. Enumerate the various kinds of levers, and state the general relation between the power and weight, when balanced on a lever.
2. Explain fully the principle of the graduation in the common and in the Danish steelyard.
3. What are the three laws of motion in dynamics, and how is their truth established?
4. Explain the construction and use of a common barometer and its vernier. Show also how a self-registering thermometer may be constructed.
5. Define specific gravity, and give a method by which the specific gravity of a body lighter than the fluid in which it is weighed may be found.
A piece of metal whose weight in water is 12 ounces is attached to a piece of wood which weighs 16 ounces in vacuo, and the weight of the two in water is 8 ounces; find the specific gravity of the wood.
6. Explain the following terms: equator, ecliptic, zenith, solstice, meridian, meridian line, nadir, horizon, perihelion, solstitial colure, magnetic variation, compression of the earth.
7. Explain how it is that in sailing round the world a day is either lost or gained.
8. Explain the following phenomena :—
(1) The changes of the seasons.
(2) The different lengths of day and night.
(3) The comparative absence of twilight in the tropics.
(4) The trade winds.
(5) The harvest moon.
(6) The phases of the moon.
9. State concisely the principal arguments by which it may be proved (1) that the earth moves round its own axis; (2) that it moves round the sun.
10. Explain fully why the clock is sometimes before and sometimes behind the sun. How often are they together? What is this phenomenon called?
11. On the 31st January,- when it is 3.15 P.M. at Dublin, Lat. 53-20, Long. 615,- what is the hour and season at Rio Janeiro, S. Lat. 23°. W. Long. 43° ?
12. Describe the common astronomical telescope, and show how its magnifying power may be measured.
13. How is a telescope made achromatic?
14. What are the various effects produced on bodies by heat? What exception is there to the law that the bulk of bodies increases with their temperature? What result would follow if this exception did not exist?
15. What hypotheses have been framed as to the formation of coal? Which do you prefer? Give your reasons.
Another paper :—
1. Explain the principle of the mechanical power known as the wheel and axle. How is the principle practically employed for obtaining large mechanical advantage?
2. Illustrate, by reference to the inclined plane and the screw,
"What is gained in power is lost in time."
3. What are the requisites of a good balance? Explain popularly the means practically employed for securing them.
4. Enunciate the first and second laws of motion, and state some considerations which suggest their truth. How is their truth finally established?
5. Explain the nature of impact between two elastic bodies. If one billiard ball moving at the rate of 4 feet per second overtakes