In having an angular aperture of 90° and a magnifying power of 500 diameters, they made out a double series of lines crossing each other at an angle of 60°, so as to produce an appearance of diamond-shaped markings, as in Fig. 9a. creasing the magnifying power to 600 diameters, three sets of > lines, longitudinal, transverse, and oblique, were brought out, producing an appearance of fine hexagonal markings, as shown in Fig. 96. Mr. Wenham, about 1854, produced a photo-micrograph of this species (represented in Fig. 10), under a power of 15,000 diameters, which gave an appearance of hexagonal structure, the centre light and the margin dark, as shown at в (Fig. 10), when all parts were accurately in focus, and a dark hexagon with a light margin, as at a (Fig. 10), where the parts were out of focus, giving an appearance of dark dots on a white ground. The inference drawn from this photograph was that the hexagonal markings were depressions, and that all appearances of dots or elevations were due to such parts being out of focus, and producing an optical illusion. "Previous to this date Gillett, by careful mounting of the object, and under the most favourable illumination, either from a white cloud, or a lamp with direct light (parallel rays, be it observed!), and a magnifying power of at least 1,200 diameters' (see Quekett on the Microscope, p. 509), had resolved the three sets of lines into dots, or elevations from the surface, as shown in Fig. 116. "In recent years Mr. Wenham, since employing the -inch objective, has been disposed to give up his former interpretation of the markings being hexagonal depressions, and inclines to Mr. Gillett's view that the areola are minute tubercular elevations, and that the intervening network is formed by the thinner portion of the valve, the structure shown in Fig, 11a, which represents Pleurosigma formosum magnified 5,500 diameters." Thus the parallel is completed; distant heavenly bodies present new features when more critically examined, just as natural objects may present almost a metamorphosis when examined with the full light of scientific microscopical investigation. LESSONS IN ITALIAN.-XXIX. REFLECTIVE VERBS. IN these verbs the subject from which the action proceeds is at the same time a passive object, and for this reason is expressed twice: (1) by the personal pronoun io, I; tu, thou; egli or esso, he or it; ella or essa, she; noi, we; voi, you; eglino, elleno, or essi, esse, they; (2) by the so-called conjunctive pronouns mi, myself, or to myself (i.e., a me); ti, thyself, or to thyself (i.e., a te); si, himself, herself, itself, or to himself, etc. (i.e., a se); ci, ourselves, or to ourselves (i.e., a noi); vi, yourselves, or to yourselves (i.e., a voi); si, themselves, or to themselves (i.e., a se). These are consequently in the accusative and sometimes in the dative case, must be placed before the verb, and will be fully explained hereafter: for example :Io mi di-fên-do, I defend myself. Noi ci di-fen-diá-mo, we defend ourTu ti di-fên-di, thou defendest thy- selves. [selves. self. Voi vi di-fén-de-te, you defend your Egli si di-fên-de, he defends him- Essi or esse si di-fên-do-no, they self defend themselves, etc. --- The personal pronouns may in this case, as well as in the conjugation of all Italian verbs, be omitted; and it is sufficient to say mi difendo, ti difendi, si difende, ci difendiamo, vi defendete, si difendono, and so on through all tenses and moods. When the pronouns mi, ti, ci, vi, and si come before a verb beginning with a vowel, their final vowel i may be omitted and an apostrophe put in its place; as M' av-vég-go (for mi aveggo), I perceive or remark. S' im-pa-dro-ní-sce (for si impadronisce), he seizes upon, or makes himself master of In the infinitive mood of these verbs the pronoun si must be removed to the end as a suffix; as, van-tár-si, to boast; ral-legrár-si, to be delighted; af-fli-ger-si, to grieve, which is equivalent to rallegrare, affligere, etc., se me-dé-si-mo. Some verbs are reflective in the strictest sense of the word, and can never be used without the above-mentioned reciprocal pronouns; as Con-tri-stár-si, to be afflicted, or cast In-na-mo-rár-si, to fall in love. In-ge-gnár-si, to endeavour, to task Im-pa-dro-nír-si, im-pos-ses-sár-si, to seize upon, or make one's self master of. La-gnár-si, to complain. Ma-ra-vi-gliár-si, to wonder. all one's powers of ingenuity and Ral-le-grár-si, to be delighted. It must, however, immediately appear that every verb may assume the reflective form, having the pronoun si added to its infinitive, whenever the action which the verb implies returns back to the subject; as— Ab-ban-do-ná-re, to abandon, or give up; a-ban-do-nár-si, to give one's self up, or over. Ab-bas-sá-re, to abase, lower; ab-bas-sár-si, to fall off, sink, to cringe. The genius of the Italian language generally requires the reflective verbs to be considered as passive, thus giving rather an illogical predominance to the passive state of the subject reacting on itself, while the unmistakable active nature of a reflective verb, which distinctly names the passive object, is dropped. For this reason the great majority of these verbs, i.e., the reflective verbs governing the accusative case of the person, in their compound tenses must be conjugated with essere instead of avere, and their participle must agree in number and gender with this accusative, preceding the verb; for example: Mi sono do-lú-to, I have grieved; ci siamo ral-le-grá-ti, we were delighted; égli s'éra fát-to co-ro-ná-re (not egli s' aveva fatto coronare), he had got himself crowned. It cannot be denied that in these cases even good writers sometimes exhibit examples of the use of avere in the place of essere, saying, for example, si a-vé-va-no lun-ga-mén-te ama-ti, for si ê-ra-no lun-ga-mén-te amá-ti, they had been in love a long while; egli s' aveva fatto coronare (as quoted above), etc. These are, however, licences of celebrated writers, and are not to be imitated. The reflective verbs governing the dative case of the person and the accusative case of the thing in their compound tenses may be conjugated either with essere or avere, and when the accusative case of the thing precedes them, their participle must agree with it; but it remains unchanged when the accusative follows: for example : : El-la si è (or si ha) strac-ciá-to il ví-so, she has lacerated her (i.e., to herself the) face. E-gli-no si só-no (or si hán-no) fát-to o-nó-re, they have been an honour (i.e., done honour) to themselves. The conjunctive pronouns mi, ti, ci, vi, si, in ordinary or familiar language, precede the reflective vers, as will appear from the paradigm of its conjugation. The only exceptions are the imperative and infinitive moods, the gerunds and participles, where they are added as suffixes to the verbs. But in a more measured or elegant style, and especially in poetry, those pronouns may be added as suffixes to all the tenses where they generally precede the verb, unless ambiguity or harsh sound should forbid it, and it is allowable, for example, to sayPên-to-mi for mi pên-to, I repent. Pên-te-si for si pên-te, he or she repents. Pen-tí-va-si for si pen-tí-va, he repented. Pen-tí-ron-si for si pen-tí-ro-no, they repented, etc. By anticipation it must be stated here that the conjunctive pronouns mi, ti, ci, vi, and si, before the words lo, it; la, her; li, them (m.); le, them (f.); and ne, of it, for it, with it, etc., are changed into me, te, ce, ve, and se: for example, pen-tír-se-ne, to repent it, or to be sorry for it, is conjugated- fo me ne pên-to, or pên-to-me-ne, I repent it, or I am sorry for it, etc. Tu te ne pên-ti, or pên-ti-te-ne. Egli se ne pên-te, or pên-te-se-ne. I. REMARKS ON THE INFINITIVE MOOD. Observe, the pronoun si only refers to the third person singular or plural, e.g., in the sentence-in-ge-gnán-do-si é-gli in mól-te ma-niê-re di ri-a-cqui-stá-re an-có-ra la tú-a a-mi-cí-zia, as he endeavoured in many ways to regain again thy friendship, the gerund ingegnandosi evidently refers to the pronoun egli of the third person singular; while in the sentence, ál-le dôn-ne piá-cque di-par-tír-si dál-la vil-la, it pleased the ladies to go away from the villa, the infinitive dipartirsi refers to donne, i.e., to the third person plural. A complete conjugation, for example, of the present and past gerunds, being in all persons of frequent use, runs as follows: 1. 1301/a1. (237 +163)2 - 22577. = 160000 22577 137423 =required number. 137423 +22577-163 = 237. When an equation is reduced by extracting an even root of a quantity, the solution does not always determine whether the answer is positive or negative. But what is thus left ambiguous by the algebraic process, is frequently settled by the statement of the problem. EXERCISE 61.-MISCELLANEOUS PROBLEMS. 1. A merchant gains in trade a sum to which 320 pounds bears the same proportion as five times this sum does to 2500. What is the amount gained? 2. The distance to a certain place is such, that if 96 be subtracted from the square of the number of miles, the remainder will be 48. What is the distance? 3. If three times the square of a certain number be divided by 4, and if the quotient be diminished by 12, the remainder will be 180. What is the number? 4. What number is that, the fourth part of whose square being subtracted from 8, leaves a remainder equal to 4 ? 5. What two numbers are those, whose sum is to the greater as 10 to 7; and whose sum multiplied into the less produces 270 ? 6. What two numbers are those, whose difference is to the greater as 2 to 9, and the difference of whose squares is 128 ? 7. It is required to divide the number 18 into two such parts, that the squares of those parts may be to each other as 25 to 16. 8. It is required to divide the number 14 into two such parts that the quotient of the greater divided by the less, may be to the quotient of the less divided by the greater as 16 to 9. 9. What two numbers are as 5 to 4, the sum of whose cubes is 5103 ? 10. Two travellers, A and B, set out to meet each other, A leaving the town C at the same time that B left D. They travelled the direct road between C and D; and on meeting, it appeared that A had travelled 18 miles more than B, and that A could have gone B's distance in 154 days, but B would have been 28 days in going A's distance. Required the distance between C and D. 11. Find two numbers which are to each other as 8 to 5, and whose product is 360. 12. A gentleman bought two pieces of silk, which together measured 36 yards. Each of them cost as many shillings per yard as there were yards in the piece, and their whole prices were as 4 to 1. What were the lengths of the pieces ? 13. Find two numbers which are to each other as 3 to 2; and the difference of whose fourth powers is to the sum of their cubes as 26 to 7. 14. Several gentlemen made an excursion, each taking the same sum of money. Each had as many servants attending him as there were gentlemen; the number of crowns which each had was double the number of all the servants, and the whole sum of money taken out was 3456 crowns. How many gentlemen were there? 15. A detachment of soldiers from a regiment being ordered to march on a particular service, each company furnished four mes as many men as there were companies in the whole 15. a EXERCISE 54. 6. 123√7. 7. -y. 8.1-2. 9. a 2as + 2a + m3. m+ n 10.-184 (a+c) mn. 11. 120/a1, or Va 120 Ja 12. a111c = √ HISTORIC SKETCHES.—XLIX. THE FALL OF JERUSALEM. "O JERUSALEM, Jerusalem, thou that killest the prophets, and stonest them which are sent unto thee, how often would I have gathered thy children together, even as a hen gathereth her chickens under her wings, and ye would not! Behold, your house is left unto you desolate." So said the Redeemer of the world as he sat upon the Mount of Olives, and looked down upon the city which was soon to be the scene of his mortal sufferings. The remarkable utterances he had made touching the Temple-that seemingly indestructible fortress, church, and treasury, which his disciples in common with other Jews regarded with something like superstitious reverence had aroused the awful curiosity of his auditory, and they inquired of him privately when it should come to pass that "there shall not be left here one stone upon another that shall not be thrown down." The Lord's answer is well known, but cannot be too often repeated. Here it is purposely quoted in order to contrast the words of his prophecy with what actually came to pass. He warned his followers against the false Christs and false prophets that should arise, and then went on to describe in exact terms what happened to the city of David at the hands of Titus. He told how that Jerusalem should be encompassed with armies; that the abomination of desolation spoken of by the prophet Daniel should stand in the holy place, "and where it ought not," and that "there will be great distress in the land, and wrath upon the people; and they shall fall by the edge of the sword, and shall be led captive into all nations. There shall be great tribulation, such as was not from the beginning of the world to this time, no, nor ever shall be; and Jerusalem shall be trodden down of the Gentiles, until the time of the Gentiles be fulfilled. This generation shall not pass away till all these things be done." These words were spoken to the apostles with pain and grief. On yet another occasion-the most awful possible-did the Lord announce, with like feelings of sympathy and distress, the "days of vengeance' " which were coming upon the land. As he was led forth from Jerusalem to execution upon Calvary, a number of women followed, weeping. He turned to them, and said, "Daughters of Jerusalem, weep not for me, but weep for yourselves and for your children. For, behold, the days are coming in the which they will say, Blessed are the barren, and the wombs that never bare, and the paps which never gave suck. Then shall they begin to say to the mountains, Fall on us; and to the hills, Cover us. For if they do these things in the green tree, what shall be done in the dry? all the earth. So mild and equable was the Persian rule, that Cyrus (B.c. 536) issued a decree authorising the return of the exiles to their country. Upwards of fifty thousand persons, under the command of Zerubbabel, grandson of the last King of Judah, thus returned, and re-established themselves in Jerusalem. This city they had to rebuild, and to renew the temple which Nebuchadnezzar had razed to the ground. Joyfully they set to work, and bravely they persevered, till the holy city once more rose from its ruins, and the Temple, over which three years were spent by them, was again the glory of Judæa. Succeeding princes-Darius Hystaspes, Xerxes, and Artaxerxes-continued to manifest towards the Jews the same liberal policy which Cyrus inaugurated. Under the last-named prince, who is called in Scripture Ahasuerus as well as Artaxerxes, the people were in jeopardy of their national existence by reason of the malice of Haman; but saved from this danger through the intercession of Queen Esther, they received from the Persian king the most astonishing concessions. Ezra was allowed to return to Jerusalem with as many of the remaining exiles as chose to accompany him, and there to rule, both in matters of state and of religion, according to his own discretion. He restored the ancient services in the Temple, re-organised the whole Jewish polity, and during the thirteen years of his official life conferred many signal benefits upon his countrymen. In the year B.C. 445 Nehemiah, once cupbearer to the King of Persia, succeeded Ezra. He fortified the city, and strengthened its great natural defences, without causing jealousy to spring up in the minds of those at home, who saw also about this time the manifold dangers, especially on the side of Greece, which threatened the empire, and were not over-careful what was done in an outlying province like Judæa. After Nehemiah's death the province was included in the government of Syria, and the high priests administered the law in Jerusalem under the eye of Persian satraps. Alexander the Great, when he overthrew the Persian empire, received the Jews to favour; but after his death, and the subdivision of his kingdoms, there came a period of trouble and loss, which reminded the Jews of the days when Nebuchadnezzar made havoc of them. In the struggles which ensued between Alexander's generals for the mastery, Jerusalem suffered dreadfully; a hundred thousand captives were sent into Egypt and Libya, and great numbers of the unfortunate people were slaughtered at the storming of their city. Between Syrian and Egyptian and Greek, the Jews had an exceedingly bad time of it. Internal divisions, fomented by religious dissensions, weakened them still further, and under Antiochus, the Greek king of Syria, their sufferings culminated in the rebellion of Jason (B.c. 170). This man having been a renegade high priest, had been ousted at the instance of Antiochus, and a Egypt, Jason took the opportunity to rise in rebellion. Antiochus was not dead, but returning to Judæa, put Jason to flight, and marching upon the metropolis, took signal vengeance for what had been done. Forty thousand of the inhabitants were slain, and as many more sold into slavery. The Holy of Holies was entered; a sow, the unclean animal, was sacrificed in mockery on the altar; and every part of the Temple was sprinkled with the water in which the creature had been boiled, in very wantonness of profanation. The image of Jupiter was set up in the midst of the inner court, and all who would not worship it were tortured till they died or adored. The observ ance of the Sabbath was forbidden; the rite of circumcision wa proscribed; and those Jews who fled into the mountains and deserts rather than face the fury of persecution, were hunted out by the Syrian soldiers, and whenever caught were put to death. Little did those who heard these words understand the full and terrible meaning of them. Little could they have thought, experienced though they were in national calamities, how sweep-report having reached Jerusalem that Antiochus was dead in ing and complete was the destruction in store for their beloved Zion. Thirty-seven years passed after the crucifixion; men remained who had not "tasted death," though they had listened to the words of the Baptist and of Christ, and had been present probably at the martyrdom of some of the chief apostles; the generation that had cried "Crucify him! Crucify him!" was yet living in Jerusalem; many of those who had shouted, "His blood be on us and on our children! were yet alive to bear the burden they had clamoured to be laid upon them. Thirty-seven years, and the Fifth Legion was encamped on the Mount of Olives; the spot on which the crucifixion took place was held by the guards of Titus; and the Roman army, sixty thousand strong, encompassed Jerusalem round about, had cast their trenches about it, and closed it in on every side. In the last paper on the subject of the Jews, a sketch was attempted of the Jewish history down to the time when the Jews fell under the Persian yoke. Under Persian rule the people lived in comparative comfort, their religion respected, their laws and customs allowed, and their independence permitted to a very considerable extent. So long as they acknowledged the foreign supremacy, paid their tribute, and kept the imperial peace, they were allowed to go on much as before, save that they had no king, and, till Cyrus ruled, were detained in Babylonia. Theologically they reverted to their former position, in which God was their King, while they ever looked forward to the coming of the Messiah who should shake the yoke of bondage from off their necks, and, re-seated on the throne of David, govern the Jewish nation, which was then to be the greatest in Mattathias, of the Asmonean family, and of the high priest class, was witness of a forced attempt at sacrifice to Syrian idols, on the part of some Jews. The poor wretches were driven to sacrifice at the point of the sword, but Mattathias, disgusted at the profanation about to be offered, drew his sword, and slew his renegade countrymen. Instantly the other Jews present turned upon their oppressors, and having punished them, fled with Mattathias and his sons to the hills, where they were speedily joined by all who had courage left to lift hand against the Syrian. A regular war began. Mattathias, ably seconded by his sons, Judas and Jonathan, fought many decisive actions with the enemy, worsting him, and died just as he was contem plating the subjugation of Jerusalem itself. Judas Maccabæus, a large army into Galilee, besieged and stormed several of the his son, took the command, and after several great victories, took possession of Jerusalem, which he restored, and purified the Temple. In a tremendous battle with the Syrians Judas was slain, but his brother Jonathan succeeded to the command, and by his ability and prowess induced the Syrian monarch to agree to a treaty, by which, Jonathan being high priest, the province of Judæa remained in a state of quasi-independence. So it remained for nearly a century, the Asmonean princes (descendants of Mattathias) holding the supremacy, though frequently falling out among themselves, and destroying one another. About the year B.C. 75 there was a disputed succession. Hyrcanus and Aristobulus, brothers, each claimed the throne, and appealed to Pompey, who had just ended his war with the King of Pontus, Mithridates. Hyrcanus was but a tool in the hands of Antipater, an Idumæan, who had become a proselyte, and aspired to the high priesthood; and this man, in concert with the Romans, arranged that Hyrcanus should be nominal head, while all real power was in the hands of Antipater. So things came about, and as a reward for the services which Antipater rendered to Julius Cæsar in his struggle with Pompey, Herod, the Idumæan's second son, was made governor of Galilee. This was the same Herod who some years later, through the favour of Mark Antony, was made King of Judæa, and was married to Mariamne, a princess of the Asmonean house. The tyrannical and cruel conduct of Herod is well attested, if by nothing else, by the Massacre of the Innocents, to ensure that he who was announced as the future King of the Jews should not survive; but he murdered also the high priest Hyrcanus, his own wife, and several of his own sons, and did other brutal things which stamped him for the fiend he was. After his death his sons, unable to agree among themselves, unable also to hold in hand the provinces committed to them, were deposed, and Judæa was made an integral portion of the Roman empire, under a procurator, the first being Pontius Pilate, who entered upon his government about A.D. 20. The great event of Pilate's administration was the death of our blessed Lord. By that act, the Jews, who voluntarily assumed the responsibility, filled up the measure of their wrath, and testifying that they were the children of those who killed the prophets, were condemned to pay the penalty of "all the righteous blood shed upon the earth, from the blood of righteous Abel unto the blood of Zacharias, son of Barachias, whom they slew between the porch and the altar." The warnings given not only by prophets, but by Christ himself, were many and distinct. Nothing could be plainer than the voice in which the result of conduct like that exhibited by the Jews continuously was made audible; indeed, it was the plainness of the speech that formed the leading feature in the charge which met with such ready concurrence from the populace before the crucifixion. Thirty-seven years after the last warnings were uttered, the disasters foretold were accomplished with dreadful exactitude. A succession of weak governors came after Pilate, who was disgraced and banished into Gaul for the misgovernment of his province, and the result was continued disturbances of the peace in Judæa, a general lawlessness which accustomed the people to insurrection, and in the end an outburst of fanaticism and patriotism combined, which threw down the gage to the strength of the whole empire. About A.D. 67 the Jews became desperate under the many insults offered to their religion and nation, and attacking the Roman garrisons in different parts of Judæa, overpowered them, slew all who surrendered, and made reconciliation, even upon full submission, impossible. The Roman governor of Syria marched against them, but was compelled to retreat, and it became necessary to employ the strength of the empire in repressing the revolt of the provincials. Nero was Emperor of Rome at the time, and, conscious of the importance of subduing at once and effectually a rising in so conspicuous a part of the empire as Judæa, directed Vespasian, who was in command of his chief army, to march against the rebels, and to inflict a signal punishment. Punishment was to be the more severe that the Roman troops hitherto sent against the Jews had by their retreat, and by several battles they had lost, tarnished the reputation of the imperial arms, and it was of paramount necessity to restore the prestige of the discomfited eagles. Vespasian accordingly marched with principal towns, and drove the malcontents to Jerusalem for refuge. When about to take steps for the reduction of the city, the news reached him that Nero was dead, and that Galba was proclaimed in his stead; then that Galba was murdered, and that Otho had donned the purple. Unwilling to do anything which might prove of vital imperial importance without specific orders from Rome, Vespasian stayed his onward march, and sent his son Titus to learn the commands of the new emperor, waiting meanwhile his return at Cæsarea; but Titus stopped short in his journey, and went back to his father about the time that Vitellius seized upon the throne, in the vacancy caused by the overthrow of Otho. The interval was occupied in reducing all the remaining posts held by the Jews in Judæa, and in preparation for the final swoop which was to make the city that stoned the prophets desolate." Meanwhile the public troubles increased at Rome to such an extent as to make it necessary to find some "still strong man," who should once more save the Capitol, and remove from the seat of empire the scandal occasioned by the administration of Vitellius. The officers of the army, who were really the governing body, held numerous meetings, and declared for their own commander, Vespasian, to whom they offered, not only the imperial crown, but their own lives and services in making good his pretensions to it. The action consequent upon Vespasian's acceptance of the offer necessarily took him away from the seat of war in Judæa. Jerusalem was for awhile preserved, or rather, was for yet a longer time given up to those many internal dissensions which threatened to anticipate the work of the avenging Romans. For the city was divided against itself in a way that would have ensured its destruction without the intervention of any foreign foe. John of Gischala headed a numerous faction, called the Zealots, but more fitly described as the robbers, who lived upon rapine, and were a terror to all who had anything to lose. These men, driven in from the country by the cordon of Roman troops ever narrowing round Jerusalem, were an enormous drain upon its resources, while the open war they kept up with other factions made them perpetually a source of dread and anxiety to the rest of the inhabitants. Opposed to them in about equal numbers were the faction of Simon, son of Gioras, a body of men gathered from the desperadoes who infested Judæa, and committed to interminable war with the rest of their countrymen who did not acknowledge the supremacy of Simon. There was also the faction of Eleazar, the high priest, who collected about him a considerable band with which to defend the upper part of the Temple. These three sets of marauders possessed the city, and regardless of the sacred ties which bound them to one another, regardless of the approach of the common enemy, waged war upon each other, and slew thousands of those who should have been available for the defence of Jerusalem. Stores of provisions which the care and prudence of the citizens had gathered in the city, to guard against such a day as was coming upon them, were wantonly destroyed by these domestic foes, the very wheat which would have sufficed the garrison for many months being burned in one of the encounters. It was under circumstances like these that Vespasian directed his thoughts to Jerusalem, as soon as he felt himself firmly seated on the imperial throne. To the command of the army in Judæa he appointed Titus, with orders to press the siege of the capital rigorously, and to compel it to make submission. Titus forthwith set his troops in motion, and finding no resistance in the open country, marched at once upon Jerusalem at the time when it was filled with strangers and people from the provinces, who had come up to celebrate the feast of the Passover. these persons were so many more consumers of provisions, while many of them were unable to give the slightest assistance in the defence of the city. All So swift was the Roman march, that little opportunity was given for the inhabitants to withdraw themselves. Some, however, including the Christian part of the community, fled betimes to Pella, and so avoided the vengeance, "not a hair of their heads being injured." Titus marched to Jerusalem, and decided by the ease with which he penetrated through the adjacent country, thought to have made it an easy prey. Indeed, so little did he reckon upon a substantial resistance, that he advanced, unsupported by his cavalry, and attended only by his |