that subcontrary propositions cannot both be false.

5. Show by means of the subcontrary propositions that contrary propositions may both be false. 6. What quantity would you assign to each of the following propositions?

(1) Knowledge is power.

(2) Nebulæ are material bodies.

(3) Light is the vibration of an ether.

(4) Men are more to be trusted than we think.

(5) The Chinese are industrious.

7. Why is it desirable in controversy to refute a statement by its contradictory and not by its contrary?

LESSON X.-Conversion and Immediate Inference.

I. Define inference and conversion.

2. What are converse and convertend propositions? 3. State the rules of valid conversion.

4. Name all the kinds of conversion.

5. By what process do we pass from each of the following propositions to the next?

(1) No knowledge is useless.

(2) No useless thing is knowledge.

(3) All knowledge is not useless.

(4) All knowledge is useful.

(5) What is not useful is not knowledge.
(6) What is useless is not knowledge.

(7) No knowledge is useless.

6. Give the logical opposites of the following proposition, and the converse of its contradictory :— "He cannot become rich who will not labour."

7. Apply negative conception to the proposition “All men are fallible;" then convert and show that the result is the contrapositive of the original.

8. Classify the propositions subjoined into the four

following groups:—

a. Those which can be inferred from (1).

b. Those from which (1) can be inferred.

c. Those which do not contradict (1), but cannot be inferred from it.

d. Those which contradict (1).

(1) All just acts are expedient acts.
(2) No expedient acts are unjust.
(3) No just acts are inexpedient.
(4) All inexpedient acts are unjust.
(5) Some unjust acts are inexpedient.
(6) No expedient acts are just.
(7) Some inexpedient acts are unjust.
(8) All expedient acts are just.
(9) No inexpedient acts are just.

(10) All unjust acts are inexpedient.

(11) Some inexpedient acts are just acts.
(12) Some expedient acts are just.
(13) Some just acts are expedient.

(14) Some unjust acts are expedient.

LESSONS VIII. IX. and X.-Examples of Propositions.

The reader is desired to ascertain the logical character of each of the following propositions; he is to state of each whether it is affirmative or negative, universal, particular, singular or indefinite, pure or modal, exclusive or exceptive, &c.; when irregularly stated he is to reduce the proposition to the simple logical order; he is then to convert the proposition, and to draw immediate inferences from it by any process which may be applicable.

(1) All birds are feathered.

(2) No reptiles are feathered.
(3) Fixed stars are self-luminous.

(4) Perfect happiness is impossible.

(5) Life every man holds dear.

(6) Every mistake is not a proof of ignorance. (7) Some of the most valuable books are seldom read. (8) He jests at scars who never felt a wound. (9) Heated metals are softened.

(10) Not one of the Greeks at Thermopylæ escaped. (11) Few are acquainted with themselves.

(12) Whoso loveth instruction loveth knowledge. (13) Nothing is harmless that is mistaken for a virtue. (14) Some of our muscles act without volition. (15) Metals are all good conductors of heat. (16) Fame is no plant that grows on mortal soil.

(17) Only the brave deserve the fair.

(18) No one is free who doth not command himself. (19) Nothing is beautiful except truth.

(20) The wicked shall fall by his own wickedness. (21) Unsafe are all things unbecoming.

(22) There is no excellent beauty that hath not some strangeness in the proportion.

(23) It is a poor centre of a man's actions, himself.
(24) Mercy but murders, pardoning those that kill.
(25) I shall not all die. (Non omnis moriar.)
(26) A regiment consists of two battalions.
(27) 'Tis cruelty to load a falling man.
(28) Every mistake is not culpable.
(29) Quadrupeds are vertebrate animals.
(30) Not many of the metals are brittle.

(31) Many are the deserving men who are unfortunate. (32) Amalgams are alloys of mercury.

(33) One kind of metal at least is liquid.

(34) Talents are often misused.

(35) Some parallelograms have their adjoining sides

(38) A man's a man.

(39) Heaven is all mercy.

(40) Every one is a good judge of his own interests. (41) All parallelograms have their opposite angles equal. (42) Familiarity breeds contempt.

(43) No one is always happy.

(44) Every little makes a mickle.

LESSON XI.-Logical Analysis of Sentences.

1. How does the grammatical predicate differ from the logical predicate?

2. Distinguish between a compound and a complex sentence; and between coordinate and subordinate propositions.

3. Enumerate the grammatical expressions which may

form

(1) A subject.
(2) An attribute.

(3) A predicate.

(4) An object.

(5) An adverbial.

4. Examine the following sentences, ascertain which are compound or complex, and point out the coordinate or subordinate propositions.

(1) Happy is the man that findeth wisdom, and the man that getteth understanding.

(2) Heat, being motion, can be converted into mechanical force.

(3) Ceres, Pallas, Juno, and Vesta are minor planets, or asteroids.

(4) Knowledge comes, but wisdom lingers.

(5) Fortune often sells to the hasty what she gives to those who wait.

(6) Thousands at His bidding speed,

And post o'er land and ocean without rest;
They also serve who only stand and wait.

(7) Pride that dines on vanity, sups on contempt.
(8) Nobody can be healthful without exercise, neither
natural body, nor politic.

(9) Nature is often hidden, sometimes overcome,
seldom extinguished.

(10) It is impossible to love and be wise.

(11) Though gods they were, as men they died. (12) He that is not industrious envieth him that is. (13) Ye are my friends, if ye do whatsoever I command you.-John xv. 14.

(14) The wisdom that is from above is first pure, then peaceable, gentle, and easy to be intreated, full of mercy, and good fruits, without partiality, and without hypocrisy.-James iii. 17. 5. Analyse in the form of a scheme or diagram any of the following sentences:

(1) The first aphorism of Bacon's Novum Organum, on p. 229.

(2) Some judgments are merely explanatory of their subject, having for their predicate, a conception which it fairly implies, to all who know and can define its nature.

(3) There be none of the affections which have been noted to fascinate or bewitch, but love and envy: they both have vehement wishes; they frame themselves readily into imaginations and suggestions; and they come easily into the eye, especially upon the presence of the objects, which are the points that conduce to fascination, if any such there be.

Further examples for analysis must be sought in Dalgleish's Grammatical Analysis, with Progressive Exercises. (Oliver and Boyd.) Edinburgh, 1866. Price 9%.