that the two following results, whether assumed or attempted to be proved, are absolute facts, namely, that fluids at rest do communicate pressures in all directions, and that a plane placed horizontally in a fluid is pressed in the same way as if the vertical portion of fluid reaching from the plane to the surface of the fluid became solid and (all the other fluid being removed) pressed upon the plane with its weight alone. The results derived from these premises may therefore be confidently relied upon when fairly and legitimately deduced from them. These however are no questions for discussion here, but are merely thrown out for the consideration of abler mathematicians. The establishing of first principles in the Physical Sciences, as they are studied in this University, has not been much attended to, even by writers of great talent and of high character as mathematicians. It is to be wished that something further were done towards determining and fixing the grounds on which the study of Natural Philosophy rests, or ought to rest; so that a more clear and distinct line of demarcation might be drawn between Axiomatic (by which term is here meant practical and experimentally personal) knowledge, and that strict method of exact reasoning by which correct conclusions are drawn from given premises and acknowledged principles. ST. JOHN'S COLLEGE, THE subjects in which those persons who are not Candidates for Honours are examined for the degree of B.A. are, I. The Acts of the Apostles in the original Greek. II. One Greek Classic; appointed in the last week of the Lent Term in every year for the year next but one following. Thus the Classical subjects for the Examinations of 1841 will be fixed on in the last week of the Lent Term of 1839. III. One Latin Classic; appointed in the same manner as the last subject. IV. Paley's Moral Philosophy. V. Such Mathematical Subjects as are contained in the following Schedule*. *The Examiners are required to publish the names of the persons whom their respective Colleges permit to offer themselves for Examination at the Bachelors' Commencement, in a list, which is to be arranged in alphabetical order, and separated into two Divisions. The distribution of the different subjects, and the times of Examination are fixed by the the following Table. Wednesday... 1 Arithmetic and Algebra.. 2 Arithmetic and Algebra. a 3 SCHEDULE OF MATHEMATICAL SUBJECTS of Examination, for the Degree of B.A. of Persons not Candidates for Honours. ARITHMETIC. Addition, subtraction, multiplication, division, reduction, rule of three; the same rules in vulgar and decimal fractions; practice, simple and compound interest, discount, extraction of square and cube roots, duodecimals. ALGEBRA. 1. Definitions and explanation of algebraical signs and terms. 2. Addition, subtraction, multiplication and division of simple algebraical quantities and simple algebraical fractions. 3. Algebraical definitions of ratio and proportion. 4. If a b c d then ad bc, and the converse : 7. Geometrical definition of proportion. (Euc. Book v. Def. 5.) 8. If quantities be proportional according to the algebraical definition, they are proportional according to the geometrical definition. 9. Definition of a quantity varying as another, directly or inversely, or as two others jointly. EUCLID. Books I. II. III; Book vi. Props. 1. 2. 3. 4. 5. 6. [The remaining portion of the Schedule forms the Table of Contents CONTENTS. 19. Prop. 1. A horizontal prism or cylinder of uniform density will pro- duce the same effect by its weight as if it were collected at its middle 20. Prop. 2. If two weights acting perpendicularly on a straight lever on opposite sides of the fulcrum balance each other, they are inversely as their distances from the fulcrum; and the pressure on the fulcrum is 21. Prop. 3. If two forces acting perpendicularly on a straight lever in 23. Prop. 4. To explain the different kinds of levers. 24. Prop. 5. If two forces acting perpendicularly at the extremities of the arms of any lever balance each other, they are inversely as the 25. Prop. 6. If two forces acting at any angles on the arms of any lever balance each other, they are inversely as the perpendiculars drawn from the fulcrum to the directions in which the forces act. 26. Prop. 7. If two weights balance each other on a straight lever when it is horizontal, they will balance each other in every position of the |