old pupils know that I was never at a loss to tell the nature of their last school from their respective characters. The truth is, there is a natural pleasure in order and punctuality, and when the subject of good discipline is left to himself, reason carries on the command, and habit enforces obedience.

Let me remind parents, that good discipline requires that there should be but little allowance made for accidents of any kind. Offences that can happen inadvertently never require more than a light punishment, and this punishmont should be inflicted without much enquiry into causes. However plausible an excuse may be, you must always discourage the boy who had need of one. Exercises lost or left at home should count as exercises not done-"Nullum numen habes si sit prudentia." Things we think we cannot help happen much more frequently when we do not suffer for them. Always urge that most accidents are faults, and shew a boy that he has more than his share, that some other boys never lose books, never have them stolen, mistake the time, or do the wrong lesson. The discipline of school, I argue, must resemble that of life, and though it may seem hard to punish inadvertency, I am sure, that if your punishments are light, it is the least error of the two. On this point I would strongly recommend for perusal Basil Hall's account of discipline in the navy. The Admiralty, he says, cannot be worried with excuses and justifications against every reprimand. Discipline requires that men

should take their chance of being misinterpreted. It teaches men to avoid not only error but the suspicion of it. This is the discipline of the world. If we incur the censure of society we have deaf judges. This is ordained for good. Public opinion always errs on the unfavourable side. Exaggerating the accidents on railways has taught greater caution. The laws of nature are enforced by punishment without allowance for motives. The suicide who drinks prussic acid is not more certain of destruction than the child who drinks fly-water. Punishment is a useful test of inadvertence if not the immediate corrective.

ON MATHEMATICAL STUDIES f.

So many able Essays have been written on the study of Mathematics, that it will be only necessary for me to allude generally to the benefit to be obtained by a due admixture of scientific with classical studies. The great contention of mind necessary to carry on mathematical and philosophical studies to any extent is of great service in giving force to the understanding and increasing the capacity of acquiring and retaining knowledge. A habit of applying the mind with such intense attention is acquired, that on whatever subjects it is brought to bear afterwards, they seem in gene

This chapter is kindly contributed by a friend highly distinguished in the University of Cambridge, who has paid great attention to the subject of preparing the youthful mind for scientific studies.

ral but child's play. The mind acquires great accuracy in distinguishing and weighing evidence of every kind, and a habit of pushing on to consequences, most advantageous in practical life. It has been often said that Mathematicians expect demonstration before they will assent to anything as a truth, but this we believe to be rather a speculative than a practical accusation, one drawn rather from what may, than from what does occur. It is only necessary to know distinctly in what subjects mathematical and moral evidence are respectively to be obtained, and enough has been done to shew the man of natural science that the same mode of reasoning cannot be applied to moral as to mathematical and physical subjects. The truth of what we call the laws of nature, in fact, though they are made the foundation of mathematical reasoning, rests simply on moral evidence. The theory of gravitation, for instance, is established in this way. Rough observations lead us to suspect the law of the inverse square of the distance. Calculations are then made on this hypothesis, and tested by very accurate observations and experiments. There being in all cases a strict accordance of the results of observations and calculations, the hypothesis must be true, i. e. we have the highest moral certainty for the truth of the principle of gravitation, because there is extreme improbability that an untrue principle should happen successfully to explain the various and complicated phænomena of the universe.

There is no danger, then, that when the grounds

of moral and mathematical reasoning are distinguished, the Mathematician should suppose he can express the truth of facts which depend on men's opinions, and passions, and feelings, in formulæ of even the most complicated nature, any more than the Moralist should suppose he can render it highly probable that the three interior angles of every triangle are equal to two right angles, or the Orator exhaust his powers of persuasion in trying to enlist the affections in favour of the truth of the pons asinorum. There remains, then, the great advantage of such a discipline as is hardly to be obtained in any other way. It is impossible to study Mathematics without having the mind thoroughly braced up. While you are at work you can do nothing without doing it with vigour. If a step in reasoning is lost you must return and put more strength to the work. We ought never to forget, however, that in the mere studying of Mathematics there is little more than the understanding employed. We must be careful to bring all the principles we obtain, which are generally studied in the most abstract way, to the test of particular examples by applying them to the solution of problems. It is thus that invention is much exercised, and it is thus that the mind derives the greatest benefit from studies of this kind. A judicious tutor will, in fact, lead his pupils, especially in beginning physical subjects, to follow the analytical instead of the synthetical method, and will bring before them several problems, from which, with a little assistance, they

will be able to deduce the principle he intends to teach them. And in early education much may be done with a view to future excellence in this kind of study. The conceptions of mechanical science, for instance, such as those of force, and weight, and velocity, and mass, and density, &c. &c., ought early to be accurately engraven upon the mind, and familiar examples pointed out to which the pupil might constantly refer when any of them is mentioned. A clear notion of the composition of forces in producing equilibrium or motion might easily be given by some practical examples. For example, if three boys take hold of three ropes tied together at one extremity, and pull with all their force at them, it would be easy to shew them how by properly adjusting the angles at which the ropes are inclined to each other, these forces may be made to balance each other, or to produce motion. And also to give them a clear idea how a force may be supposed to act at any point in its direction, supposing a rigid connection of parts to be kept up in the system. Such things as these would naturally lead to an active enquiring habit of mind, and would easily make boys bring their thoughts to bear upon the great subjects of physical enquiry. Indeed the great object of mathematical studies at the present day is to give men the language which will enable them to read the great book of creation, and however paradoxical to the uninitiated it may seem, it is now quite understood by men of science, that the way in which we shall perfect our acquaintance with the