account: hence two volumes of N,O,two volumes of nitrogen; but this is found not to be the case, for upon removing the finger, the mercury rises in the bent tube exactly one-half the volume occupied by the gas. Therefore the formula for nitric oxide must be NO, and not N,O,:

:

NON +0. 2=1+;

The gas must either be collected over mercury or by displacement, as in the case of hydrogen (Fig. 23), as it is one-half as heavy as air. Its specific gravity is 0·59, and it possesses the well-known pungent odour of "smelling salts."

When breathed it has a violent irritating power on the pulmonary passages. It is a powerful base, neutralises the strongest acids, and returns the colour to litmus paper reddened

This gas has not yet been liquefied.

Nitric trioxide, or nitrous acid (N,O,; combining weight, 76; density, 38). This gas is noted for its deep-red colour. The most ready method of preparing it is by heating in a capacious retort 1 part of starch with 8 of nitric acid. The gas liberated is almost pure N2O3.

It forms compounds called nitrites. A very minute trace of any nitrite may be detected by mixing a dilute solution of potassium iodide with starch and a little dilute hydrochloric acid. Render the liquid to be tested also acid with hydrochloric acid; then mix the two liquids; if any nitrite be present, the liquid will become blue. These salts may frequently be detected in the well-water of towns.

When this gas is reduced to a temperature of -18° Cent., the red fumes become a dark-blue liquid. When added to water, it is at once decomposed into nitric oxide and nitric acid, thus :3N,O,+H,O=2HNO, + 4NO.

Nitric tetroxide, or nitric peroxide (NO,; combining weight, 46; density, 23). The reddish-brown fumes which appear when nitric oxide meets with oxygen are chiefly of this substance. It is best prepared by heating lead nitrate in a small glass retort. The fumes which are given off are a mixture of peroxide of nitrogen and free oxygen; if they are conducted through a bent tube which is surrounded by ice and salt, the peroxide becomes condensed into a liquid. The reaction is thus expressed:

Amidogen (NH) is not known in a separate state, but it is believed to exist as a constituent of numerous compounds which chiefly belong to organic chemistry, and are termed amides. Ammonia (NH,; combining weight, 17; density, 8.5).-This compound receives its name from the fact that it was first prepared from the dung of the camels which the Arabs collected at the temple of Jupiter Ammon, the halting-place before the journey of the desert of Libya was undertaken. Nitrogen and hydrogen do not combine directly with each other, but it seems whenever they are liberated together by the decomposition of any compound containing them, they unite to form ammonia, and it appears frequently to be formed when hydrogen, in its nascent state-that is, just liberated from its combination— meets with nitrogen of the air. Thus, if iron filings be moistened and exposed to the air they become oxidised, partly at the expense of the oxygen of the water; and the hydrogen as it is liberated forms, with the nitrogen, ammonia, which is found in the compound. This is also exhibited when tin, zinc, iron, and some other metals are acted on by dilute nitric acid, thus:

9HNO, + 4Zn = 4(Zn2NO ̧) + 3H ̧0+ NH ̧.

The whole action is not expressed by this formula-for the water which dilutes the acid is decomposed-and the equation may be rectified by using the liberated constituents of the water. Any organic bodies which contain nitrogen when distilled in a closed vessel give off ammonia. Formerly this method was resorted to for its production from horn clippings, hence its name -spirits of hartshorn. It is now obtained from the refuse products of the distillation of coal in the manufacture of gas. For the laboratory it may be prepared by gently heating equal weights of quick-lime (oxide of calcium), made into a paste with water and sal-ammoniac, which is ammonium chloride. CaO+?NH,C1=CaC1, + 3H,0 +2NH.

It is very soluble in water. The liquid at 0° Cent. and 760 mm. pressure is capable of absorbing 1149 times its volume. If a jar of the gas be held with its mouth downwards to the surface of water, the water will rush into the jar as into a vacuum, and unless the glass be strong the jar will probably break.

When water containing ammonia is heated, the gas is given off, so that at 20° Cent. only half the quantity of gas is retained which the water possessed at 0° Cent.

When submitted to a pressure of 7 atmospheres at the ordinary temperature of the air, the gas becomes a liquid, which boils at -38.5° Cent., and freezes into a transparent solid at -175° Cent.

This fact has been advantageously applied by M. Carré to freeze water. A saturated solution of ammonia is placed in a strong iron vessel, which is connected by a pipe with a "receiver," which is a cavity in the thick wall of a cylindrical vessel. When heat is applied to the liquor ammonia, the gas is given off in large quantities; but not being able to escape, it finds itself under great pressure, and begins to condense into a liquid in the receiver. The interior of the cylindrical vessel is filled with water, the heat is now removed from the other vessel, and the temperature of the water it contains is reduced by pouring cold water over it. But this renders the water it contains capable of absorbing the gas again, and therefore the liquefied gas in the "receiver" begins to evaporate rapidly; this, however, it cannot do, without absorbing a large quantity of latent heat, and hence the water which the "receiver" surrounds freezes.

Ammonium (NH).-Place a globule of mercury in a cavity in a piece of sal-ammoniac, and moisten it with liquor ammonia; then if the positive wire of a battery be attached to the salt, and the mercury be touched with the negative, the globule will swell and assume all the appearance of an amalgam. When the current is suspended, the mercury returns to its ordinary state, giving off ammonia and hydrogen.

There is only one way of accounting for this, namely, that sal-ammoniac is a chloride of a metal (NH,Cl), and that in the ordinary way electrolysis took place the metal combining with the mercury formed an amalgam. But this compound only having permanence under the influence of the current, decomposes when the current is interrupted.

Nessler's test discovers the most minute quantity of ammonia. Saturate the solution supposed to contain ammonia with potash, then add potassic iodide saturated with mercuric iodide. If any ammonia be present, a "brick-dust" precipitate will appear.

The composition of ammonia is discovered by leading the gas through a red-hot porcelain tube, or by passing a series of electric sparks. Either of these methods resolves the compound into its components, which are found to occupy double the volume of the gas, as might be expected from this equation, which has been previously alluded to:NH.=N+3H 2 = 1 + 3;

that is, two volumes of NH, become, when decomposed, four volumes of the mixed gases.

LESSONS IN GREEK.-X.

THE THIRD DECLENSION (continued). THERE is yet another class in the subdivision of nouns whose nominatives append s to the stem (see page 258), of which the stem ends in v or vт. As examples, take ʼn pis, pir-os, the nose; δ δελφις, δελφιν-ος, a dolphin; ὁ γιγας, γιγαντ-os, a giant; & odovs, odovт-os, a tooth (Latin, dens, English, dentist).

could not fail deeply to impress a young painter of such plastic gifts, already emancipated by his Florentine career, and ready to proceed further in the same direction whenever opportunity offered. Raffael set to work at Rome to infuse modern art with some of the old Greek lightness and grace. The product was seen in what is known as his third, or Roman style, which differs from the Florentine in its individuality and its great combination of various excellences. No longer content with following his masters, Raffael began, in his celebrated fresco of "Philosophy, or the School of Athens," to invent a new style for himself. If we compare the freedom of the figures, the naturalness of the grouping, the depth and mastery of the perspective, and the admirable power of true and noble expression displayed in this magnificent work, with any previous masterpiece of art-even with Lionardo himself-we can see at once

therefore difficult to decide in some cases which are really his own works. But of his undoubted compositions there are quite enough to fill up the limits of a short and marvellously industrious life. In the first, or Peruginesque style, the " Marriage of the Virgin," at Milan, is the most familiar from numerous engravings, and best represents the comparative conventionality and stiffness of his boyish works, though even here it is possible to see in the germ those higher qualities which afterwards developed themselves under more favourable circumstances. Of his Florentine period, when his genius began first to allow itself somewhat freer play, we have an excellent example in the "St. Catherine" of our own National Gallery; while the "Madonna," or Virgin under a canopy, of the Pitti Palace at Florence may be taken as the best Italian specimen. "The School of Athens," of which we give an engraving, opened his

what is the nature of that supreme excellence which has made Raffael the greatest name among the whole roll of modern painters. Whether we look at the conception itself, in its totality and in its detail, or at the technical mastery with which it is expressed-whether at the glorious realisation of a grand philosophic epoch and of noble intellectual personalities, or at the harmony of its arrangement and the perfection of its design, or at the natural anatomical pose of the figures, or at the drapery, the management of light, and the perspective, or at the beauty and delicacy of the colouring, or at the power and truth of the touch-we must acknowledge alike in every particular both the highest command of hand and muscle, and the informing soul blended into a whole by the subtlest interfusion of mental gifts and manual ability.

At Rome, Raffael became the founder of a school, whose works cannot always be absolutely distinguished from his own, while many of them must have been executed under his eye, or even have received numerous touches from his hand. The bestknown among his scholars are Giulio Romano and Caravaggio. Not a few pictures by other artists have also been attributed to so famous a painter either fraudulently or ignorantly, and it is

third manner, and still necessarily remains upon the walls of the Vatican, together with the other magnificent series of frescoes of which it forms a part; not all of them, however, are entirely due to the pencil of the master himself. Perhaps his two most famous works are the oil-paintings of "St. Cecilia," at Bologna, and the "Madonna di San Sisto," in the gallery at Dresden. Equally exquisite in tenderness of feeling and in beauty of rendering are the well-known "Virgin and Child" and the "Madonna Ansidei" in our own National Gallery. But the "Transfiguration," his last work, familiar to almost every one by engravings, is often considered to be the noblest production of his genius in its more sublime and spiritual mood.

One of the best examples of Raffael's style which can be seen in England is that displayed by the seven cartoons, which were long placed upon the walls of Hampton Court Palace, but now form a part of the great national treasure at South Kensington. These cartoons are not paintings in any of the recognised methods, but are large coloured designs for the tapestry of the Sistine Chapel at Rome, and they are executed in the large and free style which suits that kind of wall-decoration. Sent to Flanders as models for the tapestry-workers, they were pur

chased by Charles I., and have ever since remained in England. Though they lack, of course, the finer touches of Raffael's finished works, they yet exhibit very well the main broad features of his style; though it is to be feared that a misapprehension of their true object and nature has often led hasty observers to misunderstand the character of Raffael's paintings. Those who have the opportunity should not fail to correct their impressions derived from these large and free designs by a study of the few other works by Raffael which may be seen in the National Gallery.

Nor must we omit to mention that Raffael, like most of the other great men of the Italian Renaissance, did not confine his attention to painting alone. As an architect, he had for a time direction of the building of St. Peter's, at Rome, that vast embodiment of the Renaissance ideas round which all the artistic work of the period centres. When we consider that he died just as he had completed his thirty-seventh year, an age at which men are now considered almost as still beginners, we can estimate once more the greatness of this great artistic epoch, which could number as contemporaries three such men as Raffael, Michel Angelo, and Lionardo.

The position which Raffael has obtained in the history of art is twofold. In the first place, his is one of the great epochmaking names, at least as great in this respect as Phidias in Greek or as Giotto in early Italian art. He forms, as it were, the boundary figure between medievalism and the modern European school. All before him we still describe as preRaffaelite, all after him seems to us purely of our own type in art. It is true, the world might in some respects with greater justice have pitched upon Lionardo as forming the first among the strictly modern painters, but the fame of the younger artist has not unnaturally eclipsed that of the elder, partly because we have more of Raffael's pictures still existing than of Lionardo's, and partly because Raffael made a real and great advance even upon the manner of his vigorous predecessor. Mankind generally love to seize upon a single personage as the central figure to symbolise and sum up a movement or an epoch, and their instinct has rightly caused them to single out the personality of Raffael as such a central figure for the whole grand artistic movement of the Italian Renaissance. But besides all this, in the second place, even apart from his historical importance in the development of art, Raffael stands out also as the greatest name in all the annals of art on the strength of his actual performances taken by themselves. He ranks first by the same sort of general consent as that by which Shakespeare ranks first among poets, or Newton among scientific thinkers. There may be many, whose opinions are entitled to the highest respect, who would place Raffael second to some other favourite painter, but almost all would place him second to one alone. And as in the old Greek story, Themistocles was adjudged by all alike the second place, while many others were adjudged the first, we may take this general consent of opinion as justly entitling Raffael to rank at the head of all the artistic roll. In his union of every high quality of technical execution and of vivid conception, in his admirably harmonious combination of all those qualities in mind, hand, and eye, which go to make up the perfect artist, he has never been equalled. Art, of course, has learned some new lessons since his time, especially in technique, but no subsequent painter has possessed such a grandly. tempered union of all the chief artistic gifts as that which distinguished Raffael. It is his breadth of grasp even more than nis subtle sweetness that has given him his unique power of extorting our admiration and our applause throughout so many

centuries.

LESSONS IN ARITHMETIC.-XXXII.

RULE OF THREE-SINGLE AND DOUBLE.

1. THIS is a name given to the application of the principles of Simple Proportion to concrete quantities. We have shown (Art. 5, Lesson XX., Vol. I., page 343) that if any three numbers be given, a fourth can always be found such that the four numbers shall be proportionals. Hence, if three concrete quantities be given, two of which are of the same kind, and the third of another kind, a fourth quantity of the same kind as the third can be found such that it shall bear the same ratio to the third quantity as the first two bear to each other;

or, what is the same thing, so that the four quantities shall be proportionals.

It is evident, since a concrete quantity can only be compared with another of the same kind (Obs. 11, Lesson XXVII., Vol. II., page 102), that the fourth quantity determined must be of the same kind as the third quantity. In order that the ratios of the two pairs of quantities may be equal, either two must be of one kind and two of another, or all four must be of the same kind.

2. Suppose we have the following question proposed :EXAMPLE. If the rent of 40 acres of land be £95, what will be the rent of 37 acres?

It is evident that the sum required must bear the same ratio to £95 that 37 acres do to 40 acres.

Hence we have, writing the ratios in the form of fractions, Sum required. 37 acres the abstract number £95 40 acres

=

37 40.

Therefore the sum required 2x £95, which can be reduced to pounds, shillings, and pence.

3. The last question might also have been solved thus :Since 40 acres cost £95,

40: 37: £95 : sum required. Then, by equating the product of the extremes and means, we get the result. We have put the first example, however, in the fractional form, in order to indicate clearly the fact that the ratio of the two quantities of the same kind (acres in this case) is an abstract number, by which the other quantity, the £95, is multiplied. When we state the question in the second way, and talk about multiplying the means and extremes together, some ccnfusion might arise from the idea of multiplying 37 acres by £95. The fact to be borne in mind is that the rule is merely the expression of the fact that the ratios of two pairs of quantities are equal.

5. The example we have given is what is called a case of direct Proportion-that is to say, if one quantity were increased, the corresponding quantity of the other kind would be increased. Thus, if the number of acres were increased, the number of pounds they cost would be increased.

If, however, the case be such that, as one of these corresponding quantities be increased, the other is proportionally diminished, the case is one of what is called Inverse Proportion. For instance :

EXAMPLE. If 35 men eat a certain quantity of bread in 20 days, how long will it take 50 men to eat it?

Here, evidently, the more men there are, the less time will they take to eat the bread; hence, as the number of men increases, the corresponding quantity of the other kind-viz., the number of days-decreases.

Hence, since 50 men are more than 35 men, the required number of days will be fewer than the 20 days which correspond to the 35 men.

In stating the proportion, therefore, in order to make the ratios equal, if we place the larger of the two terms of one ratio in the first place, we must place the larger of the two terms of the other ratio in the third place.

Thus, placing 50 men in the first place, we must put 20 days (which, we can see, will be larger than the required answer) in the third place, and then the statement would be correctly made thus:

50: 35 :: 20 days : required number of days. Therefore the required number of days =20 × days = 14 days. N.B. We might reduce the example to a case of Direct more clearly :Proportion thus, which will, perhaps, explain the above method of the bread in one day.

35 men eat 50 39

required number of days the number of men, we have— Hence, since the quantity eaten in one day will increase with

As 35 : 50 :: 0 : Therefore required time

1

required number of days; 20 x 18 14 days, as before.