same straight line.

This question might easily be solved by the more usual method of applying coordinate Geometry. But the brevity and directness of the above solution are sufficient to recommend it to the favourable notice of our readers; for it will be observed that only three or four lines of actual calculation are necessary.

22. As 25 per cent. is gained on the outlay by selling the spirit at 12s. 6d. a gallon, it follows that the cost price of a gallon of the mixture is 10g or t of 12s. 6d., which is 10s.

Now, by the sale of 84 gallons, of which the cost price is 13s. 6d. a gallon, at 10s., 84 times 3s. 6d., or 294 shillings, are lost.

And 6d. a gallon is gained by selling the added spirit at 10s. Consequently, in order to gain 294 shillings, which are lost by the sale of the other, 2 x 294, or 588 gallons of the inferior must have been sold.

The added spirit, therefore, amounted to 588 gallons in 672. Hence, by the common Rule of Three, we may determine the amount per cent.

QUESTIONS FOR SOLUTION.

29. Through any point, A, in the diameter BAC of a circle, a chord GAE is drawn, cutting the circumference in the points G and E. The points B and G are joined, and EH is drawn parallel to BG, cutting the diameter BAC (or BAC produced) in H. Prove that AE is a mean proportional between the lines AC, AH.

30. Without assuming any geometrical propositions beyond those contained in the 1st Book of the Elements of Euclid, prove that in any right-angled triangle the equilateral triangle described on the side subtending the right angle is equal to the equilateral triangles described on the sides containing the right angle.

151-Pronunciation. Orion. B.-The accent falls apon the second syllable, making the i long as in fireO-ry-on.

152-History of England. B. T. A.-The Historic Tales will be continued in a regular series, to illustrate and teach the annals of the United Kingdom."

153-Byron. W. B.-Lord Byron, the poet, was born in Holles Street, London, on the 22nd of January, 1788. He was a student at Cambridge in 1811.

154-Grammatical. J. B.-In alluding to a conversation which has taken place, it is incorrect to use the term "He says," or "says he." It should be "He said," or "said he."

155-Iron. C. E. E.-The mean ultimate resistance of wrought iron to a force of compression, as useful in practice, is twelve tons to the square inch; while the crushing weight of cast-iron is forty-nine tons per square inch.

156-English Composition. J. J.-Booth's Principles of English Composition, or Reid's Progressive Exercises, are useful little books; but to pupils earnestly desiring to attain elegance of style, perspicuity, and beauty of diction, we should recommend Blair's Lectures on Rhetoric and Belles Lettres.

157-Comparative Grammar. W. P.-The only work of the kind which we can remember, is Franz Bopp's Comparative Grammar of the Sanscrit, Zend, Greek, Latin, Lithuanian, Gothic, German, and Sclavonic Languages; translated from the German by Lieutenant Eastwick. Two vols., published in 1845.

158-Anglo-Saxon Poem. O. B. S.-In three editions, bearing date 1524, 1548, and 1563, the Lay of the Phoenix was attached to the works of Lactantius. The authorship has been given to Venantius Fortunatus, but Sirmondus declares it to be the production of Theodulphus, Bishop of Orleans. It is written in elegiac metre.

159-Reduction of Metals. M. T.-It is stated that a French chemist has succeeded in reducing to the metallic state, by exceedingly simple means, several bodies which hitherto have not been seen in that condition. Some of these are expected to replace platinum in many of its applications. The reduction of silica to the metallic condition is said to be beautifully perfect.

160-Lime. N. N.-It is stated that lime has been found in a pure state, at Applecross, on the west coast of Scotland. A large mountain, called " Tore illore," is said to consist-except an average surface of twenty feet-of lime fit for the mason or the field. The hill appears to have been a stupendous limestone rock, submitted to intense volcanic heat.

161-Yeo. R. A. W.-We have sought in vain for a satisfactory solution to the question, "What is the meaning of the prefix yeo in the word yeoman?" Of the various derivations attributed to the word yeoman, a corruption of the old term gemein-common, seems the most probable. The town of Yeovil takes its name from the river Yeo upon which it is situated.

162-Laissez faire, laissez passer. B. R.-This celebrated axiom was the reply of a merchant manufacturer to the French minister Colbert, on being interrogated by the latter respecting the subject of foreign exchange; the introduction of all foreign manufactures having been prohibited, to the great detriment of the vine-growers, who could not find prosperity save in foreign imports.

163-Great Circle Sailing. S. J. T.-Great circle sailing consists in determining a series of points in an arc of a great circle between two points on the surface of the earth, for the purpose of directing a ship's course as nearly as possible on such arc, that is, on the curve of shortest distance between the place from which she sets out, and that at which she is to arrive. [See Raper's Practice of Navigation, p. 71.]

164-Hope-Expect. J. H.-To expect is to look forward to an event with an idea that it will probably occur; to hope is to look forward to an event, with a desire that it may occur. It would not be improper, therefore, with reference to an event which, if it had occurred, would have produced important advantages to you, but which you believed was not likely to occur-to say, "I hoped that it might happen, but I did not expect that it would." 165-Classical Education. H. W.-Though we are fully alive to the great advantage derived from a knowledge of the classics, we believe that too much attention has been given to the study of Latin and Greek. A good commercial education is rarely to be obtained at what are termed "Grammar Schools," because the dead languages are taught to the exclusion of French and German, which are far more valuable to all except persons intending to enter the universities.

166-Optics. B. H. N.-When we press the side of

the eye, we see circles of light, because by the pressure from without we affect the nervous filaments of the retina internally. It will be noticed that the image appears in the opposite direction to the part touched, because the retina, so irritated, conveys to the brain under ordinary circumstances the idea of an object in a straight line, drawn from the nervous filaments affected through the aperture of the pupil to the thing looked at.

167-Animalcules. J. C.-That animalcules exist in almost all natural waters, there can be little doubt. We are not aware whether they have been sought for or discovered in the boiling springs in Iceland. To prove how ubiquitous the germs of these creatures are, we may relate that a scientific friend discovered several animalculæ in the dew-drops that trickled down the outside of a clean polished glass vessel which contained a freezing mixture. Perfectly pure distilled water is theoretically free from animal life.

168-Jews. D.R.--The massacre of the Jews in London was occasioned by an edict of Richard I., who, on the day of his coronation, September 3rd, gave strict orders that no Jew should approach the Abbey while the solemnity was being performed, "for fear of the enchantments they are wont to practice." Some of the principal Jewish merchants having failed to obey, the populace committed great outrage on their persons and property; and it is related that the citizens "slew many of them, and burned their houses."

169-Early Discoveries. J. A.-Newfoundland, Greenland, and several parts of the American coast, were probably visited by the Scandinavians at a very early period. Among the most celebrated of those early voyagers, we may name Bjarne, the Icelander, and Lief, the son of Erir, Jarl of Norway, who landed in Canada, and called it Vineland, on account of its wild grapes. Afterwards, a Norwegian, named Karlefne, established a small colony, and this circumstance furnished the material features of Lentze's picture of the "Landing of the Northmen."

170-American Indians. W. W. M.-When Columbus landed at Cat Island, he thought, in conformity with his theory of the spherical shape of the earth, that he had landed on one of the islands lying at the eastern extremity of India; and from this belief he gave the inhabitants the name of "Indians." In Heylyn's Cosmography, 1677, we read "Indies either is mistook for some part of India at the first discovery, or else because the seamen called all countries, if remote and rich, by the name India, which received its name from the river Indus."

171-Roman Inscriptions. B. F. F.- The letters S. C. A. stand for the words "Senatus consulti auctoritas," which was the usual inscription of the decrees of the senate. Nothing could be laid before the senate against the will of the consuls, except by the tribunes of the people, who might "intercede" or pronounce a veto against any decree. If such intercession was made, the sentence of the senate was called "senatus auctoritas" (opinion), as distinguished from "senatus decretum" (command). When no mention, however, is made of intercession, the term "auctoritas" is held to be the same as "decretum" or "consultum." The letters "S. P. Q. R." stands for the words "Senatus populusque Romanus."

Im

172-Ice. Water. M. T. C.-Colouring matters, salts, and alkalies, are usually expelled by water in freezing. If solutions of sulphate of indigo, diluted sulphuric acid, and diluted ammonia be partially frozen, and the unfrozen liquid dislodged, the ice will be found to be colourless, and when dissolved, perfectly free from acid or alkali. Water, as soon as it is thawed, rapidly absorbs air, and thus provides for the life of aquatic plants and animals. Ice placed in oil, so as to prevent its receiving any air from the atmosphere, explodes on reaching the temperature of 270 degrees. Water, moreover, entirely deprived of air, explodes in a similar manner at 270 degrees. mense pressure prevents water from freezing at 32 degrees. 173-Crystal Palace. W. F. F.-The dimensions of the Building for the Great Exhibition are as follows:-It is 1851 feet in length, and 456 feet in breadth in the widest part. It covers more than 18 acres. The total cubic contents are thirty-three millions of feet. The length of sash-bar used was about 205 miles, and the quantity of glass about 900,000 feet, weighing upwards of 400 tons. The total area of the ground floor is equal to 772.784 square feet, and that of the galleries to 217,100 square feet. The width of the main avenue is nearly double that of the nave of St. Paul's, while its length is four times as great. The walls of St. Paul's are 14 feet in thickness, while those of the Crystal Palace are only 8 inches. St. Paul's occupied thirty-five years in building, while the Hyde Park building was finished in less than eighteen weeks. All the dimensions of the building are multiples of 8.

174-Sight. Y. B.-The direction of the eye while appearing to gaze steadily at any object does in reality keep wandering to an imperceptible distance on every side of the object looked at, but very rapidly. This wandering is not accidental or an imperfection of sight, but an essential feature of vision; because it is not the continuance of an impression that is perceived by any of the animal nerves, but its commencement and termination, or, more strictly speaking, its increase and decrease. Persons become so used to loud noises, or noisome smells, as to be unable to perceive them; but to such, the stillness of a rural cottage, or the sweetness of the country air, are strikingly remarkable. This principle is probably analogous to that by which a magnet creates an electric current in a neighbouring wire; not by its constant presence, but by the increase or diminution of its influence, either by a variation of its position, or of its power. This wandering propensity of the eye accounts probably for the relative facility with which different sorts of marks are seen at great distances. [See Mr. Petrie's communication on the best sorts of station marks-Report of British Association.]

175-Parachutes in Mines. N. G. N.-The only practical purpose to which parachutes have been applied, is to obviate the accidents occurring in mines from the breakage of ropes or chains in the shafts. The Brussels Herald states that some experiments have been lately made on a large scale in Belgium, with a contrivance intended to remedy this evil. It is well known that miners dislike the tedious and fatiguing work of ascending and descending the shafts by means of ladders, and always prefer to trust themselves to baskets suspended by ropes, &c. The basket or cuffert in the experiments described, are so made, that in case the rope breaks, it immediately springs open, forming a sort of parachute, which is held suspended in the air by means of the strong current which is always rushing up from mines, owing to the temperature below being higher than that above. [See Terrestrial Phenomena. February, p. 105.] The effect of this apparatus has been exhibited to competent persons; several miners entrusting themselves to the basket, which was so arranged, that at a certain point the rope broke: they were sustained in the air by the open basket, so that the experiments were entirely satisfactory.

176-German. M. P.-There is no royal road to learning German, or to any thing else, and no one should commence who will not give a good deal of study and attention to it. On this and other accounts, the study of German is preferable to that of any other language, and, when acquired, the literature is richer than that of any country, except England. Of books for acquiring it expeditiously without a master, Ollendorff's and Falck Lebahn's are the best. The former requires six months, and any one will, by using Ollendorff two hours daily for that time, acquire a knowledge of the writing and speaking of the language. But it does not teach reading, which Lebahn's book does, and this we think, on the whole, is preferable. If the student got either of these books, he would require no other till he had mastered them. However, if he intended to pursue the study, he would require a Dictionary some time, and he might as well buy it at the first. Perhaps the best are Sporschil and Böttger's, or Flügel's abridged. The price of the former is four shillings and sixpence, and may be had from Williams and Norgate's, and during two years that the writer has used it, he has never missed finding a word in it. Flügel's is better in some respects, but rather dearer. Lebahn's book contains lessons in reading and writing, and also a tale, in German, "Undine," with a vocabulary of all the words. The price is about 8s., and the Key costs 43. more. Ollendorff costs 10s. and the Key 128. It may sometimes be picked up at cheap book-stalls. 177-Electro-Magnetism as a Motive Power. W. T. B. S.-Jacobi, who was aided by the Russian government in his experimental trials to construct an electro-magnetic engine which should possess many advantages over the motive powers now in use, has abandoned his experiments. A voltaic current produced by the chemical disturbance of the elements of any battery, is capable of creating, by induction, a magnetic force, this force being always in an exact ratio to the amount of matter consumed in the battery. The greatest amount of power is produced when the chemical action is the most rapid; hence it is more economical to employ a battery under an intense action, than one in which the chemical action is slow. Now it has been shown that one grain of coal consumed in the furnace of a Cornish engine, lifted 143 pounds one foot high, whereas one grain of zinc consumed in the battery lifted only 80 pounds. The cost of one hundredweight of coal being about ninepence, and of one hundredweight of zinc two hundred and sixteen pence, it follows

that magnetic power is in its consumption of material nearly twenty-five times as expensive as that produced by steam. Magnetic force, as a motive power, has other objections. The rate at which the force diminishes through space is such, that when the armature is only onefiftieth of an inch distant from the magnet, four-fifths of the power are lost, and the moment the armature is set in motion, the power of the magnet is reduced to one-half, and a current of electricity acting in opposition to the pri mary current is induced. It is probable that, under the best conditions, electro-magnetic power would, for a continuance, be fifty times more expensive than steam. These results are quoted from a paper read by Mr. Robert Hunt to the Society of Arts, May 22, 1850. It has been stated that an American professor has made some experiments, showing that electro-magnetism can be used economically as a motive power. The statements, however, have not been confirmed, and no practical results have hitherto been reported.

178-Light. T. W. Q.-Experiments to measure the velocity of light in its passage through a limited portion of the terrestrial atmosphere were made by M. Fizeau, and the results show a close approximation to those which have been obtained by observations on the satellites of Jupiter. His experiments were intended to discover the exact time required by a ray of light to pass from Suresnes to a certain spot on the heights of Montmartre, and back again to Suresnes. The distance between the two places is about two leagues, or 8,633 mètres, consequently the ray of light had to traverse 17,266 mètres. A point of intense brightness, produced by the oxyhydrogen light, was concentrated by a lens placed in the window of an apartment on a terrace at Suresnes, and being received upon a mirror at Montmartre, was reflected back again along the same line to Suresnes. Behind the point of light at Suresnes, was placed a wheel, which carried 720 teeth, and which was so adjusted that the light shone through the opening between two of the teeth. An eye placed behind the wheel when it was at rest received the impression of a full ray of light. If the wheel was moved so that 12 revolutions of the wheel passed before the eye in a second, the teeth of the wheel appeared continuous, the edge seemed semi-transparent, and a moiety of light was obstructed. The wheel having 720 teeth, each opening occupied 1440th part of the circumference, and as the first interruption or eclipse of light was produced by the above rotation, it was proved that the light had traversed 17,266 mètres, while the wheel performed 1-1440th part of a revo lution. If the speed was increased uniformly, more light was obstructed as the numbers 1, 3, 5, 7; and eventually a rapidity was obtained by which all the light was cut off, and that rate gave the value of the time necessary for a ray of light to pass from Suresnes to Montmartre and back again. Thus M. Fizeau determined that a ray of artificial light travelled at the rate of 70,000 leagues in a second of time. Astronomers have given the rate with which solar light travels at 192,500 miles in a second. This agrees very nearly with M. Fizeau's results; the differences between English and French measures being taken into account.

21-Polishing Telescope Lenses. J. R. inquires-"What is the best method for amateurs to polish lenses, and what tools are required?"

22-Punch. G. W.-What is the supposed origin of the drama performed by the puppets in Punch's show, the subject of which has remained unchanged for so many years!

23-Electrotype. X. C.-In Walker's electrotype manipulations he recommends two compositions for moulds; one is wax stearine and black lead; the other wax stearine and flake white. What are the best proportions?

24-Obsolete Law.-A correspondent writes - "Till within a few years a person was, by the law of England, liable to capital punishment for associating a whole month with gipsies." Is this the present state of the law; and are there any instances in history of this law having been en

forced?