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* Army Medical Reports. Reports on Hygiene.

Reports on Hygiene. Eyre and Spottiswoode. *Reports to Privy Council and Local Government Board by their Medical Officer.

Eyre and Spottiswoode.

On Chemistry. General principles.

Fownes' Manual of Chemistry. Churchill.
Bloxam's Chemistry. Churchill.
Roscoe's Lessons in Elementary Chemistry. Macmillan.
Attfield's Chemistry. Van Voorst.

On Analysis.

Bloxam's Laboratory Teaching. Churchill.
Bowman's Practical Chemistry. Churchill. .
Sutton's Systematic Handbook of Volumetric Analysis. Churchill.
Frankland's Water Analysis for Sanitary purposes. Van Voorst.
Wanklyn and Chapman's Water Analysis. Trübner.
Hartley's Air and its Relations to Life. Longmans.
Wanklyn's Milk Analysis. Trübner.
Wanklyn and Cooper's Bread Analysis. Trübner.
Fox, C. Sanitary Examinations of Water, Air and Food. Churchill.

On Physics.

Todhunter's Natural Philosophy for Beginners. Macmillan.
Ganot's Physics. Longmans.
Everett's Textbook of Physics. Blackie.

On Microscopy.

Carpenter's The Microscope and its Revelations. Churchill.
Macdonald's Guide to Microscopical Examination of Drinking Water. Churchill.
*Hassall's Food and its Adulterations. Longmans.

On Sanitary Engineering, Water Supply, Sewage, &c.

Eassie's Sanitary Arrangement for Dwellings. Smith, Elder and Co.
Galton's Healthy Dwellings. Macmillan. .
Corfield's Dwelling Houses, their Sanitary Construction and Arrangement. Lewis.
* Bailey-Depton, Sanitary Engineering. Spon.
*Latham's Sanitary Engineering. Spon.
* Bayles' House drainage and water service. Williams, New York.
Tomlinson's Warming and Ventilation. Lockwood.
Corfield's Treatment and Utilization of Sewage. Macmillan.
*Report of Committee appointed by President of Local Government Board on modes

of treating Town Sewage. Eyre and Spottiswoode. .
* Reports of Royal Commission on Pollution of Rivers, especially the 6th on Do-

mestic Water Supply. Eyre and Spottiswoode.
* Report from Select Committee on Public Health Act (1875) Amendment Bill, with

the Evidence. Eyre and Spottiswoode.
*R. Angus Smith's Air and Rain. Longmans.
*Ure's Dictionary of Arts, Manufactures and Mines. Longmans.

On the Laws of the Realm and Bye-laws relating to Public Health.
For England :
Public Health Act, 1875, and the Acts of Parliament relating to the various sub-

ject-matters within the domain of Hygiene passed since that date. Artisans' and Labourers' Dwellings Acts.

Vaccination Acts, For the Metropolis, or for Scotland, or for Ireland : Laws dealing with the same subject-matters as the above, and having application

to the particular part of the United Kingdom. Model Bye-laws of the Local Government Board. Eyre and Spottiswoode. Adulteration of Food and Drugs Acts.

On Statistics.

Lewis's Digest of the English Census. Stanford. The article on ‘Statistics in the Cyclopædia of Anatomy and Physiology. Longmans. *Dr Farr's letters to the Registrar-General in the early Reports of the Registrar

General. *Reports of the Registrar-General. Eyre and Spottiswoode. * Deaths in England. Average Annual Proportion of Deaths, &c. 1861—70. Parliamentary Paper C. 874 Session 1873. Eyre and Spottiswoode; and may

be had also of Hansard, or of King, King St., Westminster. On construction of Hospitals.

Miss Nightingale's Notes on Hospitals. Longmans.
Oppert's Hospitals, Infirmaries and Dispensaries, their construction, interior arrange-

ment and management. Churchill.
Galton, On the construction of Hospitals. Macmillan. .
Burdett, Cottage Hospitals. Churchill.
*De Chaumont. Hospitals in the Encyclopædia Britannica, last edition.

* The books thus marked are books of reference.

The Examination Papers set at former examinations can be obtained at the Cambridge

Warehouse, Ave Maria Lane, London, price 1s. each set, or by post ls. 2d.

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FRIDAY, October 3, 1884. 1–31.
ALGEBRA (ADDITIONAL).

(A) 1. DEFINE an arithmetical progression, and find an expression for the nth term in terms of the first term and common difference.

Find the 15th term of an arithmetical progression whose 8th and 12th terms are respectively 17 and 25.

2. Find an expression for the sum of an arithmetical progression of n terms.

Find the sum of the arithmetical progression of 2m terms of which the two middle terms are a b, and a + b.

3. Find the sum of a geometrical progression of n terms in terms of the 1st term and the common ratio.

The third and fifth terms of a geometrical progression are respectively 12 and 48. Find the sums of eight terms of the two progressions which satisfy the conditions. 4. Sum the following series

(1) 18 + 15 + 12 + ... to 13 terms,
(2) (2n – 1) + (2n – 3) + (2n – 5) + ... to n terms,
(3) +1+3+... to 6 terms,

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(4) 10+ 5 + 2 + ... to infinity. 5. If a+b+c= 0, prove that

+ + 8 +3 (a + b)(b + c)(c + a) = 0, and

co (a - b) + (b c) + b3 (c-a)=0. 6. Divide £1230 among three persons, so that if their shares be diminished by £5, £10 and £15 respectively, the remainders shall be in the ratios 3 : 4 : 5.

7. Find the two times between 3 and 4 o'clock when the hands of a watch are separated by 4 minute spaces, and the interval between each of these times and the time when the hands are together. 8. Define a logarithm, and prove that

(1) log, mn=loga m + logan,

(2) log, b.log, a=1. Shew how to reduce a system of logarithms to the base 10, to a system to the base 100.

9. Define the characteristic and the mantissa of a logarithm.

Find the characteristic of the logarithm of 500, to the base 3 and to the base ), and the logarithm of .001 to the base 10.

10. Having given logi, 3 = .4771213, find how many figures there are in 3100, and in the integral part of (3.1). 11. Find the fifth root of 5:4, having given

= '4771213, log 5 = 6989700, log 14011= 4:1464691, log 14012= 4:1465001.

001

10
100

log 3

=

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ALGEBRA (ADDITIONAL).

(B) 1. FIND an expression for the general term of an arithmetical progression, in terms of the first term and the common difference.

Find the 18th term of an arithmetical progression, whose 6th and 13th terms are respectively 22 and 43.

2. Investigate an expression for the sum of a series of n terms in arithmetical progression.

If the sum of the arithmetical progression, 18, 15, 12, &c. be 45, find the number of terms, and explain the double answer.

3. Define a geometrical progression, and find the sum of a series of n terms in geometrical progression.

Prove that in a geometrical series of an odd number of terms, the middle term is a geometric mean between the first and last terms.

4. Sum the following series

(1) 17 + 15 +13 +... to 18 terms,
(2) 1+3+5 + ... to n terms,
(3) { +1++ ... to 5 terms,

+1*
(4) 6+ 2 + f +... to infinity.
5. If a +b+c= 0, prove that

ab (a + b) + bc (b+c) +ca (c + a) + 3abc = 0, and

(b c) + 18 (c-a) + c (a - b) = 0. 6. Divide £900 between three persons, so that if their shares be increased by £10, £15 and £20 respectively, the sums shall be in the ratios 4 : 5 : 6.

7. Find the two times between 5 and 6 o'clock, when the hands of a watch are separated by 14 minute spaces and the interval between each of these times and the time when the hands are together.

8. Define a logarithm, and prove that

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(2) log. N =

log, N
log, bo

*0001

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Shew how to reduce a system of logarithms to the base 10, to a system to the base 1000.

9. Define the characteristic and mantissa of a logarithm. Find the characteristic of log, 350, and of log;063, and the logarithm of 0001 to the base 10.

10. Having given log,, 2 = '3010300, log, 3 = 4771213, find how many figures there are in 5100 and in the integral part of (54)).

11. Find the cube root of 14:4, having given in addition to the legarithms in the preceding question

log 24328 = 4:3861064,
log 24329 = 4.3861243.

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1. · Define the unit of circular measure of an angle.

If one quarter of a right angle were taken as the unit, what would be the measure of an angle of 15', and of the unit of circular measure ?

2. Define the sine and tangent of an angle; and find expressions for each in terms of the other.

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5 5. Three angles are in Arithmetical Progression, the common difference being 60°. Prove that the product of their tangents is equal to the tangent of their sum with its sign changed.

6. Prove that 2 sin A= † 1 + sin 2A + VI - sin 2 A, and determine the proper signs for the roots when A = 1880°. 7. Prove that in any triangle

sin A sin B sin C

b

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A (s b) (s —c) 8. Prove that

sin

sc) 2

bc Hence find the sines of the angles of a triangle whose sides are 7, 8 and 9 feet long 9. In a triangle b = 32, c= 40, B= 52° 32' 15"; find A and C, having given

L sin 52° 32' = 9.8996604, diff. for l' = 968,
L sin 82° 50' = 9.9965937, diff. for 1' = 159,

log 2 = -30103C0.

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