Chapter IV: Front Matter (4)

Among the rest, I threw out my conjecture, that the said appearance might be caused by a great number of little animals, floating on the surface of the sea, which, on being disturbed, might, by expanding their finns, or otherwise moving themselves, expose such a part of their bodies as exhibits a luminous appearance, somewhat in the manner of a glow-worm, or fire-fly: that these animals may be more numerous in some places than others; and, therefore, that the appearance above-mentioned being fainter and stronger in different places, might be owing to that: that certain circumstances of weather, &c. might invite them to the surface, on which, in a calm, they might sport themselves and glow; or in storms, being forced up, make the same appearance.

There is no difficulty in conceiving that the sea may be stocked with animalcula for this purpose, as we find all nature crowded with life. But it seems difficult to conceive that such small portions of matter, even if they were wholly luminous, should affect our sight; much more so, when it is supposed that only a part of them is luminous. But, if we consider some other appearances, we may find the same difficulty to conceive of them; and yet we know they take place. For instance, the flame of a candle, which, it is said, may be seen four miles round. The light which fills this circle of eight miles diameter, was contained, when it first left the candle, within a circle of half an inch diameter. If the density of light, in these circumstances, be as those circles to each other, that is, as the squares of their diameters, the candle-light, when come to the eye, will be 1027709337600 times rarer than when it quitted the half inch circle. Now the aperture of the eye, through which the light passes, does not exceed one-tenth of an inch diameter, and the portion of the lesser circle, which corresponds to this small portion of the greater circle, must be proportionably, that is, 1027709337600 times less than one-tenth of an inch; and yet this infinitely small point (if you will allow the expression) affords light enough to make it visible four miles; or, rather, affords light sufficient to affect the sight at that distance.

The smallness of the animalcula is no objection then to this conjecture; for supposing them to be ten thousand times less than the _minimum visibile_, they may, notwithstanding, emit light enough to affect the eyes, and so to cause the luminous appearance aforesaid. This conjecture I send you for want of something better ****.

FOOTNOTE:

[16] I. Badoin. _Editor._

TO MR. P. F.[17] IN NEWPORT.

_On the Saltness of Sea-Water._

_London, May 7, 1760._

SIR,

**** It has, indeed, as you observe, been the opinion of some very great naturalists, that the sea is salt only from the dissolution of mineral or rock-salt, which its waters happened to meet with. But this opinion takes it for granted that all water was originally fresh, of which we can have no proof. I own I am inclined to a different opinion, and rather think all the water on this globe was originally salt, and that the fresh water we find in springs and rivers, is the produce of distillation. The sun raises the vapours from the sea, which form clouds, and fall in rain upon the land, and springs and rivers are formed of that rain. As to the rock-salt found in mines, I conceive, that instead of communicating its saltness to the sea, it is itself drawn from the sea, and that of course the sea is now fresher than it was originally. This is only another effect of nature's distillery, and might be performed various ways.

It is evident from the quantities of sea-shells, and the bones and teeth of fishes found in high lands, that the sea has formerly covered them. Then, either the sea has been higher than it now is, and has fallen away from those high lands, or they have been lower than they are, and were lifted up out of the water to their present height, by some internal mighty force, such as we still feel some remains of, when whole continents are moved by earthquakes. In either case it may be supposed that large hollows or valleys among hills, might be left filled with sea-water, which evaporating, and the fluid part drying away in a course of years, would leave the salt covering the bottom; and that salt coming afterwards to be covered with earth, from the neighbouring hills, could only be found by digging through that earth. Or, as we know from their effects, that there are deep fiery caverns under the earth, and even under the sea, if at any time the sea leaks into any of them, the fluid parts of the water must evaporate from that heat, and pass off through some volcano, while the salt remains, and by degrees, and continual acretion, becomes a great mass. Thus the cavern may at length be filled, and the volcano connected with it cease burning, as many it is said have done; and future miners, penetrating such cavern, find what we call a salt-mine. This is a fancy I had on visiting the salt-mines at Northwich, with my son. I send you a piece of the rock-salt which he brought up with him out of the mine. ****

I am, Sir, &c.

B. FRANKLIN.

FOOTNOTE:

[17] Peter Franklin. _Editor._

TO MISS STEPHENSON.

_On the Effect of Air on the Barometer, and the Benefits derived
from the Study of Insects._

_Craven Street, June 11, 1760._

'Tis a very sensible question you ask, how the air can affect the barometer, when its opening appears covered with wood? If indeed it was so closely covered as to admit of no communication of the outward air to the surface of the mercury, the change of weight in the air could not possibly affect it. But the least crevice is sufficient for the purpose; a pinhole will do the business. And if you could look behind the frame to which your barometer is fixed, you would certainly find some small opening.

There are indeed some barometers in which the body of mercury at the lower end is contained in a close leather bag, and so the air cannot come into immediate contact with the mercury; yet the same effect is produced. For the leather being flexible, when the bag is pressed by any additional weight of air it contracts, and the mercury is forced up into the tube; when the air becomes lighter, and its pressure less, the weight of the mercury prevails, and it descends again into the bag.

Your observation on what you have lately read concerning insects is very just and solid. Superficial minds are apt to despise those who make that part of the creation their study, as mere triflers; but certainly the world has been much obliged to them. Under the care and management of man, the labours of the little silkworm afford employment and subsistence to thousands of families, and become an immense article of commerce. The bee, too, yields us its delicious honey, and its wax useful to a multitude of purposes. Another insect, it is said, produces the cochineal, from whence we have our rich scarlet dye. The usefulness of the cantharides or Spanish flies, in medicine, is known to all, and thousands owe their lives to that knowledge. By human industry and observation, other properties of other insects may possibly be hereafter discovered, and of equal utility. A thorough acquaintance with the nature of these little creatures may also enable mankind to prevent the increase of such as are noxious, or secure us against the mischiefs they occasion. These things doubtless your books make mention of: I can only add a particular late instance which I had from a Swedish gentleman of good credit. In the green timber, intended for ship-building at the king's yards in that country, a kind of worms were found, which every year became more numerous and more pernicious, so that the ships were greatly damaged before they came into use. The king sent Linnæus, the great naturalist, from Stockholm, to enquire into the affair, and see if the mischief was capable of any remedy. He found, on examination, that the worm was produced from a small egg, deposited in the little roughnesses on the surface of the wood, by a particular kind of fly or beetle; from whence the worm, as soon as it was hatched, began to eat into the substance of the wood, and after some time came out again a fly of the parent kind, and so the species increased. The season in which the fly laid its eggs, Linnæus knew to be about a fortnight (I think) in the month of May, and at no other time in the year. He therefore advised, that some days before that season, all the green timber should be thrown into the water, and kept under water till the season was over. Which being done by the king's order, the flies missing their usual nests, could not increase; and the species was either destroyed or went elsewhere; and the wood was effectually preserved, for after the first year, it became too dry and hard for their purpose.

There is, however, a prudent moderation to be used in studies of this kind. The knowledge of nature may be ornamental, and it may be useful, but if to attain an eminence in that, we neglect the knowledge and practice of essential duties, we deserve reprehension. For there is no rank in natural knowledge of equal dignity and importance with that of being a good parent, a good child, a good husband, or wife, a good neighbour or friend, a good subject or citizen, that is, in short, a good christian. Nicholas Gimcrack, therefore, who neglected the care of his family, to pursue butterflies, was a just object of ridicule, and we must give him up as fair game to the satyrist.

Adieu, my dear friend, and believe me ever

Yours affectionately,

B. FRANKLIN.

TO THE SAME.

_On the Bristol Waters, and the Tide in Rivers._

_London, Sept. 13, 1760._

MY DEAR FRIEND,

I have your agreeable letter from Bristol, which I take this first leisure hour to answer, having for some time been much engaged in business.

Your first question, _What is the reason the water at this place, though cold at the spring, becomes warm by pumping?_ It will be most prudent in me to forbear attempting to answer, till, by a more circumstantial account, you assure me of the fact. I own I should expect that operation to warm, not so much the water pumped, as the person pumping.--The rubbing of dry solids together has been long observed to produce heat; but the like effect has never yet, that I have heard, been produced by the mere agitation of fluids, or friction of fluids with solids. Water in a bottle shook for hours by a mill-hopper, it is said, discovered no sensible addition of heat. The production of animal heat by exercise is therefore to be accounted for in another manner, which I may hereafter endeavour to make you acquainted with.

This prudence of not attempting to give reasons before one is sure of facts, I learnt from one of your sex, who, as Selden tells us, being in company with some gentlemen that were viewing, and considering something which they called a Chinese shoe, and disputing earnestly about the manner of wearing it, and how it could possibly be put on; put in her word, and said modestly, _Gentlemen, are you sure it is a shoe?--Should not that be settled first?_

But I shall now endeavour to explain what I said to you about the tide in rivers, and to that end shall make a figure, which though not very like a river, may serve to convey my meaning.--Suppose a canal one hundred and forty miles long, communicating at one end with the sea, and filled therefore with sea water. I chuse a canal at first, rather than a river, to throw out of consideration the effects produced by the streams of fresh water from the land, the inequality in breadth, and the crookedness of courses.

Let A, C, be the head of the canal; C, D, the bottom of it; D, F, the open mouth of it next the sea. Let the strait pricked line, B, G, represent low water mark the whole length of the canal, A, F, high water mark:--Now if a person standing at E, and observing at the time of high water there, that the canal is quite full at that place up to the line E, should conclude that the canal is equally full to the same height from end to end, and therefore there was as much more water come into the canal since it was down at low water mark, as would be included in the oblong space A, B, G, F, he would be greatly mistaken. For the tide is _a wave_, and the top of the wave, which makes high water, as well as every other lower part, is progressive; and it is high water successively, but not at the same time, in all the several points between G, F, and A, B.--And in such a length as I have mentioned it is low water at F, G, and also at A, B, at or near the same time with its being high water at E; so that the surface of the water in the canal, during that situation, is properly represented by the curve pricked line B, E, G. And on the other hand, when it is low water at E, H, it is high water both at F, G, and at A, B, at or near the same time: and the surface would then be described by the inverted curve line, A, H, F.

In this view of the case, you will easily see, that there must be very little more water in the canal at what we call high water, than there is at low water, those terms not relating to the whole canal at the same time, but successively to its parts. And if you suppose the canal six times as long, the case would not vary as to the quantity of water at different times of the tide; there would only be six waves in the canal at the same time, instead of one, and the hollows in the water would be equal to the hills.

That this is not mere theory, but conformable to fact, we know by our long rivers in America. The Delaware, on which Philadelphia stands, is in this particular similar to the canal I have supposed of one wave: for when it is high water at the Capes or mouth of the river, it is also high water at Philadelphia, which stands about one hundred and forty miles from the sea; and there is at the same time a low water in the middle between the two high waters; where, when it comes to be high water, it is at the same time low water at the Capes and at Philadelphia. And the longer rivers have some a wave and half, some two, three, or four waves, according to their length. In the shorter rivers of this island, one may see the same thing in part: for instance, it is high water at Gravesend an hour before it is high water at London Bridge; and twenty miles below Gravesend an hour before it is high water at Gravesend. Therefore at the time of high water at Gravesend the top of the wave is there, and the water is then not so high by some feet where the top of the wave was an hour before, or where it will be an hour after, as it is just then at Gravesend.

Now we are not to suppose, that because the swell or top of the wave runs at the rate of twenty miles an hour, that therefore the current, or water itself of which the wave is composed, runs at that rate. Far from it. To conceive this motion of a wave, make a small experiment or two. Fasten one end of a cord in a window near the top of a house, and let the other end come down to the ground; take this end in your hand, and you may, by a sudden motion, occasion a wave in the cord that will run quite up to the window; but though the wave is progressive from your hand to the window, the parts of the rope do not proceed with the wave, but remain where they were, except only that kind of motion that produces the wave. So if you throw a stone into a pond of water when the surface is still and smooth, you will see a circular wave proceed from the stone as its centre, quite to the sides of the pond; but the water does not proceed with the wave, it only rises and falls to form it in the different parts of its course; and the waves that follow the first, all make use of the same water with their predecessors.

But a wave in water is not indeed in all circumstances exactly like that in a cord; for water being a fluid, and gravitating to the earth, it naturally runs from a higher place to a lower; therefore the parts of the wave in water do actually run a little both ways from its top towards its lower sides, which the parts of the wave in the cord cannot do. Thus, when it is high and standing water at Gravesend, the water twenty miles below has been running ebb, or towards the sea for an hour, or ever since it was high water there; but the water at London Bridge will run flood, or from the sea yet another hour, till it is high water, or the top of the wave arrives at that bridge, and then it will have run ebb an hour at Gravesend, &c. &c. Now this motion of the water, occasioned only by its gravity, or tendency to run from a higher place to a lower, is by no means so swift as the motion of the wave. It scarce exceeds perhaps two miles in an hour.

If it went as the wave does twenty miles an hour, no ships could ride at anchor in such a stream, nor boats row against it.

In common speech, indeed, this current of the water both ways from the top of the wave is called _the tide_; thus we say, _the tide runs strong_, _the tide runs at the rate of one, two, or three miles an hour, &c._ and when we are at a part of the river behind the top of the wave, and find the water lower than high-water mark, and running towards the sea, we say, _the tide runs ebb_; and when we are before the top of the wave, and find the water higher than low-water mark, and running from the sea, we say, _the tide runs flood_; but these expressions are only locally proper; for a tide, strictly speaking, is _one whole wave_, including all its parts higher and lower, and these waves succeed one another about twice in twenty-four hours.

This motion of the water, occasioned by its gravity, will explain to you why the water near the mouths of rivers may be salter at high water than at low. Some of the salt-water, as the tide wave enters the river, runs from its top and fore side, and mixes with the fresh, and also pushes it back up the river.

Supposing that the water commonly runs during the flood at the rate of two miles in an hour, and that the flood runs five hours, you see that it can bring at most into our canal only a quantity of water equal to the space included in the breadth of the canal, ten miles of its length, and the depth between low and high-water mark; which is but a fourteenth part of what would be necessary to fill all the space between low and high-water mark, for one hundred and forty miles, the whole length of the canal.

And indeed such a quantity of water as would fill that whole space, to run in and out every tide, must create so outrageous a current, as would do infinite damage to the shores, shipping, &c. and make the navigation of a river almost impracticable.

I have made this letter longer than I intended, and therefore reserve for another what I have further to say on the subject of tides and rivers. I shall now only add, that I have not been exact in the numbers, because I would avoid perplexing you with minute calculations, my design at present being chiefly to give you distinct and clear ideas of the first principles.

After writing six folio pages of philosophy to a young girl, is it necessary to finish such a letter with a compliment?--Is not such a letter of itself a compliment?--Does it not say, she has a mind thirsty after knowledge, and capable of receiving it; and that the most agreeable things one can write to her are those that tend to the improvement of her understanding?--It does indeed say all this, but then it is still no compliment; it is no more than plain honest truth, which is not the character of a compliment. So if I would finish my letter in the _mode_, I should yet add some thing that means nothing, and is _merely_ civil and polite. But being naturally aukward at every circumstance of ceremony, I shall not attempt it. I had rather conclude abruptly with what pleases me more than any compliment can please you, that I am allowed to subscribe myself

Your affectionate friend,

B. FRANKLIN.

TO THE SAME.

_On the same Subject._

_Craven-street, Monday, March 30, 1761._

MY DEAR FRIEND,

Supposing the fact, that the water of the well at Bristol is warmer after sometime pumping, I think your manner of accounting for that increased warmth very ingenious and probable. It did not occur to me, and therefore I doubted of the fact.

You are, I think quite right in your opinion, that the rising of the tides in rivers is not owing to the immediate influence of the moon on the rivers. It is rather a subsequent effect of the influence of the moon on the sea, and does not make its appearance in some rivers till the moon has long passed by. I have not expressed myself clearly if you have understood me to mean otherwise. You know I have mentioned it as a fact, that there are in some rivers several tides all existing at the same time; that is, two, three, or more, high-waters, and as many low-waters, in different parts of the same river, which cannot possibly be all effects of the moon's immediate action on that river; but they may be subsequent effects of her action on the sea.

In the enclosed paper you will find my sentiments on several points relating to the air, and the evaporation of water. It is Mr. Collinson's copy, who took it from one I sent through his hands to a correspondent in France some years since; I have, as he desired me, corrected the mistakes he made in transcribing, and must return it to him; but if you think it worth while, you may take a copy of it: I would have saved you any trouble of that kind, but had not time.

Some day in the next or the following week, I purpose to have the pleasure of seeing you at Wanstead: I shall accompany your good mamma thither, and stay till the next morning, if it may be done without incommoding your family too much.--We may then discourse any points in that paper that do not seem clear to you; and taking a walk to lord Tilney's ponds, make a few experiments there to explain the nature of the tides more fully. In the mean time, believe me to be, with the highest esteem and regard, your sincerely affectionate friend,

B. FRANKLIN.

TO THE SAME.

_Salt-Water rendered fresh by Distillation.--Method of relieving
Thirst by Sea-Water._

_Craven-street, August 10, 1761._

We are to set out this week for Holland, where we may possibly spend a month, but purpose to be at home again before the coronation. I could not go without taking leave of you by a line at least, when I am so many letters in your debt.

In yours of May 19, which I have before me, you speak of the ease with which salt water may be made fresh by distillation, supposing it to be, as I had said, that in evaporation the air would take up water but not the salt that was mixed with it. It is true that distilled sea water will not be salt, but there are other disagreeable qualities that rise with the water in distillation; which indeed several besides Dr. Hales have endeavoured by some means to prevent; but as yet their methods have not been brought much into use.

I have a singular opinion on this subject, which I will venture to communicate to you, though I doubt you will rank it among my whims. It is certain that the skin has _imbibing_ as well as _discharging_ pores; witness the effects of a blistering plaister, &c. I have read that a man, hired by a physician to stand by way of experiment in the open air naked during a moist night, weighed near three pounds heavier in the morning. I have often observed myself, that however thirsty I may have been before going into the water to swim, I am never long so in the water. These imbibing pores, however, are very fine, perhaps fine enough in filtering to separate salt from water; for though I have soaked (by swimming, when a boy) several hours in the day for several days successively in salt-water, I never found my blood and juices salted by that means, so as to make me thirsty or feel a salt taste in my mouth: and it is remarkable, that the flesh of sea fish, though bred in salt-water, is not salt.--Hence I imagine, that if people at sea, distressed by thirst when their fresh water is unfortunately spent, would make bathing-tubs of their empty water-casks, and, filling them with sea-water, sit in them an hour or two each day, they might be greatly relieved. Perhaps keeping their clothes constantly wet might have an almost equal effect; and this without danger of catching cold. Men do not catch cold by wet cloaths at sea. Damp, but not wet linen may possibly give colds; but no one catches cold by bathing, and no clothes can be wetter than water itself. Why damp clothes should then occasion colds, is a curious question, the discussion of which I reserve for a future letter, or some future conversation.

Adieu, my little philosopher. Present my respectful compliments to the good ladies your aunts, and to miss Pitt; and believe me ever

Your affectionate friend,

And humble Servant,

B. FRANKLIN.

TO THE SAME.

_Tendency of Rivers to the Sea.--Effect of the Sun's Rays on Cloths
of different Colours._

_Sept. 20, 1761._

MY DEAR FRIEND,

It is, as you observed in our late conversation, a very general opinion, that _all rivers run into the sea_, or deposite their waters there. 'Tis a kind of audacity to call such general opinions in question, and may subject one to censure. But we must hazard something in what we think the cause of truth: and if we propose our objections modestly, we shall, though mistaken, deserve a censure less severe, than when we are both mistaken and insolent.

That some rivers run into the sea is beyond a doubt: such, for instance, are the Amazons, and I think the Oronoko and the Mississippi. The proof is, that their waters are fresh quite to the sea, and out to some distance from the land. Our question is, whether the fresh waters of those rivers whose beds are filled with salt water to a considerable distance up from the sea (as the Thames, the Delaware, and the rivers that communicate with Chesapeak-bay in Virginia) do ever arrive at the sea? And as I suspect they do not, I am now to acquaint you with my reasons; or, if they are not allowed to be reasons, my conceptions at least, of this matter.

The common supply of rivers is from springs, which draw their origin from rain that has soaked into the earth. The union of a number of springs forms a river. The waters as they run, exposed to the sun, air, and wind, are continually evaporating. Hence in travelling one may often see where a river runs, by a long blueish mist over it, though we are at such a distance as not to see the river itself. The quantity of this evaporation is greater or less, in proportion to the surface exposed by the same quantity of water to those causes of evaporation. While the river runs in a narrow confined channel in the upper hilly country, only a small surface is exposed; a greater as the river widens. Now if a river ends in a lake, as some do, whereby its waters are spread so wide as that the evaporation is equal to the sum of all its springs, that lake will never overflow:--And if instead of ending in a lake, it was drawn into greater length as a river, so as to expose a surface equal in the whole to that lake, the evaporation would be equal, and such river would end as a canal; when the ignorant might suppose, as they actually do in such cases, that the river loses itself by running under ground, whereas in truth it has run up into the air.

Now, many rivers that are open to the sea widen much before they arrive at it, not merely by the additional waters they receive, but by having their course stopped by the opposing flood-tide; by being turned back twice in twenty-four hours, and by finding broader beds in the low flat countries to dilate themselves in; hence the evaporation of the fresh water is proportionably increased; so that in some rivers it may equal the springs of supply. In such cases, the salt water comes up the river, and meets the fresh in that part where, if there were a wall or bank of earth across from side to side, the river would form a lake, fuller indeed at some times than at others, according to the seasons, but whose evaporation would, one time with another, be equal to its supply.

When the communication between the two kinds of water is open, this supposed wall of separation may be conceived as a moveable one, which is not only pushed some miles higher up the river by every flood tide from the sea, and carried down again as far by every tide of ebb, but which has even this space of vibration removed nearer to the sea in wet seasons, when the springs and brooks in the upper country are augmented by the falling rains, so as to swell the river, and farther from the sea in dry seasons.

Within a few miles above and below this moveable line of separation, the different waters mix a little, partly by their motion to and fro, and partly from the greater specific gravity of the salt water, which inclines it to run under the fresh, while the fresh water, being lighter, runs over the salt.

Cast your eye on the map of North America, and observe the bay of Chesapeak in Virginia, mentioned above; you will see, communicating with it by their mouths, the great rivers Sasquehanah, Potowmack, Rappahanock, York, and James, besides a number of smaller streams, each as big as the Thames. It has been proposed by philosophical writers, that to compute how much water any river discharges into the sea in a given time, we should measure its depth and swiftness at any part above the tide; as, for the Thames, at Kingston or Windsor. But can one imagine, that if all the water of those vast rivers went to the sea, it would not first have pushed the salt water out of that narrow-mouthed bay, and filled it with fresh?--The Sasquehanah alone would seem to be sufficient for this, if it were not for the loss by evaporation. And yet that bay is salt quite up to Annapolis.

As to our other subject, the different degrees of heat imbibed from the sun's rays by cloths of different colours, since I cannot find the notes of my experiment to send you, I must give it as well as I can from memory.

But first let me mention an experiment you may easily make yourself. Walk but a quarter of an hour in your garden when the sun shines, with a part of your dress white, and a part black; then apply your hand to them alternately, and you will find a very great difference in their warmth. The black will be quite hot to the touch, the white still cool.

Another. Try to fire the paper with a burning glass. If it is white, you will not easily burn it;--but if you bring the focus to a black spot, or upon letters, written or printed, the paper will immediately be on fire under the letters.

Thus fullers and dyers find 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 so 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 taylor'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 sun-shiny 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 much 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 clothes 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 an 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 soleil?_ 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 blacked 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?--I am,

Yours affectionately,

B. FRANKLIN.

TO MR. HOPKINSON.

_On the Vis Inertiæ of Matter._

_Philadelphia, 1748._

SIR,

According to my promise, I send you _in writing_ my observations on your book[18]: you will be the better able to consider them; which I desire you to do at your leisure, and to set me right where I am wrong.

I stumble at the threshold of the building, and therefore have not read farther. The author's _vis inertiæ essential to matter_, upon which the whole work is founded, I have not been able to comprehend. And I do not think he demonstrates at all clearly (at least to me he does not) that there is really _such a property in matter_.

He says, No. 2. "Let a given body or mass of matter be called _a_, and let any given celerity be called c. That _celerity_ doubled, tripled, &c. or halved, thirded, &c. will be 2 _c_, 3 _c_, &c. or ½ _c_, ⅓ _c_, &c. respectively: also the _body_ doubled, tripled, or halved, thirded, will be 2 _a_, 3 _a_, or ½ _a_, ⅓ _a_, respectively." Thus far is clear.--But he adds, "Now to move the body _a_ with the celerity _c_, requires a certain force to be impressed upon it; and to move it with a celerity as 2 _c_, requires _twice that force_ to be impressed upon it, &c." Here I suspect some mistake creeps in by the author's not distinguishing between a great force applied at once, or a small one continually applied, to a mass of matter, in order to move it. I think it is generally allowed by the philosophers, and, for aught we know, is certainly true, that there is no mass of matter, how great soever, but may be moved by any force how small soever (taking friction out of the question) and this small force continued, will in time bring the mass to move with any velocity whatsoever.--Our author himself seems to allow this towards the end of the same No. 2. when he is subdividing his celerities and forces: for as in continuing the division to eternity by his method of ½ _c_, ⅓ _c_, ¼ _c_, ⅕ _c_, &c. you can never come to a fraction of velocity that is equal to 0 _c_, or no celerity at all; so dividing the force in the same manner, you can never come to a fraction of force that will not produce an equal fraction of celerity.--Where then is the mighty vis inertiæ, and what is its strength; when the greatest assignable mass of matter will give way to, or be moved by the _least_ assignable force? Suppose two globes, equal to the sun and to one another, exactly equipoised in Jove's balance; suppose no friction in the centre of motion, in the beam or elsewhere: if a musketo then were to light on one of them, would he not give motion to them both, causing one to descend and the other to rise? If it is objected, that the force of gravity helps one globe to descend, I answer, the same force opposes the other's rising: here is an equality that leaves the whole motion to be produced by the musketo, without whom those globes would not be moved at all.--What then does vis inertiæ do in this case? and what other effect could we expect _if there were no such thing_? Surely if it were any thing more than a phantom, there might be enough of it in such _vast_ bodies to annihilate, by its opposition to motion, so trifling a force?

Our author would have reasoned more clearly, I think, if, as he has used the letter _a_ for a certain quantity of matter, and _c_ for a certain quantity of celerity, he had employed one letter more, and put _f_ perhaps, for a certain quantity of force. This let us suppose to be done; and then as it is a maxim that the force of bodies in motion is equal to the quantity of matter multiplied by the celerity, (or _f_ = _c_ X _a_); and as the force received by and subsisting in matter, when it is put in motion, can never exceed the force given; so if, _f_ moves _a_ with _c_, there must needs be required 2 _f_ to move _a_ with 2 _c_; for _a_ moving with 2 _c_ would have a force equal to 2 _f_, which it could not receive from 1 _f_; and this, not because there is such a thing as vis inertiæ, for the case would be the same _if that had no existence_; but because nothing _can_ give more than it has, if 1 _f_ can to 1 _a_ give 1 _c_, which is the same thing as giving it 1 _f_; (i. e. if force applied to matter at rest, can put it in motion, and give it _equal_ force) where then is vis inertiæ? If it existed at all in matter, should we not find the quantity of its resistance subtracted from the force given?

In No. 4. our author goes on and says, "the body _a_ requires a certain force to be impressed on it to be moved with a celerity as _c_, or such a force is necessary; and therefore makes a certain resistance, &c. A body as 2 _a_ requires _twice_ that force to be moved with the _same celerity_, or it makes twice that resistance; and so on."--This I think is not true; but that the body 2 _a_ moved by the force 1 _f_ (though the eye may judge otherwise of it) does really move with the same celerity as it did when impelled by the same force; for 2 _a_ is compounded of 1 _a_ + 1 _a_: and if each of the 1 _a_'s or each part of the compound were made to move with 1 _c_ (as they might be by 2 _f_) then the whole would move with 2 _c_, and not with 1 _c_, as our author supposes. But 1 _f_ applied to 2 _a_, makes each _a_ move with ½ _c_; and so the whole moves with 1 _c_; exactly the same as 1 _a_ was made to do by 1 _f_ before. What is equal celerity but a _measuring the same space by moving bodies in the same time_?--Now if 1 _a_ impelled by 1 _f_ measures 100 yards in a minute; and in 2 _a_ impelled by 1 _f_, each _a_ measures 50 yards in a minute, which added make 100; are not the celerities as the forces equal? and since force and celerity in the same quantity of matter are always in _proportion_ to each other, why should we, when the quantity of matter is doubled, allow the force to continue unimpaired, and yet suppose one half of the celerity to be lost?--I wonder the more at our author's mistake in this point, since in the same number I find him observing: "We may easily conceive that a body as 3 _a_, 4 _a_, &c. would make 3 or 4 bodies equal to once _a_, each of which would require once the first force to be moved with the celerity _c_." If then in 3 _a_, each _a_ requires once the first force _f_ to be moved with the celerity _c_, would not each move with the force _f_ and celerity _c_; and consequently the whole be 3 _a_ moving with 3 _f_ and 3 _c?_ After so distinct an observation, how could he miss of the consequence, and imagine that 1 _c_ and 3 _c_ were the same? Thus as our author's abatement of celerity in the case of 2 _a_ moved by 1 _f_ is imaginary, so must be his additional resistance.--And here again, I am at a loss to discover any effect of the vis inertiæ.

In No. 6, he tells us, "that all this is likewise certain when taken the contrary way, viz. _from motion to rest_; for the body _a_ moving with a certain velocity, as _c_, requires a certain degree of force or resistance to stop that motion, &c. &c." that is, in other words, equal force is necessary to destroy force. It may be so. But how does that discover a vis inertiæ? would not the effect be the same _if there were no such thing_? A force 1 _f_ strikes a body 1 _a_, and moves it with the celerity 1 _c_, i. e. with the force 1 _f_: It requires, even according to our author, only an opposing 1 _f_ to stop it. But ought it not (if there were a vis inertiæ) to have not only the force 1 _f_, but an additional force equal to the force of vis inertiæ, that _obstinate power by which a body endeavours with_ all its might _to continue in its present state, whether of motion or rest_? I say, ought there not to be an opposing force equal to the sum of these?--The truth however is, that there is no body, how large soever, moving with any velocity, how great soever, but may be stopped by any opposing force, how small soever, continually applied. At least all our modern philosophers agree to tell us so.

Let me turn the thing in what light I please, I cannot discover the vis inertiæ, nor any effect of it. It is allowed by all, that a body 1 _a_ moving with a velocity 1 _c_, and a force 1 _f_ _striking another_ body 1 _a_ at rest, they will afterwards _move on together_, each with ½ _c_ and ½ _f_; which, as I said before, is equal in the whole to 1 _c_ and 1 _f_. If vis inertiæ, as in this case, neither abates the force nor the velocity of bodies, what does it, or how does it discover itself?

I imagine I may venture to conclude my observations on this piece, almost in the words of the author; that if the doctrines of the immateriality of the soul and the existence of God and of divine providence are demonstrable from no plainer principles, the _deist_ [i.e. _theist_] has a desperate cause in hand. I oppose _my theist_ to his atheist, because I think they are diametrically opposite; and not near of kin, as Mr. Whitfield seems to suppose; where (in his journal) he tells us, "_M. B. was a deist, I had almost said an atheist_;" that is, _chalk_, I had almost said _charcoal_.

The din of the market[19] increases upon me; and that, with frequent interruptions, has, I find, made me say some things twice over; and, I suppose, forget some others I intended to say. It has, however, one good effect, as it obliges me to come to the relief of your patience with

Your humble servant,

B. FRANKLIN.

FOOTNOTES:

[18] Baxter's Inquiry into the Nature of the Human Soul. B. V.

[19] Philadelphia market, in which Dr. Franklin lived. B. V.

TO JOHN PRINGLE, M. D. AND F. R. S.

_On the different Strata of the Earth._

_Craven-Street, Jan. 6, 1758._

SIR,

I return you Mr. Mitchell's paper on the strata of the earth[20] with thanks. The reading of it, and perusal of the draft that accompanies it, have reconciled me to those convulsions which all naturalists agree this globe has suffered. Had the different strata of clay, gravel, marble, coals, lime-stone, sand, minerals, &c. continued to lie level, one under the other, as they may be supposed to have done before those convulsions, we should have had the use only of a few of the uppermost of the strata, the others lying too deep and too difficult to be come at; but the shell of the earth being broke, and the fragments thrown into this oblique position, the disjointed ends of a great number of strata of different kinds are brought up to day, and a great variety of useful materials put into our power, which would otherwise have remained eternally concealed from us. So that what has been usually looked upon as a _ruin_ suffered by this part of the universe, was, in reality, only a preparation, or means of rendering the earth more fit for use, more capable of being to mankind a convenient and comfortable habitation.

I am, Sir, with great esteem, yours, &c.

B. FRANKLIN.

FOOTNOTE:

[20] See this paper afterwards printed in the _Philosophical Transactions_.

TO THE ABBE SOULAVIE.

Occasioned by his sending me some notes he had taken of what I had
said to him in conversation on the Theory of the Earth. I wrote
it to set him right in some points wherein he had mistaken my
meaning.[21]

_Passy, September 22, 1782._

SIR,

I return the papers with some corrections. I did not find coal mines under the calcareous rock in Derbyshire. I only remarked, that at the lowest part of that rocky mountain which was in sight, there were oyster shells mixed in the stone; and part of the high county of Derby being probably as much above the level of the sea, as the coal mines of Whitehaven were below it, seemed a proof, that there had been a great _bouleversement_ in the surface of that island, some part of it having been depressed under the sea, and other parts, which had been under it, being raised above it. Such changes in the superficial parts of the globe, seemed to me unlikely to happen, if the earth were solid to the centre. I therefore imagined, that the internal parts might be a fluid more dense, and of greater specific gravity than any of the solids we are acquainted with, which therefore might swim in or upon that fluid. Thus the surface of the globe would be a shell, capable of being broken and disordered by the violent movements of the fluid on which it rested. And as air has been compressed by art so as to be twice as dense as water, in which case, if such air and water could be contained in a strong glass vessel, the air would be seen to take the lowest place, and the water to float above and upon it; and as we know not yet the degree of density to which air may be compressed, and M. Amontons calculated, that its density increasing as it approached the centre, in the same proportion as above the surface, it would at the depth of [___] leagues, be heavier than gold, possibly the dense fluid occupying the internal parts of the globe might be air compressed. And as the force of expansion in dense air when heated is in proportion to its density, this central air might afford another agent to move the surface, as well as be of use in keeping alive the subterraneous fires; though, as you observe, the sudden rarefaction of water coming into contact without those fires, may also be an agent sufficiently strong for that purpose, when acting between the incumbent earth and the fluid on which it rests.