METEOROLOGY. ground from the extreme cold of winter. In very cold seasons the temperature of the ground under the snow is often many degrees higher than that of the air around; the importance of this to the young plants can easily be understood. Sleet seems to be caused by snow-flakes becoming partially melted in their fall. The snow is sometimes produced in the higher regions of the atmosphere, being caused by a current of air at a very low temperature. The air below is, however, several degrees wanmer, and hence the flakes are partially melted in falling, and as they come in contact with one another, unite, and thus produce the larger flakes so frequently noticed. Sometimes the moisture of the air falls to the ground in the shape of small pieces of ice, known as hail. There is some difficulty in accounting fully for this, especially as it is most common in tropical regions and during the heat of summer. It usually falls, too, at the hottest part of the day. Its formation is probably to be explained by a very cold current of air suddenly rushing into one at a much higher temperature, and nearly saturated. The rain thus formed is at once 185 vessel down into the snow till it touches the ground. Then take it up with the snow in it, and, setting it in a warm place, let it stand till the snow is melted. The depth of water can then be measured, and this amount should be added to the rainfall of the day, as shown by the gauge. Waterspouts and whirlwinds constitute another very remarkable class of meteoric phenomena, which we will notice here, though they seem to belong partly to aërial and partly to aqueous meteors. When two currents of air are impelled obliquely against one another, a whirlwind or eddy is produced. These may constantly be seen on a small scale during summer, when the gusts of wind will catch up small particles of straw, dust, or loose materials, and whirl them round in a spiral, sometimes carrying them a little way up in the air. In sandy deserts this is witnessed on a much grander scale. The sand is caught up by the wind, and formed into tall, stout columns, which rotate on their axes, and move about, sometimes with a slow, stately motion, at other times travelling very rapidly, and in irregular directions. The appearance presented congealed into small lumps of ice. This theory is supported by the greater frequency of hail-storms in mountainous regions, where these cold blasts are produced by the proximity of fields of snow and ice. Hailstones are usually of a globular form, and regular in shape. If they be cut through, their internal structure is likewise found to be regular, as if composed of crystals radiating from a centre. They vary in size from about a tenth of an inch upwards to several inches in diameter. Many well-authenticated instances are on record in which they have attained the size of pigeons' eggs, and they have been known much larger. In many places much damage is done to the crops by hailstorms, the tender plants being beaten down and destroyed. In the south of France the annual damage to the vines from this cause is very great and serious. Sometimes birds, and even larger animals, have been killed by the hail, and great injury has been caused to windows and roofs of houses. The fall of snow or hail is not indicated by a rain-gauge, and hence the reading of this does not represent the full amount of water that falls upon the ground. Usually snow is found to occupy some ten or twelve times the bulk of an equal weight of water; but when the temperature is high it lies closer than this. Some observers merely measure the depth of the snow in a place where it is not affected by drifts, and then take one-tenth of this to represent the equivalent rain-fall. This is not, however, a very accurate plan; the better way is to plunge an open tin by a large number of these sand-columns has been described by various travellers, and is, indeed, very remarkable. The dust whirlwinds of India are similar phenomena. Their presence is first indicated by a dark cloud seen in the horizon; this rapidly spreads, and bursts upon the observer. The air is quite thick with the dust which is carried up by the wind, and sometimes the storm may be seen advancing, and presenting the appearance of a number of spiral clouds hurrying rapidly onwards. The air is highly electrical, this being probably produced by friction of the particles of dust in the air. Sometimes the agitation of the air becomes even more violent, and then we have the tropical whirlwinds, which uproot trees, overturn buildings, and seem to carry everything before them. When these whirlwinds occur over large bodies of water, they often give rise to waterspouts. A dark cloud appears, and is whirled round by the wind so as to produce a conical mass of vapour, reaching nearly to the surface of the water, which is likewise so violently agitated that frequently it appears to be connected with the lower end of the vapoury column. Many have supposed that the water is actually sucked up from the sea by the spiral motion, but this is now known to be a fallacy, as water that falls from the spout on the surface of vessels is found to be fresh, and not salt, as it would be were this theory true. A great quantity of rain is often produced as these waterspouts break. Sometimes they travel on to the land, and the mass of water suddenly liberated from them has often power enough to hollow out a large excavation. Their origin is not fully understood. There is no doubt but that they are in many respects closely allied to whirlwinds, but the electrical condition of the air seems likewise to have much to do with their formation, as they are frequently accompanied by flashes of lightning. The chief danger to ships in the neighbourhood of them arises from the violence of the gusts of wind, and the sudden way in which they shift about to different points of the compass. We will now turn our attention to the remaining meteors, most of which may be classed as the luminous or optical phenomena of the atmosphere. The most important of these are the electrical, such as the lightning and the aurora borealis. The identity of lightning and electricity was conclusively proved more than a century ago, by the celebrated kite experiment of Franklin, in which he succeeded in drawing sparks from a key attached to the string of his kite. The string became moistened by the rain, and thus was converted into a conductor, down which the electric fluid passed in a continuous stream. This experiment was performed just before a thunder-storm; the air is, however, always charged more or less with electricity, the presence of which may be made manifest by a delicate electroscope. In the instrument commonly employed, and represented in Fig. 10, the disc of the ordinary gold-leaf electroscope is replaced by a slender rod, terminating in a metal point or ball. The metal screen, A, serves to protect the glass bottle from the rain, and thus improves the insulation. Two strips of gold leaf are fastened to the inner end of the rod, and by their divergence they show the quantity of electricity present in the air. The apparatus should be placed in a somewhat elevated position. Sometimes insulated conducting wires are fixed to lofty poles, and the electricity of the air examined in this way. When this is done, a large metal ball connected with the earth should be placed at a few inches from the wire, in case the lightning should pass along it, and produce disastrous effects. Fatal accidents have, indeed, arisen from want of due precaution, and experiments of this kind should only be repeated with great care. From long-continued series of observations, it is found that the air is almost always charged with positive electricity, the intensity of which increases with the elevation. The few occasions on which negative electricity has been observed were for the most part during heavy rain. The amount of electricity present in the air is at its maximum in mid-winter; it is subject also to a daily fluctuation, attaining a maximum twice each day-the first time in the morning, and then again a little after sunset. There has been much inquiry as to the origin of this electricity. The following appear to be its principal sources:When pure water is evaporated, no electricity is evolved; but if any salt or impurity be present in the water, electricity at once appears. Now sea, river, and lake water all contain impurities, and as the amount of evaporation that goes on is, as we have seen, very great indeed, much of the atmospheric electricity may probably be set down to this cause. Friction is another cause of electricity. The wind strikes against terrestrial objects; it is also frequently charged with dust and particles of watery vapour, which rub against each other, and thus add to the friction, and in this way electricity is set free. Vegetation and combustion seem also to increase the amount of free electricity. To the latter of these causes must be attributed the brilliant flashes of lightning which accompany volcanic eruptions (Fig. 11). TERMS USED IN COMMERCE-VI. NOTING OF A BILL.-A note taken of its presentation for acceptance or payment, customarily effected on a second presentation by a notary, as proof of the claim having been duly made. NULL AND VOID.-Of no effect. OPEN ACCOUNT.-An account in Dr. and Cr. form, exhibiting all open transactions between two parties, setting down the amounts of those transactions that are determined but not matured, and estimating the out-turn of those still pending, so that the balance shows a close estimate of the respective position of the parties concerned in the account. OPEN POLICY.-In marine insurance, where a certain sum is insured, leaving the declaration of the goods and their values to be subsequently made. ON DIT (People say).-Placed at the beginning of a sentence to denote that what follows is a flying rumour. OPTIONS.-Speculative transactions on the Stock Exchange, where persons give so much per cent. for the option of buying or selling so much stock at a fixed price on a certain fixed day. OVERCHARGE.-An excessive charge or price. PANIC.-A sudden fright, especially when without cause. Used commercially to denote a general distrust with regard to money matters. PAR-Exact corresponding value, neither enhanced by premium nor depreciated by discount. LESSONS IN SPANISH.-XIX. THE PRONOUN. PERSONAL PRONOUNS. THE personal pronouns of the nominative case, when used, may come either before or after the verb, except the latter be in the imperative mood, or the sentence be interrogative, in which cases the nominative generally follows the verb; as, viva ella, may she live; ha hablado él? has he spoken? As the verb-ending generally indicates of itself the person and number that its nominative must be, the nominative personal pronouns are seldom expressed in Spanish, unless when necessary to distinguish the persons or genders, or to be em phatic, or when a relative pronoun is to follow; as El que tiene dinero, tiene cuidados, he who has money has cares. El y ella son prudentes, he and she are prudent. Nosotros seramos castigados, y no vosotros, we shall be punished, and not you. The pronoun se, oneself, is sometimes used with a reflective or reciprocal verb, and then it is to be rendered in English by himself, herself, itself, themselves, or one another, as the sense may require; as in the following example: Ellas se aman, They love themselves (or, they love one another). The first objective case of all the personal pronouns is also employed with reflective or reciprocal verbs; asNosotros nos aman, we love our- Yo no quero alabarme, I wish not selves (or each other). to praise myself. Yo me alabo, I praise myself. The pronoun se is also frequently used with the verb in the active voice, of the third person singular or plural, to express the passive voice; as in this example: La casa se quemó, The house was burned (the house burnt itself). The first objective case of all the personal pronouns is some. times used with a reflective verb in a passive sense; as— Yo me admiro, I am surprised (I surprise myself). Vosotros os alegrais, you are rejoiced (you rejoice yourselves). Strictly speaking, se cannot be used in the nominative case. and should therefore always be considered as governed by a verb. Thus, in such sentences as se dice, se cree, se piensa, the literal rendering is, it says itself, it believes itself, it thinks itself, or it is said, it is believed, it is thought. Still, in translating, it is often more convenient to imagine se as an indefinite pronoun of the nominative case, used in the sense of they; as, se dice, they say, that is, people say; se piensa, they think. Se and other pronouns of the first objective case are often used in Spanish with neuter and active intransitive verbs reflectively, and in such cases seem redundant in English; asDe allí se pasó á la ciudad, thence he passed (himself) to the city. Yome arrepiento, I repent (myself). Se arrepiente, he repents (himself). Se is sometimes used in the sense of to him, to her, to them, to you (i.e.,.to your worship). This use of se takes place only when another personal pronoun of the objective case and of the third person immediately follows it; as Tengo una cuchara; se la daré,* I have a spoon; I will give it to him. We cannot say, le la daré, I will give it to him, but se la dari. LESSONS IN SPANISH. To add more clearness or strength to a sentence, both objective cases of pronouns are often employed; the second objective case then being placed either before the first objective or else after the verb, except the first objective case comes after the verb (as in the case of infinitives, gerunds, and imperatives), when the second objective must come after the first; asÁ mí me dijeron, or me dijeron á Diciendole á ella, telling her. mí, they told me. Díme á mí, tell me. Mismo is often used with nouns also; as, la misma María, Mary herself; los mismos soldados, the very soldiers or the soldiers themselves. When by the pronoun it is meant anything to which we cannot apply a gender, ello is used. Its first objective lo is employed by the same rule. Thus if it be said, "he has been told to love his enemies, and he does it," the pronoun it refers to the clause of the sentence, "to love his enemies," and of course has no gender. In such a case, lo (not le nor la) would be used. Lo is used in Spanish for so in English, when the latter means it; as 187 Quien often means he who, she who, one who; and quienes is used for they who; as Quien calla otorga, he who is Porque los enseñaba, como silent, consents. quien tiene autoridad, for he María fué quien lo dijo, Mary taught them as one who has authowas she who said it. rity. Such expressions as it is I, it is thou, it is he, it is she, it is we, etc., are rendered in Spanish by I am, thou art, he is, she is, we are, etc.; as AGREEMENT OF THE VERB WITH ITS SUBJECT. The verb agrees, in number and in person, with its subject or nominative, expressed or understood; as Soy general, I am a general. Ella ama la verdad, she loves the truth. When a verb has two or more it is put in the plural; as Americanos aman las the Americans love Los riquezas, riches. subjects, each in the singular, Pedro ó Diego vendran, Peter or James will come. Mi padre y mi madre me aman, my father and my mother love me. When a verb has two or more subjects of different persons, it is put in the plural, and agrees with the first person in pre ference to the other two; as Tú y yo estamos buenos, thou and I (i.e., we) are well. Mi hermano y yo estamos malos, my brother and I (i.e., we) are ill. If the second person should be used with the third, without any first person, the verb must be in the second person plural :Tú y ella estais buenas, Thou and she (i.e., you) are well. When a relative pronoun is the subject of the verb, the latter must agree, in person and number, with the noun or pronoun to which the relative relates; as Vosotros que sois sábios, ye who are wise. Yo soy que hablo contigo, it is I who speak with thee. A collective noun, taken in a general sense, that is, a noun representing the whole of the persons or things mentioned, requires the verb to be of the singular number; as— El ejército de los Caldéos per- The army of the Chaldeans pursued the king. siguió al rey, sense, that is, representing a part of the whole of the collective A subject which is a collective noun, taken in a partitive noun, and conveying plurality of idea, requires the verb to be in the plural; as Parte creían lo que les decía, y Part believed what he told them, parte no lo creían, and part believed it not. This last rule is not always followed, even by the best Spanish authors. In cases in which a verb appears to have two subjects, it must agree with that noun to which it seems more particularly to belong; as Los gages del pecado son muerte, The wages of sin are (is) death. USE OF THE MOODS AND TENSES OF VERBS. THE INFINITIVE, GERUND, AND PARTICIPLE. The present tense of the infinitive expresses affirmation in an indefinite manner, without reference to number or person; as, decir, to say; dar, to give. The infinitive is used in Spanish when in English the present participle, preceded by a preposition, is used; as En derramar torrentes de san- Vengo de comer, I come from gre, in spilling (to spill) torrents of dining (to dine), i.e., from dinner. blood. The infinitive is frequently used as a verbal noun or present participle, by placing the masculine definite article before it; as in these examples : Al caer del dia, at the fall (at the El murmurar de las fuentes, the to fall) of the day. murmuring (the to murmur) of the El leer me gusta, reading (the to fountains. read) pleases me. The infinitive is often rendered in English by the present *This is different, as will be perceived, from the rule in English syntax, which requires two singular nouns connected by a disjunctive conjunction, to have the verb agree with them in the singular form. These last examples, it will be perceived, require the participle to agree with the noun governed (cartas). Tener and llevar are, as above, sometimes used as a kind of auxiliary verbs, and can always be rendered by have; thus each of these examples may be translated, he has written three letters. The past participle is in Spanish used with a noun or pronoun in the case absolute; thus, hallado means found, and absolutely, being found; enviado means sent, and absolutely, being sent; recibido means received and being received. In general, the participle is placed before the noun of the case absolute, with which it agrees (though the rules of Spanish construction admit of its being placed after the noun); as Tormada Vera-Cruz, el General Vera Cruz being taken, General Scott salió para Jalapa, Scott set out for Jalapa. TENSES OF THE INDICATIVE MOOD. The present tense expresses an existing state or an action occurring at the time in which we are speaking; asMi hermano escribe, my brother Estas doncellas son amadas, writes. these maidens are beloved. The verb estar can be used with the gerund in Spanish, as in English the verb to be with the present participle; as The verbs ir (to go) and venir (to come) do not admit of the verb estar coming before their gerund as in the above rule. Thus we cannot say in Spanish, yo estoy yendo and yo estoy viniendo, but yo voy and yo vengo (I go and I come), I am going and I am coming. The imperfect tense is used to express what is past, and, at the same time, present, with regard to something else which is past; that is, it is a past tense which was still present at the time spoken of. It may always be employed in Spanish when in English the word was can be used with the present participle, PLANE TRIGONOMETRY.-1V. XVIII. Application of the foregoing Formula. It will be readily seen how the power to work out numerical values for functions of different angles is extended by the results of the last few sections. We may now obtain values for the half or third, or for twice or three times any of the angles whose values were computed geometrically in Section V., and for any combinations arising by addition or subtraction of angles so calculated. In this way, by steps which cannot be followed here, the entire table of natural sines and cosines has been constructed, and by means altogether foreign to this treatise the corresponding logarithms have been worked out for every degree and minute from 0° to 90° (see, amongst other works, Galbraith and Haughton's Mathematical Tables). Moreover, the numerous formulæ derived from the "four fundamental formulæ" are of great use in helping us to simplify trigonometrical expressions, and to change them into forms more suitable for logarithmic calculation, or otherwise more convenient to deal with. The following cases, given as examples, show how apparently formidable expressions can be turned into simple ones, easily solved, by mere knowledge how to make use of the formule: 4. Express tan. Tan. A + cot. A = + 1 cos. A 1+ cos. A sin. A sin. A sin. A 2 cos. A -2 sin. A cos. A A + cot. A by a single function. sin. A cos. A_sin.2 A+cos. A + cos. A sin. A sin. A cos. A 2 2 sin. A cos. A sin. A 2 sin. 2 A = 2 cosec. 2 А. 1 sin. A cos. A to a single function. This is similar to 5. Reduce Case 1. 1 + cos. A Sin. A 2 sin. A cos. A sin. 2 cos. A 1 + cos. A cos. Cos. A sin. (90°-A) = 1+sin. A 1+cos. (90°-A) = 2 sin. (45°-A) cos. (45°-A) 2 cos.2 (45°-A) sin. (45°- A) = tan. (45° - A). 7. Bring cos. A - sin. A to a single function. Cos. A sin. A = (cos. A + sin. A) (cos.2 A - sin.2 A) = 1 x cos. 2 A = cos. 2 А. 8. Bring sec. A + tan. A to a single function (remember that 90° + A = complement of A, and bear in mind signs of angles in second quadrant). 189 17. Solve the simultaneous equations, sin. x + sin. y = a. cos. x + cos. y = t. By (41) and (43)2 sin. 2 cos. (x + y) cos. (x + y) cos. (x - y) = a. (x - y) = b. (sin.2 sin. ++ cos.2+) But the last factor of left-hand side = 1, ..cos. (x - y) = (a2 + b). = a2 + b2. From these two results the unknown quantities x and y may be found by addition and subtraction. XIX. Subsidiary Angles. -Trigonometrical calculations may often be simplified in form by introducing a subsidiary or imaginary angle, by which the sum or difference of two or more magnitudes may be expressed by a product or quotient-often a matter of importance in calculating with logarithms. An example or two will best explain our meaning: Solve the equation, 2 = a sin. A + b cos. A. Now assume a subsidiary angle 0, such that substitute this value in above equation. b a = tan. 0, and This is a much more manageable expression to deal with, being already known by the assumption. As tan. @ may be anything from 0 tos, the relative values of a and b are immaterial; but had it been desired to introduce sin. 0, it would have been necessary to see that the ratio assumed to represent it did not exceed unity, as sin. O cannot exceed 1. Solve the equation a sin. a b cos.ac. Reducing this equation, we obtain the following quadratic 13. Show that sin. (A + B) sin. (A - B) = sin. A sin. B. for sin. : By (33) and (34)— Sin. (A + B) sin. (A - B) = sin. A cos. B - cos. A sin. B = sin.2 A (1- sin. B) - sin." B (1 - sin." A) = sin. A sin. A sin. B sin. B + sin. A sin.2 B = sin. A-sin.2 B. 14. Show that cos. (A + B) cos. (A - B) = cos.2 A sin. B. Proceed as in last case, by (35) and (36). 15. Solve the equation, a tan. x = b cos. 2. Multiply both sides by cos. z; then a sin. x = b cos. x = b (1 - sin.2x); (a2 + b2) sin.x Cos. A cos. В cos. A cos. B sin. B (65) |