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much or more use than that commonly learned at schools, serving to a just formation of the mind, enlarging its capacity, and strengthening it so as to render the same capable of exact reasoning, and discerning truth from falsehood in all occurrences, even subjects not mathematical. For which reason it is said the Egyptians, Persians, and Lacedæmonians seldom elected any new kings but such as had some knowledge in the mathematics; imagining those who had not men of imperfect judgments, and unfit to rule and govern.
Though Plato's censure, that those who did not understand the 117th proposition of the 13th book of Euclid's Elements ought not to be ranked among rational creatures, was unreasonable and unjust, yet to give a man the character of universal learning, who is destitute of a competent knowledge in the mathematics, is no less so.
The usefulness of some particular parts of the mathematics, in the common affairs of human life, has rendered some knowledge of them very necessary to a great part of mankind, and very convenient to all the rest, that are any way conversant beyond the limits of their own particular callings.
Those whom necessity has obliged to get their bread by manual industry, where some degree of art is required to go along with it, and who have had some insight into these studies, have very often found advantages from them sufficient to reward the pains they were at in acquiring them. And whatever may have been imputed to some other studies, under the notion of insignificance and loss of time, yet these, I believe, never caused repentance in any, except it was for their remissness in the prosecution of them.
Philosophers do generally affirm that human knowledge to be most excellent which is conversant among the most excellent things. What science, then, can there be more noble, more excel
lent, more useful for men, more admirably high and demonstrative, than this of the mathematics?
I shall conclude with what Plato says, in the seventh book of his Republic, with regard to the excellence and usefulness of geometry, being to this purpose:
"Dear friend-You see, then, that mathematics are necessary, because, by the exactness of the method, we get a habit of using our minds to the best advantage. And it is remarkable that, all men being capable by nature to reason and understand the sciences, the less acute, by studying this, though useless to them in every other respect, will gain this advantage, that their minds will be improved in reasoning aright; for no study employs it more, nor makes it susceptible of attention so much; and those who we find have a mind worth cultivating, ought to apply themselves to this study."
THE ART OF PROCURING PLEASANT
Inscribed to Miss * * * *, being written at her request.
As a great part of our life is spent in sleep, during which we have sometimes pleasant and sometimes painful dreams, it becomes of some consequence to obtain the one kind and avoid the other; for, whether real or imaginary, pain is pain and pleasure is pleasure. If we can sleep without dreaming, it is well that painful dreams are avoided. If, while we sleep, we can have any pleasing dreams, it is, as the French say, autant de gagné, so much added to the pleasure of life.
To this end it is, in the first place, necessary to
be careful in preserving health, by due exercise and great temperance; for in sickness the imagination is disturbed, and disagreeable, sometimes terrible, ideas are apt to present themselves. Exercise should precede meals, not immediately follow them; the first promotes, the latter, unless moderate, obstructs digestion. If, after exercise, we feed sparingly, the digestion will be easy and good, the body lightsome, the temper cheerful, and all the animal functions performed agreeably. Sleep, when it follows, will be natural and undisturbed; while indolence, with full feeding, occasions nightmares and horrors inexpressible; we fall from precipices, are assaulted by wild beasts, murderers, and demons, and experience every variety of distress. Observe, however, that the quantities of food and exercise are relative things; those who move much may, and, indeed, ought to, eat more; those who use little exercise should eat little. In general, mankind, since the improvement of cookery, eat about twice as much as nature requires. Suppers are not bad if we have not dined; but restless nights naturally follow hearty suppers after full dinners. Indeed, as there is a difference in constitutions, some rest well after these meals; it costs them only a frightful dream and an apoplexy, after which they sleep till doomsday. Nothing is more common in the newspapers than instances of people who, after eating a hearty supper, are found dead abed in the morning.
Another means of preserving health, to be attended to, is the having a constant supply of fresh air in your bedchamber. It has been a great mistake, the sleeping in rooms exactly closed, and in beds surrounded by curtains. No outward air that may come in to you is so unwholesome as the unchanged air, often breathed, of a close chamber, As boiling water does not grow hotter by longer boiling, if the particles that receive greater heat
can escape, so living bodies do not putrefy if the particles, so fast as they become putrid, can be thrown off. Nature expels them by the pores of the skin and the lungs, and in a free, open air they are carried off; but in a close room we receive them again and again, though they become more and more corrupt. A number of persons crowded into a small room thus spoil the air in a few minutes, and even render it mortal, as in the Black Hole at Calcutta. A single person is said to spoil only a gallon of air per minute, and therefore requires a longer time to spoil a bedchamber-full; but it is done, however, in proportion, and many putrid disorders hence have their origin. It is recorded of Methusalem, who, being the longest liver, may be supposed to have best preserved his health, that he slept always in the open air; for, when he had lived five hundred years, an angel said to him, "Arise, Methusalem, and build thee a house, for thou shalt live yet five hundred years longer." But Methusalem answered and said, "If I am to live but five hundred years longer, it is not worth while to build me a house; I will sleep in the air, as I have been used to do." Physicians, after having for ages contended that the sick should not be indulged with fresh air, have at length discovered that it may do them good. It is therefore to be hoped that they may in time discover likewise that it is not hurtful to those who are in health, and that we may then be cured of the aerophoba, that at present distresses weak minds, and makes them choose to be stifled and poisoned rather than leave open the window of a bedchamber or put down the glass of a coach.
Confined air, when saturated with perspirable matter,* will not receive more; and that matter
What physicians call perspirable matter is that vapour which passes off from our bodies, from the lungs, and through
must remain in our bodies and occasion diseases; but it gives some previous notice of its being about to be hurtful, by producing certain uneasiness, slight indeed at first, such as with regard to the lungs is a trifling sensation, and to the pores of the skin a kind of restlessness, which is difficult to describe, and few that feel it know the cause of it. But we may recollect that sometimes, on waking in the night, we have, if warmly covered, found it difficult to get asleep again. We turn often, without finding repose in any position. This fidgetiness (to use a vulgar expression for want of a better) is occasioned wholly by an uneasiness in the skin, owing to the retention of the perspirable matter, the bedclothes having received their quantity, and, being saturated, refusing to take any more. To become sensible of this by an experiment, let a person keep his position in the bed, but throw off the bedclothes, and suffer fresh air to approach the part uncovered of his body; he will then feel that part suddenly refreshed; for the air will immediately relieve the skin, by receiving, licking up, and carrying off, the load of perspirable matter that incommoded it. For every portion of cool air that approaches the warm skin, in receiving its portion of that vapour, receives therewith a degree of heat that rarefies and renders it lighter, when it will be pushed away, with its burden, by cooler and, therefore, heavier fresh air, which for a moment supplies its place, and then, being likewise changed and warmed, gives way to a succeeding quantity. This is the order of nature, to prevent animals being infected by their own perspiration. He will now be sensible of the difference between the part exposed to the air and that which, remaining sunk in the bed, denies the air access; for this part now mani
the pores of the skin. The quantity of this is said to be five ighths of what we eat.-AUTHOR,