as the square of the distance, and the polar equation of the path described. 12. Determine the period of a very small oscillation of a particle suspended by a string of given length from a fixed point. OPTICS. Time allowed, 3 hours. 1. Show that, when a small plane area is illuminated by a pencil of rays emanating from a point, the illumination at any point of the area α cosine of angle of incidence (distance of origin)* 2. Describe the general principle of the method by which Foucault determined the velocity of light. Obtain a formula which will enable you to calculate the velocity from the data of the experiment. 3. Find the equation determining the geometrical focus of a pencil after direct refraction at a spherical surface. Hence show how the refractive index of a plate of glass can be determined by means of a microscope; and express the refractive index in terms of the quantities obtained by the observation. 4. Define what is meant by the magnifying power of a lens; and find an expression for the magnifying power for given positions of the object and eye with respect to a convex lens; also find the limits for a direct magnified image. 5. Give a brief account of the phenomena of absorption in coloured media. Explain how it is that a solution of chromium chloride is green in small thickness or weak solutions, but red in great thickness or strong solutions. 6. Describe briefly the optical phenomena shown by plates of adularia, apatite, brookite, barytes, when placed in convergent light between crossed Nicols. Explain very shortly the origin of the phenomena, and point out the inference, if any, which may be drawn as to the system of the substance. 7. Give briefly the laws of the rotation of the plane of polarization of light by liquids and crystals. What practical uses are made of this property? 8. Describe briefly the construction of a Nicol's prism; and show how to determine the limits of the field of poparized light. 9. Describe shortly the method by which the wave length of a wave of definite refrangibility is determined; and explain the cause of the phenomena observed. 10. Give a short general account of the variations in the optic characters of crystals under change of temperature. Describe shortly the variations observed in plates of gypsum, and certain varieties of orthoclase. OPTICS. (Practical Examination.) 1. Measure the angle of the optic axes for red and blue light (given by glass plate) in the Section A. 2. Determine the index of refraction of one of the prisms B with sodium light. 3. Determine the focal length of the lens mounted on the table. 4. Determine the radii of the surfaces of the lenses, in which one surface in each is a plane, by means of the spherometer. (Formula and data of spherometer given.) 5. Examine and describe briefly the phenomena observed in the polarizing microscope of the sections 1, 2, 3, 4, and 5. State briefly the origin of each part of the phenomena, and determine the directions of maximum and minimum of the elasticity. Point out what inferences (if any) can be drawn as to the crystal system. GREEK ARCHEOLOGY. Time allowed, 3 hours. 1. Is the earliest Greek art original? 2. Discuss, from the point of view of archæology, the following passages: (α) Odyssey xxii., 125-143. Ορσοθύρη δέ τις ἔσκεν ἐϋδμήτῳ ἐνὶ τοίχῳ, . τοῖς δ ̓ Αγέλεως μετέειπεν, ἔπος πάντεσσι πιφαύσκων, τῷ κε τάχ ̓ οὗτος ἀνὴρ νῦν ὕστατα τοξάσσαιτο. ὡς εἰπὼν ἀνέβαινε Μελάνθιος, αἰπόλος αἰγῶν, (β) Euripides Orestes, 1369-72. [The words are spoken by a Phrygian slave who has escaped out of the palace.] 3. Certain votive tripods were extant in Plutarch's time, inscribed ̓Αντιοχὶς ἐνίκα, Αριστείδης ἐχορήγει, ̓Αρχέστρατος ἐδίδασκε. Plutarch considers that they are wrongly attributed to Aristides the Just, ὡς ἐλέγχει τὰ γράμματα, τῆς μετ ̓ Ευκλείδην ὄντα γραμματικής. Comment on this, and on the following passage (Athenæus x., 454 b), which introduces a speech from Euripides' Theseus Βότηρ δ ̓ ἐστιν ἀγράμματος αὐτόθι δηλῶν τοὔνομα τοῦ Θησεώς ἐπιγεγραμμένον οὕτως· Κύκλος τις ὡς τόρνοισιν ἐκμετρούμενος· τὸ λοίσθιον δὲ τῷ τρίτῳ προσεμφερές. Write the inscription on the tripods as it appeared to Plutarch, and the name Theseus as described by the herdsman. 4. What has been ascertained with regard to the existence of a raised stage in Greek theatres ? 5. Describe any one work of the Phidian epoch, and contrast with the productions of that epoch the productions of the Pergamene school. 6. Give some account of the study of Greek Vases, and estimate its place in archæological research. 7. What are the principal results of recent exploration in Asia Minor ? (4000) Ε 8. Assign to their dialects, punctuate, and translate :— (α) Σώταιρος εἵλετο | ἐλέφαντα παρέχεν ὁπόσ[ου] κα σωπω[ν] = == στρώματος τοῦ ἔν | δοι καὶ τοὺ προδόμου Η · ἔνγνος Εὐκλῆς. (β) 'Α πόλις Φαρσαλίουν τοῖς καὶ οὓς ἐξ ἀρχᾶς συμπο λιτευομένοις καὶ συμπο | λ[εμεισάντε]σσι πάνσα προθυμία ἔδουκε τὰν πολιτείαν καττάπερ Φαρσαλίοις τοις ] ἐ[ξ ἀρχᾶς πολιτευομένοις ἐδούκαεμ μὰ ἐμ Μακουνίαις τᾶς ἐχομένας του Λουέρχου | γα[ς μόραν πλέθρα ἐξείκοντα ἑκάστου εἱβάτα ἔχειν πατρουέαν τὸμ πάντα χρόνον. (γ) Α Γράτρα τοῖς Γαλείοις ΓΑΤΡΙΑΝ (i.e., Πατρίαν, proper name, Blass : πατριὰν, others) θαρρην καὶ γενεὰν καὶ ταὐτῶ | αἰ ζέ τις κατιαραύσειε Γάρρην OP (i.e., ρ Blass: αἱ ζή τις κατιαραύσειε Γάρρενορ others) Γαλείω αἰ ζὲ μηπιθεῖαν τὰ ζί | καια δρ μέγιστον τέλος ἔχοι καὶ τοὶ βασιλᾶες ζέκα μναῖς κα | ἀποτίνοι Εέκαστος τῶν μὴπιποεόντων κα[τ] θυταὶς τοῦ Ζὶ Ὀλυν | πίοι ἐπένποι ζέ κ ̓ ἐλλανοζίκας. In the last extract, discuss the variants. 9. Give an historical account of either Painting or Gemcutting in Greek art. |