There is scarcely any thing in nature more wonderful to a contemplative person, and more worthy to be studied, than the effect of certain proportions in the theory of music, which can never be examined and understood without some knowledge of the doctrine concerning the composition and resolution of ratios, a curious and useful branch of the mathematics. Pythagoras was so captivated with the mathematical sections of a musical string, and their practical application to some other arts, that he is reported to have exhorted his disciples, as he lay upon his death-bed, to study the monochord. And all this, as a matter of contemplation, for the improvement and enlargement of the mind, is worth the attention of a scholar, though he never intends to strike a note of music all the days of his life. How ignorant and even barbarous, would it be in a gentleman of education to remonstrate, that all this is nothing to him, because his father did not intend him for a fiddler?

In philosophy, especially under the present state of it, the use of mathematical learning is unquestionable. What gentleman of taste would not envy Sir George Shuckburgh for his late learned labours upon the Alps, where he had the opportunity of trying so many curious experiments, by an application of the present theory of that useful instrument the barometer, as improved by Mr. De Luc? But no gentleman can be qualified to amuse himself and serve the public in that way, without some considerable skill in calculation, the experiments being very intricate, and abounding with niceties which must be accurately understood and attended to.

A course of the most ingeniously contrived experiments on the velocity of projectiles, and the resistance of the air to bodies moving swiftly in it, were

invented by the late Mr. Robins the engineer, which for their elegance are by no means beneath the admiration of a scholar; who will never repent of the labour necessary for understanding them. They have been farther carried on very lately from small arms to ordnance by Dr. Hutton, a member of the Royal Society. Whatever the value of these experiments may be in themselves (and they are chiefly valuable to military artists), they have had at least one good effect, in which all men of literature have an interest; they have given occasion to a discourse from the late worthy president Sir John Pringle, which for its learning, curiosity, elegance of style, and propriety of oratory, must be admired by all judges as a pattern in that kind of writing.

Now I have carried you thus far into the uses of mathematical learning, let me warn you against the danger we are under from the abuses of it. Mankind are very ingenious in using things; and they are almost as ingenious in abusing them. That great and good man bishop Berkely brought a heavy charge against the mathematicians of his age; first, because they deviated wantonly, and with some perplexity and apparent contradiction, into a boundless field of useless subtilties. And secondly, because many of them were found to be ill affected to the greatest subjects of religion, which are infinitely more important in human life. It has been said that he carried the matter too far, and laid himself open to the criticisms of his adversaries: but he had too much learning and too much acuteness to make himself ridiculous in the management of any argument. There was some foundation of truth in what he advanced: for if the mind is not upon its guard, a mathematician is disposed to look for that sort of sensible demonstration in other subjects, which

is to be found only when we reason about quantities; and therefore he rejects much truth with a high hand, as if it were deficient in point of evidence: which is unreasonable and absurd. I am as perfectly convinced, that there was such a man as Julius Cæsar, and that he was murdered in the Capitol at Rome, as I am that the three angles of a triangle are equal to two right ones; but I am not convinced upon the same kind of evidence: I cannot prove it by lines and angles. What then? I can no more doubt of the one than of the other: but I believe the one on visible descriptive evidence, depending upon certain axioms, or undeniable truths relating to quantities: and I believe the other on undeniable testimony, and the coins subsisting every where at this day, which bear his image and superscription, as also by his writings, which no man living was able to forge. I must therefore believe that there really was such a person, or I could soon shew you, that I must believe something more incredible; and that would be just as irrational as to deny a geometrical proposition with its own proper evidence.

The ingenious Mr. Robins above mentioned, who as a mathematician, a dextrous experimentalist, and a writer of a clear and classical style, was equal to most men living, was so unaccountably wild in his reasonings on some other subjects, that I have been told, he held the doctrine of future punishment to be a fable, because he could not see a soul burned at Charing-cross: as if the Scripture could not be true, because it is not a book of geometry; or there could be no future state, because we cannot prove it by an air pump. De Moivre, another eminent mathematician, who left France as a protestant refugee, is said to have derided himself afterwards for leaving his country to preserve his religion, which he lost past recovery when he had

been some time in England. I had occasion once to enquire after a great proficient in mathematical learning, whose works I had seen while I had no knowledge of his person. My bookseller at London, of whom I enquired, gave me a particular account of him; adding to the rest, that he was a true mathematician, for he was a great reprobate, and every word he spoke was attended with an oath. I mention this, to shew, that a notion had gone abroad, whether justly or not, that the generality of mathematicians are disposed, as such, to irreligion and profaneness. Two reasons may be given for this, supposing it to be true. The mathematics are open to students who have not had the advantages of a liberal education, and want the assistance of collateral learning to open their minds, and keep them within the bounds of truth and modesty. And as the fashion of the last and present age, with the fame so justly attributed to our great Newton, have placed the mathematical sciences so much higher than they used to be in the scale of literature, students who excel in them are under a temptation, incident to us all, to over-rate themselves and their knowledge. Thus they fall into vanity, pedantry, narrow-mindedness, and scepticism; neglecting and even despising all other learning, which is equally, and, in some respects, more valuable, for improving the heart and rectifying the judgment: ignorant of things, with which they are most intimately concerned; and placing all their pride in a sort of learning, to the exercise of which perhaps they will never be called, when they come forth into the business of life.

One thing I would whisper in the ear of scepticism before I quit the present subject, which is this; that the more a man knows, the farther he sees into truth: as he sees farther into truth, the objects of his belief

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will be continually increasing: and therefore Doubting, as such, is not a sign of wisdom: as he advances in knowledge, he will find by experience that he doubted from ignorance.

LETTER VII.

ON READING AND PRONUNCIATION.

You are sensible we have taken some pains, and with good reason, in the practice of reading with propriety. It is a matter of the last importance in education, though too generally neglected: in public schools it is seldom thought of. Several years are spent in charging the memory with words, while few days are employed in forming the voice and judgment to utter them in a powerful and agreeable

manner.

A scholar may be such in theory when his head is stored with languages, and he can interpret the writings of the Greeks and Romans; but he is no scholar in practice till he can express his own sentiments in a good style, and speak them in a proper manner. A mathematician understands the rationale of musical sounds; but the musician, who charms the ear, and touches the passions, is he who can combine sounds agreeably, according to the rules of art in composition, and perform them well upon an instrument. The dead philosophy of music in the head of a mathematician is like the learning of a Greek and Latin scholar, who can neither write nor read; and there are many such to be found.