gallons in the smaller cask. Required the number of gallons in each, and the price by the gallon.

17. If the square of a certain number be taken from 40, and the square root of this difference be increased by 10, and the sum be multiplied by 2, and the product divided by the number itself, the quotient will be 4. What is the number?

18. A person bought a certain number of oxen for 80 guineas. If he had received 4 more oxen for the same money, he would have paid one guinea less for each. Find the number of oxen. 19. It is required to divide 24 into two such parts that their product shall be equal to 35 times their difference.

20. The sum of two numbers is 60, and their product is to the sum of their squares as 2 to 5. What are the numbers ?

21. Divide 146 into two such parts, that the difference of their square roots may be 6.

22. What two numbers are those whose difference is 16 and their product 36?

23. Find two fractions whose sum shall be, and the sum of their reciprocals 6 times as much.

24. Required to find two numbers whose difference is 15, and half of their product is equal to of the cube of the less number.

25. A company incurred a bill of £8 8s. One of them absconded before it was paid, and in consequence those who remained had to pay four shillings apiece more than their just share. How many were there in the company?

26. A gentleman bequeathed £7 4s. to his grandchildren; but before the money was distributed two more were added to their number, and consequently the former received one shilling spiece less than they otherwise would have done. How many grandchildren did he leave?

27. The length added to the breadth of a rectangular room makes 42 feet, and the room contains 432 square feet. Required the length and breadth.

28. A says to B, "The product of our years is 120; and if I were 3 years younger, and you were 2 years older, the product of our ages would still be 120." How old was each?

29. Should the square of a certain number be taken from 89, and the square root of their difference be increased by 12, and the sum multiplied by 4, and the product divided by the number itself, the quotient will be 81. What is the number?

21

walk is the same as the area within the walk. Required the breadth of the space between the wall and the walk.

40. A and B started from two cities 247 miles apart, and travelled the same road till they met. A's progress was 1 mile per day less than B's, and the number of days before they met was greater by 3 than the number of miles B went per day. How many miles did each travel?

41. Two persons, A and B, invest £2,000 in business. A's money remained in trade 17 months, and he received £1,710 for his share of the profit and stock; B's money was in trade 12 months, and he received £1,040 for his share of the profit and stock. What was each partner's stock?

42. A merchant bought a piece of cloth for 162 florins; the number of shillings which he paid per yard was of the number of yards. Required the length of the cloth, and the price per yard.

43. There was a cask containing 20 gallons of wine; a quantity of this was drawn off and put into another cask of equal size, and then this last was filled with water; and afterwards the first cask was filled with the mixture from the second. It appears that if 6 gallons are now drawn from the first and put into the second, there will be equal quantities of wine in each cask. How much wine was first drawn off ?

44. A man bought 80 lbs. of pepper and 100 lbs. of ginger for £65, at such prices that he obtained 60 lbs. more of ginger for £20 than he did of pepper for £10. What did he pay per pound for each?

EXERCISE 64.

1

5. (√2 + a + 26).

6. (±√h-n+4-2)2.

7. (±√16+ a + b - 4).

EXERCISE 65.

2

21. 4 or 7.

22. 243 or 28.

13. 4 or 1.

.

14. 1 or 1 ±2/15. 15. 4 or 1.

16. 4,-8, or 1-43 -37-7

17. 9, 4, or

2

8. 1 or 28. 9. 4 or 1.

18.(

23. 4 or 24. 9a or 25. 9 or 26. 2 or 27. 2 or

25. a. 12. 3. 144.

10. 49 or 401.

and breadth?

32. What number is that, which being added to its square

root will make 156?

33. The circumference of a grass plot is 48 yards, and its area is equal to 35 times the difference of its length and breadth. What are its length and breadth ?

34. A gentleman purchased a building plot, and in the centre dit erected a house 54 feet long and 36 feet wide, which covered just one-half his land. This arrangement left him a fower-border of uniform width all round his house. What was the width of his border, what the length and breadth of his plot, and how much land did he buy?

35. A general wished to arrange his army, which consisted of 30,886 men, in a solid body, so that each rank should exceed ach file by 59 men. How many must he place in rank and file? 36. A man has a painting 18 inches long, and 12 inches wide, which he orders the cabinet-maker to put into a frame of uniform width, and to have the area of the frame equal to that of the painting. Of what width will the frame be?

37. A man having to walk 54 miles, finds that if he increases his speed half a mile per hour, he will perform his task 14 hours sooner than if he walked at his usual rate. Find that rate.

38. A merchant sold a quantity of goods for £39, and gained 18 much per cent. as the goods cost him. How much did he pay for the goods?

39. Suppose in a garden, 400 feet long and 300 feet broad, there is a walk 10 feet wide all round the garden, equidistant from and parallel to the wall, and that it divides the garden into two equal parts; that is, the area betwixt the wall and

(m± √ in2 + +4P) 4p)

2

LESSONS IN LATIN.-LII.
GOVERNMENT BY VERBS.

A VERB may govern a noun; for example

Amo filium, I love a son.

Here the noun filium is dependent on the verb amo; by the force of the verb amo, the nominative form, filius, is changed into filium, the accusative form, or the form of the object.

With the noun, one pronoun or more may be connected; also one adjective or more; in which case the pronoun and the adjective will be in the same gender, number, and case as the noun, presenting an instance of concord or agreement; as

Amo filium meum minorem natu, I love my younger son. Instead of a noun, the object of a verb may be a pronoun; asAmo te, I love thee.

All verbs do not govern nouns. In general, the verbs which govern nouns are transitive verbs in the active voice. Intransitive verbs, inasmuch as their action does not pass over to an object, do not govern nouns.

genitive, the dative, the accusative, the ablative. Here you see in the Latin a great divergence from the English, in which the object is always in the accusative or the objective (so called from its being the case of the object) case. I subjoin instances of each of these governments:

VERBS WITH THEIR GOVERNMENTS.

1. The Object in the Genitive.-Miserere mei, pity me.

2. The Object in the Dative.-Medetur OCULIS, he cures the eyes. 3. The Object in the Accusative.-Docet PUEROS, he teaches boys. 4. The Object in the Ablative.-Fungitur MUNERE, he performs (his) duty.

Some verbs have in the same sentence two governments; as in this example :

Docet PUEROS MUSICAM, he teaches the boys music.

A verb may also have two objects in unlike cases; asDat librum puero, he gives a book to the boy. Both librum and puero depend on dat, and consequently dat is said to govern them. The general rule may be given in

these terms

Transitive verbs in the active voice have two governments, the near and the remote; the near is the accusative, the remote is the dative.

The same verb may govern two different cases; as

Sapiens eget nullâ RE, the wise man wants nothing.
Egrotus eget medicine, the sick man wants medicine.

The verb eget takes, in one sentence, the ablative; in another, the genitive. These diversities of form generally involve some diversity of signification. Egeo signifies to be without, not to have; also to need, to require. In the first sense egeo takes an ablative the ancient wise man could be without nothing, for he possessed all things, inasmuch as he wanted (wished for) nothing. The sick man, on the contrary, has occasion for medicine, inasmuch as he is sick.

The two meanings are so much alike that they are sometimes exchanged the one for the other; thus we may find medicina in the ablative, and the genitive employed when the ablative might have been expected.

Having given a general view of the government of verbs, I shall take up each case in succession; and first,

VERBS WHICH GOVERN THE GENITIVE.

Verbs which denote an active or quiescent state of the feelings require their object to be in the genitive case; such as misereor, miseresco; as

EORUM MISERERI oportet, it is proper to pity them. Instead of a verb, you may have an adjective with est; asEst PATIENS laboris, he is enduring of (he endures) labour. Certain impersonal verbs take a genitive together with an accusative for their object; as

Piget ME STULTITIÆ, I am ashamed of my folly.

This, literally rendered, is, it shames me of my folly, showing a compound object to the verb piget.

A neuter pronoun, corresponding in relation with the noun in the genitive, stands in the accusative; as

ID ne pudet te? art thou not ashamed of that?

Verbs which signify to remember and to forget, also to remind and to admonish, take their object in the genitive. Such words are memini, I remember; reminiscor, I call to mind; recordor, I recollect; obliviscor, I forget; moneo, I put thee in mind; admoneo, I admonish; commoneo, I advise; commonefacio, I

warn; as

tive. Recordor may also have after it the preposition de, with its case.

Instead of the simple verb, we may have its equivalent in an adjective, and the copula est. Thus, instead of he forgets, we may say, he is forgetful. Consequently, a number of adjectives denoting states of mind are followed by the genitive; as, prudens (for providens), foreseeing, prudent; gnarus, knowing; peritus, skilful; conscius (knowing with), conscious, aware of; rudis, destitute of, untrained; memor, mindful.

Here we may place the phrase certiorem facere, to inform, which has a genitive object; as

Certiorem me fecit tui CONSILII, he informed me of thy plan. Some adjectives are denominated verbal, inasmuch as they are derived from verbs, and have a verbal meaning; thus, edax, ' from edo, I eat, signifies eating. Verbal adjectives in ax, as, capax, edax, ferax, rapax, tenax, govern a genitive case; as, tenax propositi, firm to (his) purpose. Certain participles, also, when used as adjectives, take a genitive-as, amans patriæ; appetens gloriæ; diligens veritatis; metuens futuri; sitiens sanguinis. The participle differs from the adjective in this, that while the participle denotes a single act, the adjective denotes an habitual state. When, then, these participles are used as participles, they require the government of the verbs to which they belong. Sitiens, employed as an adjective, has a genitive; but when used as a participle, it governs an accu sative like its verb; as

Tiberius sitiens SANGUINEM, Sejanum interfici jussit.

Tiberius, thirsting for blood, commanded Sejanus to be put to death. Verbs which denote fulness, abundance, or want, take their object in the genitive case. Adjectives of similar import govern a genitive case; as-

Adolescentem suæ TEMERITATIS implet. He fills the youth with his own rashness. This is an instance of a verb with a double object, an accusative of the person, and a genitive of the thing.

The verb potiri, to make yourself master of, takes the genitive in the phrase rerum potiri, to seize the helm of government, to obtain power over; though generally potiri requires the ablative.

Adjectives, too, denoting such a state of mind as is implied in having power, possessing ability, or the reverse, take a genitive after them. Hence arises combinations which the student may be glad to see translated-as, virtutis compos, endued with virtue; mentis impos, weak of (in) mind; sui potens, master of himself; exsors culpæ, free from blame; rationis particeps, sharing in the possession of reason; rationis expers (ex and pars), having no part, no share, that is, devoid of reason.

The adjective proprius, denoting that which belongs or peculiar to a person, takes a noun after it in the genitive case ; as in this example :

VIRI PROPRIA est fortitudo, courage is a property of man. special property of an object; as— So proprium in the neuter is employed to designate the

Id est vitium SENECTUTIS PROPRIUM, this is the special fault of old age. By an ellipsis of proprius you may explain what is commonly called the genitive of possession or quality; as

Hic liber FRATRIS mei est, this book is my brother's. VIRORUM FORTIUM est dolorem pati, to bear grief is the part of brave men. Vir est SUMME PIETATIS, he is a man of the greatest piety. The quality is sometimes put in the ablative; asAristoteles vir erat SUMMO INGENIO. Aristoteles was a man of the greatest ability. Allied with the usage of proprium is the phrase nostrum est, vestrum est, meum est, etc.; as—

NOSTRUM EST parentes amare. It is our duty to love our parents.

We also

CINNAM MEMINI, Syllam vidi, I remember Cinna, I saw Sylla.

This is specially the case if the object is a pronoun in the neuter gender. Recordor, I call to mind, requires an accusa

From the idea of partaking or sharing in anything seems to

accused of; manifestus, proved guilty (Scotch, proven); noxius, criminal, liable to punishment; compertus, detected; as

Manifestus est RERUM CAPITALIUM.
He was clearly convicted of a capital crime.

And hence is explained the genitive used with verbs which signify to accuse, acquit, condemn. With such verbs, the crime is in the genitive, and the person accused or acquitted is in the accusative; as-

Ne quis ante ACTARUM RERUM accusaretur.
Let no one be accused of former deeds.

23

The penalty to which a convicted person was condemned may be in the genitive or in the ablative; for example

1. Genitive.-Damnavit eos CAPITIS, he condemned them to death. 2. Ablative.-Damnavit hostem TERTIA PARTE agri, he condemned the enemy (to lose) the third part, etc.

As the penalty, so the price is put in the genitive or the ablative. If the exact sum paid for an object is stated, it must be in the ablative case. If any indefinite word is employed, that word is put in the genitive; as

QUANTI emisti librum? CENTUM ASSIBUS.

For how much did you buy the book? a hundred asses.

In a similar manner the genitive is used after verbs which denote to value, esteem, or regard; as

Diviti a sapienti viro MINIMI putantur.
Riches are little thought of by a wise man.

In

This genitive bears the name of the genitive of price. agreement with it stand several neuter adjectives, used substantively, in the genitive case: for example, magni, at a great price, or greatly; pluris, more, for more; maximi, at a very great price, very dear; so plurimi; also parvi, minoris, minimi; quanti? how much? tanti, so much; tanti quanti, so much as; tantidem, for the same sum; quantivis, for whatever you please; nihili, of no value; flocci (floccus, a lock of wool), as in flocci facere, not to care a straw for; nauci (naucum, a trifle), as in homo non nauci, a worthless fellow; pili (pilus, a hair), as in non facit pili cohortem, he does not value the cohort a bit; pensi (pensum, a task), as in pensi habere, to care for; assis (as, a small Roman coin), as in non assis facere, not to care a farthing for.

LESSONS IN GEOLOGY.-XXIII.

THE JURASSIC FORMATION-OOLITE.

To the Oolite is attached a peculiar interest since William Smith, "the father of English Geology," lent his sagacious mind to tabulate its subdivisions first.

It runs in a band, varying from thirty to ninety miles in breadth, from the Yorkshire coast, a little south of the Tees, to Lyme Regis in Dorsetshire. When we cross this belt, passing from the south-east to the north-west, we find it consists of three series of low hills separated by considerable valleys. The three hills are the three divisions of the systemthe Upper, Middle, and Lower Oolite; whilst the clays of the formation are to be found in the valleys, a fact which points to the reason of the existence of the hills and dales. The following is a table of the members of the system :

tonshire it gives evidence of a more decidedly marine deposit, assuming more of a sandstone character. In Oxfordshire, as at Colley weston near Peterborough, the Stonesfield slate is rich in organic remains. Several insects have been discovered, and the wing-covers of beetles, beautifully preserved, indicating a close proximity to the land. But by far the most celebrated fossils yielded by the Stonesfield slate are the jaws of certain small mammiferous quadrupeds, which at least indicate the existence of three distinct genera, the Amphitherium, Phascolotherium, and Stereognathus (Fig. 113). The fact that

the jaw-bone is in one piece indicates that it did not belong to a fish or to a reptile. The number of teeth, their double fangs, and the complicated crowns of the molars, besides the peculiar structure of the hinge of the jaw, all tend to show that the creature was a mammal.

It was noticed that the lowest process or projection at the hinge end of the jaw was bent inwards. Now the marsupial quadrupeds, which are the stepping-stone between creatures who bring forth their young alive and those who propagate their species by eggs, have this peculiarity of the jaw-bone; hence the mammals of the Stonesfield slate were pronounced to be marsupials; but this cannot be affirmed, for the bend of the process is not great, and there are certain placental mammals whose lower jaw exhibits a certain inflection of the pro

cess.

The flora of the era was extensive, as may bo gathered from the fact that at Brora, in Sunderlandshire, there is the thickest stratum of coal found in any English secondary rock. It has been mined for a long period, the bed being three and a-half feet thick.