But it is generally reckoned that they oppose when they differ in quality only. They are divided, according to quantity and quality, into four classes, named A, E, I, O; A stands for universal affirmative, E universal negative, I particular affirmative, and O particular negative.

Q. How does the truth or falsity depend upon the matter?

A. The matter of a proposition means the real connexion of the terms in respect of their meaning. There are three kinds of matter, -necessary, impossible, and contingent; and in each of these the propositions are either true or false. In necessary matter, where we cannot avoid the predicate being applicable to the subject, both the universal and particular affirmatives are true; in impossible matter, we cannot believe the predicate applicable to the subject, hence both the negatives are true, and affirmatives false; and in contingent, we cannot affirm or deny universally the predicate of the subject, and of course, both the particulars are true. Thus we see both the contraries, namely A and E, in contingent matter false, and the subcontraries, I and O, true. The subalterns may be both true or both false.

BHAIROWNATH MANGESH.

4. Q. State and prove the six rules of syllogism?

A. Rule 1st,-A syllogism must have three and only three terms. 2nd, It must have three and only three propositions. 3rd,-It must have only one middle term; which should be univocal, and it must be distributed in one of the premises, or there should be no fallacy of undistributed middle term, for if we have two middle terms there will be four terms in a syllogism, which violates the first rule ; when we have the middle term undistributed, we compare the major and minor terms with part of the middle term, and so we cannot say that they are compared with the same part of the middle term, and therefore we cannot draw the conclusion. 4th,--The term which was undistributed in the premise should not be distributed in the conclusion, or there should be no " illicit process," for if the term which was undistributed in the premise be distributed in the conclusion, there will be properly speaking two middle terms, which violate the third rule. 5th,-One premise at least must be affirmative, for if we have two negative premises, then the two terms which disagree with the same third cannot be said to agree with one another,

and consequently, if we have two negative premises we cannot draw the conclusion. 6th,-If one of the premises be negative the conclusion must be negative, for if it not be it violates the second canon.

GANPAT MADOWJI.

5. Q. How many moods are possible?-show that only eleven satisfy the rules of syllogism.

A. There are four propositions, namely A, E, I, and O; now the combination of each of them with the four is four; that is, A will combine with A, E, I, and O; therefore, the combination in pair of these four will be 16; that is, A will have four combinations with each of the four, and so the other three. If A be added to the 16 combinations stated above, and E to another 16, I to a third, and O to a fourth, then there will be 64 combinations :

:

Eleven of these combinations which satisfy the six rules, are A A A, A EE, AII, A OO, E A E, IAI, OA O, A EO, E AO, A A I. The other of the 64 violate some of the six rules.

ΕΙΟ,

TALAKCHUND MANICKCHAND.

6. Q. Given O to be the major, what is the mood and figure? A. Given O the major premise, here the mood is OA O, and there cannot be any other mood. If it be OIO it violates the rule, being both particular premises, nor O A E, here we have the illicit process, and with the others. The figure is the third figure. If it be in the first figure, then we have undistributed middle, which is not valid. In the second figure we get an illicit process. In the fourth also we get an illicit process.

VINAYEKRAO BHASKERJI.

7. Q. O cannot be a premise in the first figure?

A. If O be the major premise the other premise must be A or E, since one at least of the premises must be universal, but E is rejected because we will have two negative premises, consequently we have OA left. But the middle term in the first figure is subject predicate, and as O does not distribute its subject, nor A its predicate, consequently the middle term is undistributed. Now if O be the minor premise we will have an illicit process of the major, therefore O is inadmissible in the first figure.

NOWROJI BIRAMJI.

9. Q. What are the rules of definition ?-and point out the error, if any, in the following definitions :

1.-Parallel lines are lines perpendicular to the same line.

2.-Triangles whose angles are equal, and the sides about the equal angles proportional, are similar.

A. There are two kinds of definition-the real and the nominal definition. Definition must be adequate to the term defined. It must neither contain more nor less signification which is meant by the term to be defined. It must consist of genus and the difference. If the parallel lines be in the same plane they will be perpendicular to the same line, but if this be not the case, one of them will only be a perpendicular to the same, while the other will fall without it. If we say triangles whose angles are equal, this only is sufficient to show that they are similar. To say that triangles whose angles are equal, and the sides about the equal angles, proportional, are similar, would merely be a repetition of the same thing.

BALKRISHNA SADASHEO.

2.-REPORT OF THE CLASSES IN MATHEMATICS.

In former Reports I have entered into such minute details in explanation of the manner of teaching, and of the course of study in the different classes, that I presume it is now unnecessary to refer to them. Both of these have been unchanged during the past year, and as each class has read the portion appointed, my Report is little more than a repetition of the course of study.

CLARE SCHOLARS.

Since the commencement of the session in June they have been revising and extending the knowledge of geometry and algebra that they possessed before their entrance into the College. In geometry they have gone over six Books of Euclid, the properties of transversals, poles and polars, with a great number of deductions. In algebra they have studied nearly all De Morgan's Treatise, including the chapters on series, construction and use of tables of logarithms. The subject of physical geography has been introduced for the first time, and it has been a favorite study. It may be mentioned as a proof of this, that some of the pay-students who did not attend the regular classes attended the lectures on physical geography. It possesses the great advantage of being easily made a vehicle for conveying all kinds of physical knowledge, and thus formed an excellent introduction to that study. The class-books were-Mrs. Somerville's Physical Geography, Humboldt's Cosmos, and Johnston's Physical Atlas.

WEST SCHOLARS.

From January till the Scholarship Examination in April, this class studied plane and spherical trigonometry, with its application to surveying, astronomy, and dialling. As much time as could be spared from their other business was devoted to the use of the sextant, theodolite, and levelling instruments; and a very good general knowledge of the manner of applying them in actual business was obtained. Since June they have gone over Waud's Analytical Geo

metry, as far as the general properties of curves of the no order, and have read the chapters of Salmon's Analytical Geometry on the straight line and circle. In the lectures on physical geography they were united with the Clare Scholars, as the subject was new to them also but in future I shall have a separate course of practical mechanics for the second year, to relieve the study of pure mathematics, and as a preparation for the theoretical mechanics of the third.

2ND NORMAL SCHOLARS.

During the past year they have studied Young's Differential Calculus, with the exception of the chapters on the geometry of three dimensions, and have made considerable progress in mechanics. Nearly all statics in Young's Mechanics has been read, and they will be quite able to complete before April the course for the highest scholarship. There has not been so much time devoted to the study of mathematics this year as formerly, on account of the greater attention to literature, history, political economy, and logic. The actual business performed in the class was the same, but the previous preparation for the daily examination has been less. It is an effort too great for almost any student to attempt to study simultaneously the very extended courses of history, political economy, logic, chemistry, botany, and mathematics; and as many of our students show decided talents for particular branches, it will be necessary, I think, to permit them to indulge the particular bent of their genius, without depriving them of their scholarships. In order not to make mere mathematicians, or mere literateurs, it would be advisable not to permit this indulgence until the end of the second year.

1ST NORMAL SCHOLARS.

Before the scholarship examination in April last they read all Young's Mechanics, with the exception of the chapter on central forces. After the examination, they were allowed to choose the subject for the next session, and the subject selected was astronomy. The greater part of Brinkley's Astronomy, including a portion of the Appendix, was read; but, from different causes, all the class (which contained six at the commencement of the session) but one had left before the examination, and as there was no corresponding class in the other branches, it was not deemed expedient to examine him.