"Thus fullers and dyers find that black cloths, of equal thickness with white ones, and hung out equally wet, dry in the sun much sooner than the white, being more readily heated by the sun's rays. It is the same before a fire; the heat of which sooner penetrates black stockings than white ones, and is apt sooner to burn a man's shins. Also beer much sooner warms in a black mug set before the fire, than in a white one, or in a bright silver tankard.

"My experiment was this: I took a number of little square pieces of broad cloth from a tailor's pattern-card, of various colours. There were black, deep blue, lighter blue, green, purple, red, yellow, white, and other colours, or shades of colours. I laid them all out upon the snow in a bright sunshiny morning. In a few hours, (I cannot now be exact as to the time,) the black being warmed most by the sun, was sunk so low as to be below the stroke of the sun's rays; the dark blue almost as low, the lighter blue not quite so low as the dark, the other colours less as they were lighter; and the quite white remained on the surface of the snow, not having entered it at all.

"What signifies philosophy that does not apply to some use? May we not learn from hence, that black cloths are not so fit to wear in a hot sunny climate, or season, as white ones; because, in such clothes the body is more heated by the sun when we walk abroad, and are at the same time heated by the exercise, which double heat is apt to bring on putrid dangerous fevers?--that soldiers and seamen, who must march and labour in the sun, should, in the East or West Indies, have a uniform of white?--that summer hats for men or women, should be white, as repelling that heat which gives head-achs to many, and to some the fatal stroke that the French call the _coup de soliel_?--that the ladies' summer hats, however, should be lined with black, as not reverberating on their faces those rays which are reflected upwards from the earth or water?--that the putting a white cap of paper or linen, within the crown of a black hat, as some do, will not keep out the heat, though it would if placed without?--that fruit-walls being blackened, may receive so much heat from the sun in the day-time, as to continue warm, in some degree, through the night, and thereby preserve the fruit from frosts, or forward its growth?--with sundry other particulars, of less or greater importance, that will occur from time to time to attentive minds?"

_Thirty Soldiers having deserted, so to place them in a Ring, that you may save any Fifteen you please, and it shall seem the Effect of Chance._

This recreation is usually proposed thus: Fifteen Christians and fifteen Turks being in a ship at sea, in a violent tempest, it was deemed necessary to throw half the number of persons overboard, in order to disburden the ship, and save the rest; to effect this, it was agreed to be done by lot, in such a manner, that the persons being placed in a ring, every ninth man should be cast into the sea, till one half of them were thrown overboard. Now, the pilot, being a Christian, was desirous of saving those of his own persuasion: how ought he therefore to dispose the crew, so that the lot might always fall upon the Turks?

This question may be resolved by placing the men according to the numbers annexed to the vowels in the words of the following verse:--

_Po-pu-le-am Jir-gam Ma-ter Re-gi-na fe-re-bat._ 4 5 2 1 3 1 1 2 2 3 1 2 2 1

from which it appears, that you must place four of those you would save first; then five of those you would punish. After this, two of those to be saved, and one to be punished; and so on. When this is done, you must enter the ring, and beginning with the first of the four men you intend to save, count on to nine; and turn this man out to be punished; then count on, in like manner, to the next ninth man, and turn him out to be punished; and so on for the rest.

It is reported that Josephus, the author of the Jewish History, escaped the danger of death by means of this problem; for being governor of Joppa, at the time that it was taken by Vespasian, he was obliged to secrete himself with thirty or forty of his soldiers in a cave, where they made a firm resolution to perish by famine rather than fall into the hands of the conqueror; but being at length driven to great distress, they would have destroyed each other for sustenance, had not Josephus persuaded them to die by lot, which he so ordered, that all of them were killed except himself and another, whom he might easily destroy, or persuade to yield to the Romans.

_Three Persons having each chosen, privately, one out of three Things,--to tell them which they have chosen._

Let the three things, for instance, be a ring, a guinea, and a shilling, and let them be known privately to yourself by the vowels _a_, _e_, _i_, of which the first, _a_, signifies one, the second, _e_, two, and the third, _i_, three.

Then take 24 counters, and give the first person 1, which signifies _a_, the second 2, which represents _e_, and the third 3, which stands for _i_; then, leaving the other counters upon the table, retire into another room, and bid him who has the ring take as many counters from the table as you gave him; he that has the guinea, twice as many, and he that has the shilling four times as many.

This being done, consider to whom you gave one counter, to whom two, and to whom three; and as there were only twenty-four counters at first, there must necessarily remain either 1, 2, 3, 5, 6, or 7, on the table, or otherwise they must have failed in observing the directions you gave them.

But if either of these numbers remain, as they ought, the question may be resolved by retaining in your memory the six following words:--

_Salve certa anima semita vita quies._ 1 2 3 5 6 7

As, for instance, suppose the number that remained was 5; then the word belonging to it is semita; and as the vowels in the first two syllables of this word are _e_ and _i_, it shews, according to the former directions, that he to whom you gave two counters has the ring; he to whom you gave three counters, the gold; and the other person, of course, the silver, it being the second vowel which represents 2, and the third which represents 3.

_How to part an Eight Gallon Bottle of Wine equally between two Persons, using only two other Bottles, one of Five Gallons, and the other of Three._

This question is usually proposed in the following manner: A certain person having an eight-gallon bottle filled with excellent wine, is desirous of making a present of half of it to one of his friends; but as he has nothing to measure it out with, but two other bottles, one of which contains five gallons, and the other three, it is required to find how this may be accomplished?

In order to answer the question, let the eight-gallon bottle be called A, the five-gallon bottle B, and the three-gallon bottle C; then, if the liquor be poured out of one bottle into another, according to the manner denoted in either of the two following examples, the proposed conditions will be answered.

8 5 3 8 5 3 A B C A B C 8 0 0 8 0 0 3 5 0 5 0 3 3 2 3 5 3 0 6 2 0 2 3 3 6 0 2 2 5 1 1 5 2 7 0 1 1 4 3 7 1 0 4 4 0 4 1 3

_A Quant.i.ty of Eggs being broken, to find how many there were without remembering the Number._

An old woman, carrying eggs to market in a basket, met an unruly fellow, who broke them. Being taken before a magistrate, he was ordered to pay for them, provided the woman could tell how many she had; but she could only remember, that in counting them into the basket by twos, by threes, by fours, by fives, and by sixes, there always remained one; but in counting them in by sevens, there were none remaining. Now, in this case, how was the number to be ascertained?

This is the same thing as to find a number, which being divided by 2, 3, 4, 5, and 6, there shall remain 1, but being divided by 7, there shall remain nothing; and the least number, which will answer the conditions of the question, is found to be 301, which was therefore the number of eggs the old woman had in her basket.

_To find the least Number of Weights, that will weigh, from One Pound to Forty._

This problem may be resolved by the means of the geometrical progression, 1, 3, 9, 27, 81, &c. the property of which is such, that the last sum is twice the number of all the rest, and one more; so that the number of pounds being forty, which is also the sum of 1, 3, 9, 27, these four weights will answer the purpose required. Suppose it was required, for example, to weigh eleven pounds by them: you must put into one scale the one-pound weight, and into the other the three and nine-pound weights, which, in this case, will weigh only eleven pounds, in consequence of the one-pound weight being in the other scale; and therefore, if you put any substance into the first scale, along with the one-pound weight, and it stands in equilibrio with the three and nine in the other scale, you may conclude it weighs eleven pounds.

In like manner, to find a fourteen-pound weight, put into one of the scales the one, three, and nine-pound weights, and into the other that of twenty-seven pounds, and it will evidently outweigh the other three by fourteen pounds; and so on for any other weight.

_To break a Stick which rests upon two Wine Gla.s.ses, without injuring the Gla.s.ses._

Take a stick, (see Plate,) AB. fig. 1, of about the size of a common broomstick, and lay its two ends, AB, which ought to be pointed, upon the edges of two gla.s.ses placed upon two tables of equal height, so that it may rest lightly on the edge of each gla.s.s. Then take a kitchen poker, or a large stick, and give the other a smart blow, near the middle point _c_, and the stick AB will be broken, without in the least injuring the gla.s.ses: and even if the gla.s.ses be filled with wine, not a drop of it will be spilt, if the operation be properly performed. But on the contrary, if the stick were struck on the underside, so as to drive it up into the air, the gla.s.ses would be infallibly broken.

_A Number of Metals being mixed together in one Ma.s.s, to find the Quant.i.ty of each of them._

Vitruvius, in his Architecture, reports, that Hiero, king of Sicily, having employed an artist to make a crown of pure gold, which was designed to be dedicated to the G.o.ds, suspected that the goldsmith had stolen part of the gold, and subst.i.tuted silver in its place: being desirous of discovering the cheat, he proposed the question to Archimedes, desiring to know if he could, by his art, discover whether any other metal were mixed with the gold. This celebrated mathematician being soon afterwards bathing himself, observed, that as he entered the bath, the water ascended, and flowed out of it; and as he came out of it, the water descended in like manner: from which he inferred, that if a ma.s.s of pure gold, silver, or any other metal, were thrown into a vessel of water, the water would ascend in proportion to the bulk of the metal. Being intensely occupied with the invention, he leaped out of the bath, and ran naked through the streets, crying, "I have found it, I have found it!"

The way in which he applied this circ.u.mstance to the solution of the question proposed was this: he procured two ma.s.ses, the one of pure gold, and the other of pure silver, each equal in weight to the crown, and consequently of unequal magnitudes; then immersing the three bodies separately in a vessel of water, and collecting the quant.i.ty of water expelled by each, he was presently enabled to detect the fraud, it being obvious, that if the crown expelled more water than the ma.s.s of gold, it must be mixed with silver or some baser metal. Suppose, for instance, in order to apply it to the question, that each of the three ma.s.ses weighed eighteen pounds; and that the ma.s.s of gold displaced one pound of water, that of silver a pound and a half, and the crown one pound and a quarter only: then, since the ma.s.s of silver displaced half a pound of water more than the same weight of gold, and the crown a quarter of a pound more than the gold, it appears, from the rule of proportion, that half a pound is to eighteen pounds, as a quarter is to nine pounds; which was, therefore, the quant.i.ty of silver mixed in the crown.

Since the time of Archimedes, several other methods have been devised for solving this problem; but the most natural and easy is, that of weighing the crown both in air and water, and observing the difference.

_To make a mutual Exchange of the Liquor in two Bottles, without using any other Vessel._

Take two bottles, which are as nearly equal as possible, both in neck and belly, and let one be filled with oil, and the other with water; then clap the one that is full of water dexterously upon the other, so that the two necks shall exactly fit each other; and as the water is heavier than the oil, it will naturally descend into the lower bottle, and make the oil ascend into its place. In order to invert the bottle of water without spilling the contents, place a bit of thin writing paper over the mouth of the bottle; and when you have placed the bottle in the proper position, draw out the paper quickly and steadily.

_How to make a Peg that will exactly fit Three different Holes._

Let one of the holes be circular, the other square, and the third an oval; then it is evident, that any cylindrical body, of a proper size, may be made to pa.s.s through the first hole perpendicularly; and if its length be just equal to its diameter, it may be pa.s.sed horizontally through the second, or square hole; also, if the breadth of the oval be made equal to the diameter of the base of the cylinder, and its longest diameter equal to the diagonal of it, the cylinder, being put in obliquely, will fill it as exactly as any of the former.

_To place Three Sticks, or Tobacco Pipes, upon a Table, in such a manner that they may appear to be unsupported by any thing but themselves._

Take one of the sticks, or pipes, (see Plate,) AB, fig. 2, and place it in an oblique position, with one of its ends, B, resting on the table; then put one of the other sticks, as CD, across this in such a manner that one end of it, D, may be raised, and the other touch the table at C. Having done this, take the third stick E, and complete the triangle with it, making one of its ends E rest on the table, and running it under the second, CD, in such a manner that it may rest upon the first, AB; then will the three sticks, thus placed, mutually support each other; and even if a small weight be laid upon them, it will not make them fall, but strengthen, and keep them firmer in their position.

_How to prevent a heavy Body from falling, by adding another heavier Body to it on that side towards which it inclines._

On the edge of a shelf, or table, or any other horizontal surface, lay a key, (see Plate,) CD, fig. 3, in such a manner, that, being left to itself, it would fall to the ground; then, in order to prevent this, take a crooked stick DFG, with a weight, H, at the end of it; and having inserted one end of the stick in the open part of the key, at D, let it be so placed, that the weight H may fall perpendicularly under the edge of the table, and the body by these means will be effectually prevented from falling.

The same thing may be done by hanging a weight at the end of a tobacco-pipe, a stick, or any other body; the best means of accomplishing which will be easily known by a few trials.

_To make a false Balance, that shall appear perfectly just when empty, or when loaded with unequal Weights._

Take a balance, (see Plate,) DCE, fig. 4, the scales and arms of which are of such unequal weights and lengths, that the scale A may be in proportion to the scale B, as the length of the arm CE is to the length of the arm CD; then will the two scales be exactly in equilibrio about the point C; and the same will be the case, if the two arms CD, CE, are of equal length, but of unequal thickness, provided the thickness of CD is to that of CE, as the weight of the scale B is to that of A.

For example; suppose the arm CD is equal to three ounces, and the arm CE to two, and that the scale B weighs three ounces, and the scale A two; then the balance, in this case, will be exactly true when empty; and if a weight of two pounds be put into the scale A, and one of three pounds into B, they will still continue in equilibrio. But the fallacy in this, and all other cases of the same kind, may be easily detected, in shifting the weights from one scale to the other.