Et latet et lucet Phaëthontide condita gutta, Ut videatur apis nectare clausa suo. Credibile est ipsam sic voluisse mori. Flentibus Heliadum ramis dum vipera serpit, Fluxit in obstantem succina gemma feram ; Concreto riguit vincta tepente gelu. Vipera si tumulo nobiliore jacet. With what interest, too, do we read the lines of one who was an eyewitness of the devastation made by the first great eruption of Vesuvius, in the year after Christ 79. Strabo, who wrote not long before, had spoken of the mountain as environed by most beautiful fields, but cindery in its aspect, “so that," he says,* one might conjecture that the place was the scene of a great conflagration, and had fire-craters, which have since been extinguished by the deficiency of the feeding matter :” Thus then Martial (iv. 44): Hic est pampineis viridis modo Vesbius umbris, Presserat hic madidos nobilis uva lacus. Hoc nuper Satyri monte deders choros. Hic locus Herculeo numine clarus erat. Nec Superi vellent hoc licuisse sibi. Vesuvius this, so late with vineyards green, E’en angry gods ne'er knew such vengeance dire. There is a very touching epigram (ii. 66) on a poor slave cruelly struck by her mistress for a trifling fault in dressing her hair. It shows Martial to have been a man of humanity, and superior to the common views of the Romans on the subject of slavery : One single curl beyond its bounds had strayed ; * Lib. v. cap. iv. Let scissors clip, or asps among it sit, Then, then her face that mirror shall befit. The following has an elegant simplicity (v. 42) : Callidus effracta nummos fur auferet arca, Prosternet patrios impia flamma lares ; Non reddet sterilis semina jacta seges. Mercibus extructas obruet unda rates. Quas dederis, solas semper habebis opes. The fire your home lay low, Your farm no crops bestow. Which to your friends is given; Is what you've lent to beaven. There is at once a fine pathos and a keen satire in the following (v. 37); written on the untimely death of a fair verna, or slave-girl, in the poet's family. The sincere grief for one in the humblest station is contrasted with the “mockery of woe” which a hypocrite assumes on getting rid of a wealthy wife : More charming than the swan with plumage grey, Softer than lambkin from Tarentum's stream, More glowing than the eastern gem's bright gleam ; Or freshest snows that lily-leaves emboss ; Than Rhenish top-knots or the ermine's gloss; Or Attic honey from the comb run bright: The squirrel dull, the phonix no rare sight, Whom the stern law of over-grasping fate, My love, my sport, my only joy of late. And while he beats his breast and rends his hair, I've lost a wife, and yet to live I dare, O Pætus, Pætus, stoic that thou art, And yet to live awhile canst find the heart ! The following piece of banter is exquisite in its way (xi. 18); Lupus ! a farm near town you gave to me; The savour that your kitchen yields, would be. We must apologize for concluding with a sorry pun ; but the play in the original between pradium and prandium, is not a whit better, if it be not two or three degrees worse. One more extract (i. 109) and we have done. It is on a pet lapdog, and was probably composed in imitation of Catullus's well-known ode, * Passer deliciæ meæ puellæ.” Issa 's more full of sport and wanton play That he will raise and lift her from the bed. Both real or both depicted you would say. If there are two Roman writers who show forth imperial Rome in its living reality, its social habits, its morality, its luxury, its domestic relations; if there are any two who, in a remarkable manner, illustrate each other; if there are two of congenial talent, sentiment, and poetical aspirations ; if, in fine, there are any two who must be studied together, not merely as friends and contemporaries, but as the only great poets of the silver age, those two are Juvenal and Martial. The former is much and diligently read in schools and colleges ; we repeat, that the latter has not yet found his proper place in either. ARITHMETICAL NOTES AND QUERIES. TO THE EDITOR OF THE ENGLISH JOURNAL OF EDUCATION. SIR, It has often struck me, while examining children in our elementary schools on arithmetic, that they might be familiarized with the principles and some of the more obvious applications of the higher rules while they are learning the simple and compound rules. Indeed it appears to me that the authors of all the works on arithmetic that have come under my notice, purposely keep the student in the dark concerning the more advanced rules, purely for the sake of classification ; for a little reflection will show that, while professedly occupied solely with the simple and compound rules, they are unconsciously working proportion and fractions. As your object is, less to explain and propagate existing methods of instruction, than to try to improve them by means of criticism, I have thought that you may, perhaps consider my Arithmetical Notes and Queries worthy of a place in your Journal. Should they also be fortunate enough to elicit the opinions of any of your readers who are engaged in education, both your purpose and my own will be fully answered. First, then.- Why is the notation of decimals reserved for that peculiar section of arithmetic? Why should it not be taught together with the notation of integers ? If they were two different systems, their separation would be reasonable, but they are precisely the same. They form an unbroken series, of which each term is ten times the value of its neighbour on the right, and one tenth of the value of its neighbour on the left. The former is its decuple, and the latter its decimal. The only reason why the notation of decimals appears to differ from that of integers is, that they are numerated in opposite directions. But this is only because, for obvious reasons, the unit is taken as the point of departure ; and if the numeration of integers be taught as it ought to be, this will not occasion any difficulty. For the pupil should be taught to numerate from millions to units as well as from units to millions. Thus, in a number composed of integers and decimals, such as 4506.234, he would numerate from the thousands down to the thousandths. After a little practice all the strangeness of decimal numeration would disappear, and a child would not be more puzzled to read or note •0005 than 50000. The perception of the analogy which exists between the two would, however, be greatly facilitated by placing the decimal point over the units, as follows, 500000005. By this method of instruction a decimal would become as clear and familiar an idea as an ordinary number. Decimals should also be introduced among the examples in the simple rules, either alone or connected with integers. In teaching division, however, it would be necessary to confine the decimals to dividends, on account of the difficulty of dividing by a decimal. This would be left for the special treatise on Decimals. I would, secondly, inquire, why all the opportunities presented by simple division for giving a notion of ratio proportion and vulgar fractions should be thrown away, as they are in our books on arithmetic. When a boy has worked a sum in that rule, he might, surely, be informed that the quotient he has found is the ratio between the divisor and the dividend, and the idea of ratio might be explained to him. After that, two sums might be given out, resulting in the same quotient, and he might be made to observe that, in these sums, the ratio between the first divisor and the first dividend, and that between the second divisor and the second dividend, were the same ; and he might be informed that, when this is the case, the four numbers in question are said to be in proportion. After the idea of proportion has been well explained, examples might be given for practice in finding the ratios, both on slates and mentally, in the latter of which exercises children very soon become expert. After a sum in division has been worked, the divisor and dividend might be multiplied by the same number, and the division worked over again with these products. It would then be shown that the quotient or ratio was unaltered, and the reason of it would be easily explained. The conclusion would then be drawn that, for the same reason, the quotient will not be altered if the divisor and dividend be divided by the same number. And in all the subsequent examples in this rule the pupil might be taught to find the common factors in the divisor and dividend, and strike them out before beginning the division. With equal ease might a notion of vulgar fractions be conveyed by means of division. Give some examples in that rule in which the divisors progressively increase, the dividend remaining the same, till, in one case, they are equal. Show that the quotient, or ratio, between these two equal numbers is unity; that it is so in all similar cases; and that equality is but a particular case of proportion. I need not detail the method of of proving from this that, where the divisor is greater than the dividend, the quotient will be less than unity. That quotient is a fraction, and the pupil, acquainted with decimals, will easily find it by executing the division. A vulgar fraction will then be shown to be nothing but the |