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Enclosure. Extract from a letter from the War Office to the Colonial Office, dated 9th March, 1883.— "I am to observe that a communication has been received from the Civil Service Commissioners, from which it appears that, upon its being notified to them that a person residing in any of the more important distant colonies is desirous of passing in the colony the ' preliminary' examination for admission to Sandhurst, they will be prepared to forward to the Governor of the colony in question a sealed packet of examination-papers, accompanied by instructions as to the mode of conducting the examination ; or, should the demand for examination in the colony bo likely to be recurrent, they would be willing, for the purpose of avoiding delay, to supply the Governor with papers beforehand, to be used by him when the occasion should arise. This course will accordingly be adopted, in preference to the arrangement, originally proposed, of holding preliminary examinations in the colonies under the authority of chartered colonial Universities." No. 3. Downing Street, 9th April, 1883.—Sir, —With further reference to the despatch of the Officer Administering the Government of the 3rd of October, I have the honour to transmit to you, for communication to your Government, an extract of a letter which has been received from the War Office, in respect of the proposal of the authorities of the New Zealand University that students who had passed the first local examination for the degree of 8.A., and are candidates for admission into the army, should be placed on the same footing as graduates and students of the Imperial Universities. As regards the further point raised in the enclosure to the Administrator's despatch above referred to, you will observe, from another despatch of this day's date, that the arrangement under which the colonial Universities were empowered to conduct preliminary examinations for Sandhurst has been superseded by a system which will admit of more general application.—l have, &c., Deeby.—Governor Sir W. F. D. Jervois, G.C.M.G., C.8., &c. Enclosure. Extract from a letter from the War Office to the Colonial Office, dated 9th March, 1883.— " With reference to my letter of the Bth December last, and to the papers which you forwarded on the 22nd of the following month, relative to the curriculum at the New Zealand University, I have the honour to acquaint you, by direction of the Secretary of State for War, for the Earl of Derby's information, that, in the absence of any information as to the standard of attainment required in the several subjects comprising the first B.A. examination at the above University, it is impossible to decide whether the examination referred to can be accepted as equivalent to the examinations of the Home Universities, as set forth in paragraph 2 (b) of the Eegulations for Admission to the Eoyal Military College at Sandhurst." AEITHMETIC. 1. A man bought 184 shares at 15s. 6d.; sold 75 at 17s. 9d., and 40 at 19s. lid.; then came a fall, and he had to part with the remainder at lis. 6d.: how did he come out of the transaction ? 2. Extract the square root of (lH2 8+3 3+4 8+5 3+6 3+7 3+B:,+9 3). 3. Find (i+i+i-i) + of £556 10s. Ofd. 4. If the G.C.M. of two numbers be 5*7, and L.C.M. 68*4, find the two numbers. 5. Prove that every cipher added to the left of a decimal fraction reduces its value tenfold. Express £ and *-£ as decimals, and divide each result by 1,000. 6. Find the difference between simple and compound interest on £605 15s. 6d. at 6J per cent, in four years. 7. The number of children attending school in New Zealand was as follows :— Government Private Schools. Schools. 1871 ... ... ... ... ... 14,953 16,757 1881 ... ... ... ... ... 87,811 13,538 Find the increase and decrease per cent, in the two cases. 8. A sheet of glass is 3ft. 9in. long by 2ft. 7-Jin. wide : how much must be cut off the length so that it may cover a surface of one square yard ? 9. What is the difference between a banker's and the true present worth of a three months' bill for £75 10s. 6d., drawn on the 10th June and discounted the same day at 7-J per cent. ? 10. An average of 16,200 persons pass a certain corner every day between 8 a.m. and 6 p.m., and the average for the remainder of the time is 9 per minute. Every second person is a man, every fifth a woman, and the rest are girls and boys in the proportion of one of the former to two of the latter. How many of each pass between the Ist March and the 10th April, inclusive ? 11. What alteration would be made in a person's income by selling £4,500 out of the Three-per-cents at 98, and buying 5-per-cent. debentures at 102 ? GEOGEAPHY. 1. How do you account for the aurora australis, monsoons, Sargasso Sea, and icebergs? 2. By what different names are rotary storms known in different regions? Describe them. 3. Draw an outline map of the East Indian Archipelago, Australia, New Zealand, New Hebrides, New Caledonia, and Fiji Islands, so as to show their relative positions. 4. Where are the following, and for what are they noted: Agra, Boston, Chicago, Moscow,, Toulouse, Herzegovina,. Durban, and Meerut ? 5. Name the principal harbours of New Zealand, and state the distance by sea each is from the most central one. 6. Describe the distinctive animal and vegetable life of Australia.