Letheby finds, as the result of examination of dietaries, that an average adult loses during idleness 180 grains of nitrogen and 3816 grains of carbon; during routine work, about 300 grains of nitrogen and 5000 of carbon. One may regard the amount of nitrogen required as averaging 300 grains, and of carbon 4800 grains. It is found in accordance with this that an average adult doing moderate work requires 4 ozs. of nitrogenous food, 4 of fats, 144 of carbohydrates, I of salt; making a total of 22 ozs. (Moleschott). This is equivalent to a little over 40 ozs. of moist solid food. If we add 40 to 60 ozs. of water, we have a complete diet. Reckoned as grains, the proportion of nitrogen to carbon is as 1 to 16; while the proportion of nitrogenous food to carbonaceous (fatty and amyloid) is 1 to 4 or 6. The apparent discrepancy is owing to the fact that nitrogenous food contains a large proportion of carbon in addition to its nitrogen,

etc.

Given the number of grains of carbon and nitrogen required by each individual, and a table showing the number of grains of these elements in a given weight of any article of food, a dietary can at once be constructed. The inadvisability of limiting one's diet to a single article of diet will at once be seen, as no one food contains the elements required in the proper proportion. In order to obtain sufficient nourishment from any one food, an excess of either nitrogen or carbon must be taken. If an excess of nitrogen is taken (as in meat food), the nitrogenous material tends to accumulate in the system in an incompletely oxidised condition, producing gout; if an excess of carbon, its incomplete oxidisation leads to corpulence.

Thus if one subsisted on beef alone, 2 lbs. would be required to furnish enough carbon, and there would be a considerable surplus of nitrogen. If one subsisted on bread alone, to obtain 300 grains of nitrogen, 3 lbs. would be required, and this would give a large excess of carbon. If one lived on eggs alone, which average 1 ozs. in weight, and yield nearly 18 grains of nitrogen, in order to obtain 300 grains of nitrogen, over 16 eggs would have to be eaten. The economy and advisability of a mixed diet will be obvious from these instances.

(1) 9 ac. 3 rd. 26 po. at £22 10s. per acre. Ans. £223 os. 7 d. (2) How many yds. would cost £68 17s. 6d. if 25 yds. cost £9 8s. 74d.?

211 Ans. 182 yds. 2 qr. 1 nl.

yds. at 7s. 6d. per doz. yds.

2

articles at 16s. 6d. each.

(1) Int. on £438 from June 1st to September 13th, at 3 per cent. per annum.

(2) Simplify

30'12 x .005.

'0006

Ans. £4 7s. 4 d. 759.

(4) If 6 men reap 4'5 acres in 375 days, in how many days will 9 men reap 22.5 acres?

Ans. 12 days.

(5) A garrison of 5000 soldiers has provisions for 3 months, how many must be sent away, so as to last 8 months? Ans. 3125 men.

Matriculation Hints.

BY HENRY A. REATCHLOUS, M.A. (LOND.), B.Sc.,

Westminster Training College.

THE passages of Greek and Latin set from books not previously mentioned at the examination just concluded are given in another part of this number of the PRACTICAL TEACHER. A translation of them will appear next month.

French.-All who read these notes have no doubt made some progress in French. We need not therefore give directions to beginners. It may fairly be said that French is at the same time both easy and difficult. It is a language of which most people know a little, and few very much. Anything like sound instruction in French is very hard to get anywhere. In most cases the pupil must become tutor and use his French-master to give him the pronunciation of the words and the correct rendering of the sentences. The matter of pronunciation may seem of no importance with a view to a written examination. This is not so. It very much assists the memory to repeat aloud as well as read and write the grammatical forms and the examples to the rules of syntax; and without some knowledge of the sounds the student will rarely read aloud. A knowledge of French is becoming of more and more importance, both for pleasure and profit. In most cases it will not be taken up specially with a view to pass the examination. The student will not begrudge the time he spends upon it, nor be always on the look-out lest he should do too much. And let it be added his chances of success will be very much increased thereby; for it is not easy to say exactly how little will just secure a pass, and we would recommend nobody to try to find out for himself.

The student who tries to exercise his own judgment as to the books he will use and the methods he will adopt is sure to be struck and possibly confused by the disagreement of his guides. And this confusion will be all the greater if he fails to recognise that they are not all aiming at the same result. With some the ability to understand a few simple sentences and to reply to them is considered to be of more importance than being able to translate correctly a page of Molière. At that rate an English child of eight may be said to know English better than the foreigner who is able to understand the masterpieces of our language, but not able to converse fluently in it. And there can be no doubt that if conversational fluency is all that is required, our ordinary methods might be revolutionised with advantage. In order to acquire rapidly, and know perfectly the comparatively few things that would be necessary, we might be content to remain in ignorance of the thousand useless details that now fill the grammars and dismay the pupils: But with many the power to read and write French is of more importance than the ability to converse in it, and our methods must vary accordingly. While the requirements of examiners should not be too carefully studied, they should not be entirely disregarded, Most of us in this much-examined nation are at the present time, to some extent at least, servi servorum, the slaves of examiners who are not free themselves.

The examination in French consists of three passages of French, two of which have to be translated

into English. There are also grammatical questions mostly restricted to the accidence upon the passages. There is no one book that can be recommended as much better than many others. When some such work as Smith's French Principia,' Pt. I., or Fasnacht's Progressive Course,' Pts. I. and II., has been mastered, reading should be pursued with vigour. Smith's Principia,' Pt. II., has an excellent vocabulary clearly printed. The extracts are followed by useful questions, which should be studied. Private students would do well to procure the answers from the publishers. Another reading-book containing similar extracts, but without questions or vocabulary, is the 'Modern French Reader,' published by Trubner, 2s. 6d. If the student gets tired of short pieces, he may try the selection from About's works, published by Hachette, 25. 'First Lessons in French,' by H. C. Bowen, Is.; and Prendergast's French in the Mastery Series, 2s., are both useful, and without taking too much notice of the directions at the beginning, which are impracticable for nine persons out of ten, students would learn from these two books what they will most likely not get elsewhere.

A few good grammars deserve notice: we call attention to Eve and Baudiss's, Fasnacht's 'Synthetic Grammar,' and Brachet's 'Historical Grammar.' Contanseau's Dictionary is clearly printed and quite full enough for ordinary purposes, so is Cassell's: Spier's, in two volumes, Littré's 'Abridgment,' and the 'Pocket Dictionary,' by John Bellows, are books which should be remembered and examined when opportunity serves. The student can then judge which will suit him best.

Natural Philosophy. - The student is recommended to get a balance and a set of weights; most likely he can have access to them without buying; no large school should now be without them. Good work can be done with inexpensive apparatus. The main point in a balance is its sensibility, i.e., its readiness to turn upon the addition of a very small weight. To secure this there should be little friction, and the beams should be as long and light as is consistent with their remaining rigid when carrying the heaviest weights they are intended for. The arms should be of exactly the same length. We can see at once if they are so by putting two equal weights into the two pans. If one arm is longer than the other, the pan which is attached to it would descend.

The student is no doubt aware that if the arms were of unequal length, he could still obtain the true weight of a body by weighing it first in one scale and then in the other, and taking for the true weight the square root of the product of the two apparent weights. A better method is to put the body to be weighed in one scale pan, and counterpoise it with white sand, then remove the body and put weights to counterpoise the sand. These give the weight of the body.

This is called Double Weighing, and is a very accurate method.

Let now a considerable number of objects be weighed for practice, such as coins, pieces of metal, glass, and stone. Weigh a bottle when empty, and again when full; the difference will give the weight of the liquid in grammes, and then, such is the simplicity of the metric system, we can state at once the capacity of the bottle, because a cubic centimetre

of water weighs a gramme. Now attach a fine wire to one arm of the balance, and fix on the other end of it a piece of metal. Weigh the metal in air first, afterwards weigh it when it hangs in the water; notice the loss of weight. This loss of weight in grammes gives us the volume of the body weighed in cubic centimetres. Conversely take a body that can be easily measured, and find its volume in cubic centimetres, then weigh it successively in air and water; it will be found to lose as many grammes in weight as it occupies cubic centimetres in volume. This is a verification of the law of Archimedes, that bodies immersed in water lose a part of their weight which is exactly equivalent to the weight of the volume of water they displace. If we know the weight of a body when weighed in water, and also the volume of the fluid which it displaced, we can calculate its weight in air by adding on the weight of the water displaced. We shall return to this subject when dealing with specific gravity. Meantime, it would be well to notice the effect on the weight of the body immersed if a considerable amount of salt be put into the water; and if the balance is sufficiently sensitive, the effect of substituting very hot for very cold water. Water is densest at 4°C., and if we call its density unity at 4°C., at 10° it is '99974; at 15°, '99915; and at 20°, '99827.

It will, no doubt, have occurred that if a body. weighed in water loses a part of its weight, equal to the weight of the fluid displaced, bodies weighed in air do the same, and it is so. And when we remember that a litre of air at standard temperature and pressure weighs 1.3 gm., which is the same as saying that a cubic foot weighs 13 oz., it will be seen that it is too much to be neglected where the greatest accuracy is required. As the weight of a litre of air will depend on the temperature and pressure, and also upon the amount of moisture in the air, it is necessary to read the thermometer and barometer, and find the dewpoint in the room when such delicate experiments are made. For example, suppose a body weighs 50 gms. in air, we must find the volume of the body, and then the weight of the same volume of the air in which the body was weighed let this be 05 gm. Again, suppose the volume of the air displaced by the weights used weighs or gm., then the true weight of the body in vacuo would be 50+05-01=50'04 gm. Corrections for the weight of air displaced are often unnecessary, but questions are occasionally set which imply a knowledge of them.

In studying the laws of falling bodies, an Attwood's machine is most helpful. The only essential part is a grooved wheel, turning with as little friction as possible. This is usually accomplished by letting the axle lie on the circumference of the other wheels. A watchmaker will generally supply the wheels, and help to fit them up. We advise the student to make a machine for himself. He will be amply rewarded for his labour.

(To be continued.)

UNIVERSITY OF ST. ANDREWS. L.L.A. EXAMINATIONS, 1884.-The results of the above examination have just been issued, from which it appears that 363 candidates entered for examination in twenty different subjects, and that of these eighty-one passed in the requisite number of subjects to enable them to obtain the title of L.L.A.