POLITICAL ECONOMY. Time allowed, 3 hours. 1. Define Capital, and distinguish Fixed and Circulating Capital. 4. Explain the phenomena of a commercial panic. 5. What are the advantages of Free Trade? 6. In what sense does "demand " determine value? 7. State at length Adam Smith's rules of Taxation. 8. What is the relation of the interest of money to the price of land? 9. What determines the amount of wages in various occupations ? 10. To what extent is the rate of Profits identical in the various employments of capital? PURE MATHEMATICS. Euclid (I.-VI.), Algebra (to Binomial Theorem), Trigonometry (to solution of triangles). Time allowed, 3 hours. 1. Prove that any two sides of a triangle are together greater than the third side. If P be a moveable point in a given straight line, and A and B two fixed points, prove that the sum of the distances AP, BP is the least possible when the lines AP, BP are equally inclined to the given straight line. 2. The opposite angles of any quadrilateral figure inscribed in a circle are together equal to two right angles. 3. Prove that the two tangents which can be drawn from any external point to a circle are of equal lengths. If a quadrilateral figure circumscribe a circle, the sums of its opposite sides are equal. 4. Describe an isosceles triangle having each of the angles at the base double of the vertical angle. What use is made of this proposition in Euclid, Book IV.? 5. Define similar triangles, and prove that if two triangles are equiangular, they are also similar. 6. Find the greatest common measure, and also the least common multiple, of the expressions 2x3+6x2+9x+27, and 3+10x2+33x+36. Find also the greatest common measure, and the least common multiple, of the three expressions— x-y1, x8-y3, and a4a3y+2x2y2—xy3+y1. 7. Resolve into four factors the expression (x2-ax+a2) (x2+ax+a2) (x1—a2x2+a1)=x2+a1x1+a3. FACTORY INSPECTOR. FACTORY INSPECTOR. 8. Solve the equations 9. The hands of a watch are at right angles to each other at 3 o'clock; when are they next at right angles? 10. Having given the first term, and the common ratio of a geometrical progression, find the sum of a given number of terms. Find the sums of the series-- (1.) 128-64+32-&c. to 12 terms. (2.) 1+2n+3n2+4n3+ &c. to n terms. 11. Write down, to four terms each, the expansions of (1+x), and (1-x)-, in powers of x. Find the coefficient of xr in the expansions of (x+1)(x+2) -x. 1+x. 12. Define the sine and cosine of an angle, and find the sine and the cosine of 30°. Find an expression for all the angles which have the same sine as a given angle, and solve the equation— sin (26+)=cos (+). 13. Prove the formula (1.) sin (A+B)=sin A cos B+cos A sin B. (2.) sin A+sin B=2 sin A+B cos A-B. (3.) cos 2(A+B) + cos =sin 2A. (4.) cos A+ 60°+ cos A =√2 cos A+45°. 2B - 2 cos (A + B) cos A cos B 14. Find an expression for the radius of a circle inscribed in a given triangle. If a circle be drawn touching the side BC of a triangle ABC, and also touching the sides AB, AC produced, find an expression for its radius, and prove that the distance between the centre of this circle and the centre of the inscribed circle is equal to FACTORY 15. Show how to solve a triangle when two sides and the included angle INSPECTOR. are given. If ABC be the triangle, and if a=65, b=16, and C=60°, find the other angles, having given Memoria mea ingenti virtute, diversis moribus fuere viri duo, M. Cato et C. Cæsar. His genus, ætas, eloquentia prope æqualia fuere: magnitudo animi par, item gloria; sed alia alii. Cæsar beneficiis atque munificentia magnus habebatur; integritate vitæ Cato. Ille mansuetudine et misericordia clarus factus; huic severitas dignitatem addiderat. Cæsar dando, sublevando, ignoscendo; Cato nihil largiundo gloriam adeptus est. In altero miseris perfugium erat, in altero malis pernicies : illius facilitas, hujus constantia laudabatur. Postremo Cæsar in animum induxerat laborare, vigilare; negotiis amicorum intentus, sua negiegere; nihil denegare, quod dono dignum esset; sibi magnum imperium exercitum, novum bellum exoptabat, ubi virtus enitescere posset. At Catoni studium modestiæ, decoris, sed maxume severitatis erat. divitiis cum divite, neque factione cum factioso; sed cum strenuo virtute, cum modesto pudore, cum innocente abstinentia certabat; esse, quam videri, bonus malebat; ita, quo minus gloriam petebat, eo illum magis sequebatur. Non Tempore ruricolæ patiens fit taurus aratri, Tempus, ut extentis tumeat, facit, uva racemis, Hoc tenuat dentem terram findentis aratri, Hoc etiam sævas paulatim mitigat iras, FACTORY INSPECTOR. Translate into Latin: But when the two armies were drawn up ready to fight, Mettus proposed that the quarrel should be decided by the combat of champions chosen from each army, and Tullus agreed to the proposal. Now it chanced that there were three brothers in each army, equal in age, strength, and valour. Horatii was the name of the three Roman brethren, Curiatii of the Alban. These were chosen to be the champions, and an agreement was made, with solemn rites, that victory should be adjudged to that people whose champions should conquer in the strife. Then the two armies sate down opposite one another as spectators of the combat, but not like common spectators, for each man felt that the question at issue was whether Rome was to be mistress of Alba or Alba of Rome. Long and bravely fought the champions. At length all the Curiatii were grievously wounded; but of the Horatii two lay dead upon the plain, while the third was yet untouched. So the surviving Horatius, seeing that, single-handed, he could not prevail, pretended to flee before his three opponents. Ὁ δὲ Κῦρος εἶπεν, Αλλ' ἐγὼ, ὦ ἄγγελέ τε καὶ Μῆδοι, οὐδέν, ἔφη, θαυμάζω εἰ Κυαξάρης, πολλοὺς μὲν πολεμίους τότε ἰδών, ἡμᾶς δὲ οὐκ εἰδὼς ὅ,τι πράττομεν, ὀκνεῖ περί τε ἡμῶν καὶ περὶ ἑαυτοῦ· ἐπειδὰν δὲ αἴσθηται πολλοὺς μὲν τῶν πολεμίων ἀπολωλότας, πάντας δὲ ἀπεληλαμένους, πρῶτον μὲν παύσεται φοβούμενος, ἔπειτα γνώσεται, ὅτι οὐ νῦν ἔρημος γίγνεται, ἡνίκα οἱ φίλοι αὐτοῦ τοὺς ἐκείνου ἐχθροὺς ἀπολλύουσιν. Ἀλλὰ μὴν μέμψεως γε πῶς ἐσμεν ἄξιοι, εὖ τε ποιοῦντες ἐκεῖνον καὶ οὐδὲ ταῦτα αὐτοματίσαντες ; ἀλλ ̓ ἐγὼ μὲν ἐκεῖνον ἔπεισα ἐᾶσαι με λαβόντα ὑμᾶς ἐξελθεῖν· ὑμεῖς δὲ οὐχ ὡς ἐπιθυμοῦντες τῆς ἐξόδου ἠρωτήσατε εἰ ἐξίοτε καὶ νῦν δεῦρο ἥκετε, ἀλλ ̓ ὑπ ̓ ἐκείνου κελευσθέντες ἐξιέναι, ὅτῳ ὑμῶν μὴ ἀχθομένῳ εἴη. καὶ ἡ ὀργὴ οὖν αὕτη, σάφ ̓ οἶδα, ὑπό τε τῶν ἀγαθῶν πεπαυθήσεται καὶ σὺν τῷ φόβῳ λήγοντι ἀπεισι. XENOPHON. Πέλοπα κατόμνυμ ̓ ὃς πατὴρ τουμοῦ πατρὸς Ἡ τῶν ἐμῶν ἕκατι θύεσθαι γάμων EURIPIDES. FACTORY INSPECTOR. Translate into Greek': The immense booty, as well as the renown, which Pausanias had acquired at Platea, had filled him with pride and ambition. When he returned home, he felt it irksome to conform to the simplicity and sobriety of a Spartan life, and to submit to the commands of the Ephors. He had given a signal instance of the pride with which he was inflated by causing Simonides to attribute the glory of the Persian defeat solely to himself in the epigram which he composed for the tripod dedicated at Delphi; a piece of vanity which gave such offence to the Lacedæmonians that they caused the inscription to be erased, and another to be substituted in its place. Nevertheless, in spite of these symptoms, he had been again entrusted with the command. During the whole course of it his conduct was marked by the greatest vanity and insolence; towards the end it was also sullied by treason. |
