a. Prove that, if the surface be closed, SS(R-R)e sin OdAdo = 0, and hence infer that if rt – 52 be finite throughout the surface, it must be a sphere. N. B.-0, 0, are the polar angles which determine the position of the normal. 4. The equation of an attracting surface of given superficial area, whose potential with regard to a given point is a maximum, is P фе R R r 01 (r) + a P being the perpendicular on the tangent plane, r the radius vector from the attracted point, or the law of the attraction, and 01 (~) =S ordr. 5. Give a sketch of the progress of the Calculus of Variations, pointing out the principal contributions of the brothers Bernouilli, Euler, Lagrange, Jacobi, and Sarrus. I I + MR. LESLIE. 1. The order of the equation B=0, furnished by the Calculus of Variations for the determination of the function which renders S V dx a maximum, may be depressed-(a) if V does not contain the independent variable ; (6) if m of the quantities y, y', &c., be wanting. In the latter case, find when the solution is determinate. dy dx 2. If the solution of the differential equation f (x, y, y ...y()) = 0 be given, prove that the complete integral of the linear equation df ,df df +z' + &c. + z(n) dy is also given. Hence the solution of dB=0 can be deduced from that of ßro. 3. Prove that oßro may be written in the form d 21 DuzD....UDADU, ... Duz Duidy=0, D= dx and hence show that d2 V Dun Dun-1.. Durdy 82 Vdo = dx. =O dy' dy(n) dy(n)? Un Un-1. 4. Show how to calculate U1, U2, &c., in terms of the particular solutions of oß= 0, and hence prove that d2V A2 dx Vdx=s .dy u v w'.. dy where A = A'= u(n) v(an) w(n) . oyin) u(n-1) v(n-1) win-1) 2, , w .. being n different solutions of 8B = 0. 5. If a curve joining two points be such that the surface generated by its revolution about a given line may be a minimum, prove that it is a catenary; and determine the limits within which the solution of the question is possible. 6. Prove that the conditions requisite for a minimum, in the last question, cannot be satisfied, unless the point of intersection of the tangents drawn to the curve at the extreme points lie between the curve and the given line. 7. Prove that a sphere is the only closed surface of revolution which includes a maximum solid under a given surface. (a). If the surface be not closed, discuss the nature of the generating curve. 8. Find a curve such that the area bounded by the curve, its extreme radii of curvature, and the arc of the evolute between them, may be a minimum. (a). Show that, if the extreme points be given, its equation can be reduced to the form dy dx EXAMINATION FOR THE DEGREE OF BACHELOR IN MEDICINE. DK. BANKS 1. What are the forms of delirium which may occur in typhus fever? 2. How is the delirium tremens of typhus distinguished from that of the drunkard 3. Give thc characters which distinguish inflammation of the brain and its membranes from typhus fever. 4. What are the distinctions between pneumonia and hypostatic consolidation of the lung in typhus ? 5. Contrast the mental states in typhus and typhoid fever. 9. What are the characters of the pulse in fatty degeneration of the heart? 10. How would you treat the disease ? and what are the remedial agents which may prove dangerous ? ANATOMY AND PHYSIOLOGY. PROFESSOR M'DOWEL. 1. What parts constitute the mesocephalon? 3. What effects would you expect to follow an interruption of nervous influence in one of the nerves of the third pair ? 4. Describe the crystalline lens. What advantages follow from its not being of uniform density ? Compare its form in the young and in the old. 5. Enumerate the parts contained in the parotid gland, and give their relative positions. 6. Enumerate in order the tributaries of the inferior vena cava. 7. What are kreatine and kreatinine ? 8. The microscopic characters of cartilage, and of white and yellow fibrous tissue ? 9. Describe a Pacinian corpuscle. 10. Mention any osteological conditions characteristic of the mammalia. MATERIA MEDICA. DR. OSBORNE. 1. The difference between oil of turpentine and the other volatile oils ? 2. Why are the observations made on the medical properties of plants in the writings of Theophrastus, Dioscorides, and other ancient authors, for the most part of no value at the present time ?-and, on the contrary, how is the value of modern observations secured for the future? 3. What inconvenience might result from the following prescription :R Carb. Magnes. 3i. Sulphuris loti. M. 5. The difference between the effects of brandy and whiskey are well known and recognised ; how explained ? 6. It having been resolved on to use tobacco in a case of obstructed bowels in an adult, write a prescription in full to carry this resolution into effect. 7. What facts tend to prove that chlorine, although a deodorizer, yet is not a disinfectant? 8. All vegetable acids passing through the kidneys are changed into carbonic acid, with a few exceptions. What are the exceptions ? 9. Arrange the salts of the alkalies and alkaline earths used in medicine in the order of their solubility in water, prefixing a mark on those soluble in alcohol. 10. The test, antidote, and dose of sulphuric acid ? CHEMISTRY. DR. APJOHN. 1. In the manufacture of nitrate of silver, fine silver should be used; how is it obtained ? 2. How is ferri sulphus granulatum made, and why does its solution become black on adding to it a single drop of nitric acid, and lose its black colour with effervescence on adding an excess of the acid ? 3. Metallic iron may be at once converted into sesquichloride by aqua regia; what is the reaction which conducts to such a result ? 4. Assuming atmospheric air to consist of nitrogen, oxygen, carbonic acid, and aqueous vapour, how would you determine the amount of each of these constituents ? 5. Enumerate the chlorides mentioned in the Pharmacopoeia; write the formula of each; and indicate the process by which it is made. 6. Sulphate of quina may contain sulphate of cinchona, starch, sugar, salicine, or crystallized sulphate of lime; how would you detect these different impurities? 7. What solvent would you employ for the purpose of extracting strychnia from the contents of the stomach; and how would you prepare the residue left on evaporation for the application of the colour test? 8. Write the formula for ferrocyanide of potassium; enumerate the products which are formed when it is distilled with dilute sulphuric acid; and explain the reaction which it exerts on a persalt of iron. 9. What is Trommer's test, and to what purpose in animal chemistry is it applied ? 10. What is the rule for knowing the direction of the electric current in a voltaic machine, and what are the methods in use for measuring its intensity ? BOTANY. DR. HARVEY. 1. Describe the origin, usual structure, and appearance of wood-tissue, and the changes that take place in it as it advances to maturity. 2. Describe the processes of absorption, digestion, and assimilation, in plants. 3. Give examples of plants with valvate, induplicate, and contorted æstivation of sepals or petals, or both. 4. Define the terms, raphe, chalaza, micropile, primine, and secundine, as applied to ovule or seed. 5. Explain the inflorescence of Euphorbia. 6. Name and give the natural orders of the plants producing Tamarinds and Jujubes. 7. Distinguish Solanacee, on the one hand, from Convolvulacee, and on the other from Scrophularinee. 8. How are Loganiaceæ known from Cinchonaceæ ? 9. Name and describe in correct botanical terms the plant marked No. 1,-giving the several characters of its stem; leaves, their arrangement, stipulation, composition, form, cutting of margin, surface (whether glabrous, hairy, scabrous, tomentose, &c.), venation ; inflorescence; bracteæ; flower, its calyx, corolla, insertion of stamens; ovary, style, stigma. 10. Name, and describe similarly, No. 2. EXAMINATION FOR DEGREE OF MASTER IN SURGERY. DR. ADAMS 1. Give a description of the acute oedema of the larynx of Bayle and Cruveilhier. 2. Under what variety of circumstances does the disease suddenly supervene? 3. Supposing the disease fully established, and a paroxysm of dyspnoea to have occurred, what prognosis is to be formed ? 4. Supposing the necessity of making an artificial opening into the air passages in such a case is deemed indispensable, what operation, generally speaking, would you deem preferable ? 5. The surgical instruments and appliances you would have in readiness ? 6. From what injuries or from what surgical operations have you known, or read of, diffuse inflammation to have arisen ? 7. What is the nature of the fever which in general attends on a diffuse phlegmon or diffuse inflammation ? 8. What are usually the precursory symptoms of death when it occurs sult of diffuse inflammation and suppuration ? 9. When fatal phlebitis has occurred after amputation of the thigh, in what internal organs would you look for the anatomical characters of the disease ? 10. Suppose you are called to the case of a young soldier who had had as the |