TWO DISCOURSES OF THE OBJECTS, PLEASUKES, AND ADVANTAGES, I. OF SCIENCE: n. OF POLITICAL SCIENCE. BY HENRY LORD BROUGHAM, F.R.S, AND MEMBER OF THE NATIONAL INSTITUTE OF FKANCE. LONDON: CHARLES KNIGHT & CO., LUDGATE STREET. 1846. ADVERTISEMENT. The Discourse of the 'Objects, Pleasures, and Advantages of Science/ was originally published as the Introductory Treatise to the ' Library of Useful Knowledge.' It was the first step in that remarkable advance in the Instruction of the People, by the means of cheap books, which was commenced by the Society for the Diffusion of Useful Know- ledge nearly twenty years ago. The Discourse of the ' Objects, Pleasures, and Advantages of Political Knowledge' was published at a later period as the Introductory Treatise to Lord Brougham's ' Political Philosophy.' Both Discourses are reprinted in this Volume by permission of the noble author, under an arrangement with the Society for the Diffusion of Useful Knowledge as to the Copyright of each. OBJECTS, ADVANTAGES, AND PLEASUEES OF SCIENCE. Digitized by tine Internet Arciiive in 2010 witii funding from Boston Library Consortium IVIember Libraries littp://www.arcli ive.org/details/dialoguesoninsti00brou2 ( r ) INTRODUCTION. In order fully to understand the advantages and the pleasures which are derived from an acquaint- ance with any Science, it is necessary to become acquainted with that Science ; and it would there- fore be impossible to convey a complete knowledge of the benefits conferred by a study of the various Sciences which have hitherto been cultivated by philosophers, without teaching all the branches of them. But a very distinct idea may be given of those benefits, by explaining the nature and objects of the different Sciences : it may be shown, by ex- amples, how much use and gratification thtre is in learning a part of any one branch of knowledge ; and it may thence be inferred, how great reason there is to learn the whole. It may easily be demonstrated, that there is an advantage in learning, both for the usefulness and the pleasure of it. There is something positively agreeable to all men, to all at least whose nature is not most grovelling and base, in gaining knowledge for its own sake. When you see anything for the B 2 8 OBJECTS, ADVANTAGES, AND first time, you at once derive some gratification from the sight being new ; your attention is awakened, and you desire to know more about it. If it is a piece of workmanship, as an instrument, a machine of any kind, you wish to know how it is made ; how it works ; and what use it is of. If it is an animal, you desire to know where it comes from ; how it lives ; what are its dispositions, and, gene- rally, its nature and habits. You feel this desire, too, without at all considering that the machine or the animal may ever be of the least use to yourself practically ; for, in all probability, you may never see them again. But you have a curiosity to learn all about them, because they are new and unknown. You accordingly make inquiries ; you feel a gratification in getting answers to your ques- tions, that is, in receiving information, and in knowing more, — in being better informed than you were before. If you happen again to see the same instrument or animal, you find it agreeable to re- collect having seen it formerly, and to think that you know something about it. If you see another instrument or animal, in some respects like, but differing in other particulars, you find it pleasing to compare them together, and to note in wha* they agree, and in what they differ. Now, all this kind of gratification is of a pure and disinterested nature, and has no reference to any of the common purposes of life ; yet it is a pleasure — an enjoy- PLEASURES OF SCIENCE. 9 ment. You are nothing- the richer for it ; you do not gratify your palate or any other bodily appe- tite ; and yet it is so pleasing, that you would give something out of your pocket to obtain it, and would forego some bodily enjoyment for its sake. The pleasure derived from Science is exactly of the like nature, or, rather, it is the very same. For what has just been spoken of is, in fact, Science, which in its most comprehensive sense only means Knowledge, and in its ordinary sense means Know- ledge reduced to a System ; that is, arranged in a regular order, so as to be conveniently taught, easily remembered, and readily applied. The practical uses of any science or branch of knowledge are undoubtedly of the highest import- ance ; and there is hardly any man who may not gain some positive advantage in his worldly wealth and comforts, by increasing his stock of information. But there is also a pleasure in seeing the uses to which knowledge may be applied, wholly indepen- dent of the share we ourselves may have in those practical benefits. It is pleasing to examine the nature of a new instrument, or the liabits of an un- known animal, without considering whether or not they may ever be of use to ourselves or to any bod}''. It is another gratification to extend our in- quiries, and find that the instrument or animal is useful to man, even although we have no chance of ever benefiting by the information : as, to find that 10 OBJECTS, ADVANTAGES, AND the natives of some distant country employ the animal in travelling* ; — nay, though we have no desire of benefiting by the knowledge ; as for ex- ample, to find that the instrument is useful in per- forming some dangerous surgical operation. The mere gratification of curiosity ; the knowing more to-day than we knew yesterday ; the understanding clearly what before seemed obscure and puzzling ; the contemplation of general truths, and the com- paring together of diflferent things, — is an agree- able occupation of the mind ; and, beside the pre- sent enjoyment, elevates the faculties above low pursuits, purifies and refines the passions, and helps our reason to assuage their violence. It is very true, that the fundamental lessons of philosophy may to many, at first sight, wear a for- bidding aspect, because to comprehend them re- quires an effort of the mind somewhat, though certainly not much, greater than is wanted for un- derstanding more ordinary matters ; and the most important branches of philosophy, those which are of the most general application, are for that very reason the less easily followed, and the less entertaining when apprehended, presenting as they do few par- ticulars or individual objects to the mind. In dis- coursing of them, moreover, no figures will be at present used to assist the imagination ; the appeal Is made to reason, without help from the senses. But be not, therefore, prejudiced against the doc- PLEASURES OF SCIENCE. 11 trine, that the pleasure of learning the truths which philosophy unfolds is truly above all price.. Lend but a patient attention to the principles explained, and giving us credit for stating nothing which has not some practical use belonging to it, or some important doctrine connected with it, you will soon perceive the value of the lessons you are learning, and begin to in- terest yourselves in comprehending and recollecting them ; you will find that you have actually learnt something of science, while merely engaged in seeing what its end and purpose is ; you will be enabled to calculate for yourselves, how far it is worth the trouble of acquiring, by examining samples of it ; you will, as it were, taste a little, to try whether or not you relish it, and ought to seek after more ; you will enable yourselves to go on, and enlarge your stock of it ; and after having first mastered a very little, you will proceed so far as to look back with wonder at the distance you have reached beyond your earliest acquirements. The Sciences may be divided into three great classes : those which relate to Number and Quan- tity— those which relate to Matter- — and those which relate to Mind. The first are called the Mathematics^ and teach the property of numbers and of figures ; the second are called Natural Philosophy^ and teach the properties of the various bodies which we are acquainted with by means of our senses ; the third are called Intellectual or 12 OBJECTS, ADVANTAGES, AND Moral Philosophy, and teach the nature of the mind, of the existence of which we have the most perfect evidence in our own reflections ; or, in other words, they teach the moral nature of man, both as an individual and as a member of society. Connected with all the sciences, and subservient to to them, though not one of their number, is His- tory, or the record of facts relating to all kinds of knowledge. I. MATHEMATICAL SCIENCE. The two great branches of the Mathematics, or the two mathematical sciences, are Arithmetic, the science of number, from the Greek word signify- ing nymber, and Geometry, the science of figure, from the Greek words signifying measure of the earth, — land-measuring having first turned men's attention to it. When we say that 2 and 2 make 4, we state an arithmetical proposition, very simple indeed, but connected with many others of a more diflficult and complicated kind. Thus, it is another proposition, somewhat less simple, but still very obvious, that 5 multiplied by 10, and divided by 2 is equal to, or makes the same number with, 100 divided by 4 — both results being equal to 25. So, to find how many farthings there are in 1000/., and how many PLEASURES OF SCIENCE. 13 minutes in a year, are questions of arithmetic which we learn to work by being taught the principles of the science one after another, or, as they are com- monly called, the rules of addition, subtraction, multiplication, and division. Arithmetic may be said to be the most simple, though among the most useful of the sciences ; but it teaches only the pro- perties of particular and known numbers, and it only enables us to add, subtract, multiply, and divide those numbers. But suppose we wish to add, subtract, multiply, or divide numbers which we have not yet ascertained, and in all respects to deal with them as if they were known, for the pur- pose of arriving at certain conclusions respecting them, and, among other things, of discovering what they are ; or, suppose we would examine pro- perties belonging to all numbers ; this must be performed by a peculiar kind of arithmetic, called Universal diYiihiTHiXic, or Algebra.* The common arithmetic, you will presently perceive, carries the seeds of this most important science in its bosom. Thus, suppose we inquire what is the number which multiplied by 5 makes 10 ? This is found if we divide 10 by 5, — it is 2: but suppose that, before finding this number 2, and before knowing what it is, we would add it, whatever it may turn * Algebra, from the Arabic words signifying the reduc- tion of fractions ; the Arabs having brought the knowledge of it into Europe. B 3 14 OBJECTS, ADVANTAGES, AND out, to some other number ; this can only be done by putting some mark, such as a letter of the alphabet, to stand for the unknown number, and adding that letter as if it were a known number. Thus, suppose we want to find two numbers which, added together, make 9, and, multiplied by one another, make 20. There are many which, added together, make 9 ; as 1 and 8 ; 2 and 7 ; 3 and 6 ; and so on. We have, therefore, occasion to use the second condition, that multiplied by one another they should make 20, and to work upon this con- dition before we have discovered the particular numbers. We must, therefore, suppose the numbers to be found, and put letters for them, and by rea- soning upon those letters, according to both the two conditions of adding and multiplying, we find what they must each of them be in figures, in order to fulfil or answer the conditions. Algebra teaches the rules for conducting this reasoning, and obtaining this result successfully ; and by means of it we are enabled to find out numbers which are unknown, and of which we only know that they stand in certain relations to known numbers, or to one another. The instance now taken is an easy one ; and you could, by consider- ing the question a little, answer it readily enough ; that is, by trying different numbers, and seeing which suited the conditions ; for you plainly see that 5 and 4 are the two numbers sought; but you PLEASURES OF SCIENCE. 15 see this by no certain or general rule applicable to all cases, and therefore you could never work more difficult questions in the same way ; and even questions of a moderate degree of difficulty would laive an endless number of trials or guesses to answer. Thus a shepherd sold his flock for 80/. ; and if he had sold four sheep more for the same money, he would have received one pound less for each sheep. To find out from this, how many the flock consisted of, is a very easy question in algebra, but would require a vast many guesses, and a long time to hit upon by common arithmetic : * And questions infinitely more difficult can easily be solved by the rules of algebra. In like manner, by arithmetic you can tell the properties of particu- lar numbers ; as, for instance, that the number 348 is divided by 3 exactly, so as to leave nothing over : but algebra teaches us that it is only one of an infinite variety of numbers, all divisible by 3, and any one of which you can tell the moment you see it ; for they all have the remarkable property, that if you add together the figures they consist of, the sum total is divisible by 3. You can easily perceive this in any one case, as in the number mentioned, for 3 added to 4 and that to 8 make 15, which is plainly divisible by 3 ; and if you divide 348 by 3, you find the quotient to be 116, with nothing over. But this does not at all prove that * It is 16. 16 OBJECTS, ADVANTAGES, AND any other number, the sum of whose figures is divisible by 3, will itself also be found divisible by 3, as 741 ; for you must actually perform the division here, and in every other case, before you can know that it leaves notliing over. Algebra, on the con- trary, both enables you to discover such general pro- perties, and to prove them in all their generality.* By means of this science, and its various appli- cations, the most extraordinary calculations may be performed. We shall give, as an example, the method of Logarithms, which proceeds upon this principle. Take a set of numbers going on by equal differences ; that is to say, the third being as much greater than the second, as the second is greater than the first, and the common dif- ference being the number you begin with ; thus, 1, 2, 3, 4, 5, 6, and so on, in which the common difference is 1 : then take another set of numbers, * Another class of numbers divisible by 3 is discovered in like manner by algebra. Every number of 3 places, the figures (or digits) composing which are in arithmetical progression, (or rise above each other by equal differences,) is divisible by 3: as 123, 789, 357, 159, and so on. The same is true of numbers of any amount of places, provided they are composed of 3, 6, 9, &c., numbers rising above each other by equal differences, as 289, 299, 309, or 148, 214, 280, or 307142085345G48276198756, which number of 24 places is divisible by 3, being composed of 6 numbers in a series whose common difference is 1137. This pro- perty, too, is only a particular case of a much more gene- ral one. PLEASURES OF SCIENCE. 17 such tliat each is equal to twice or three times the one before it, or any number of times the one before it, but the common multi])lier being- the number you bej^in with : thus, 2, 4, 8, 16, 32, 64, 128; write this second set of numbers under tlie first, or side by side, so that the numbers shall stand opposite to one another, thus, 12 3 4 5 6 7 2 4 8 16 32 64 128 you will find, that if you add together any two of the upper or first set, and go to the number oppo- site their sum, in the lower or second set, you will have in this last set the number arising from mul- tiplying together the numbers of the lower set corre- sponding or opposite to the numbers added together. Thus, add 2 to 4, you have 6 in tlie upper set, opposite to which in the lower set is 64, and multiplying the numbers 4 and 16 opposite to 2 and 4, the product is 64. In like manner, if j'ou subtract one of the upper numbers from ano- ther, and opposite to their difference in the upper line, you look to the lower number, it is the quotient found from dividing one of the lower numbers by the other opposite the subtracted ones. Thus, take 4 from 6 and 2 remains, opposite to which you have in the lower line 4 ; and if you divide 64, the number opposite to 6, by 16, the number opposite to 4, the quotient is 4, The upper set are called the logarithms, of the lower 18 OBJECTS, ADVANTAGES, AND set, which are called natural numbers; and tables may, with a little trouble, be constructed, giving the logarithms of all numbers from 1 to 10,000 and more: so that, instead of multiplying or dividing one number by another, you have only to add or subtract their logarithms, and then you at once find the product or the quotient in the tables. These are made applicable to numbers far higher than any actually in them, by a very simple process : so that you may at once perceive the prodigious sav- ing of time and labour which is thus made. If you had, for instance, to multiply 7,543,283 by itself, and that product again by the original number, you would have to multiply a number of 7 places of figures by an equally large number, and then a number of 14 places of figures by one of 7 places, till at last you had a product of 21 places of figures — a very tedious operation ; but, working by logarithms, you would only have to take three times the logarithm of the original number, and that gives the logarithm of the last product of 21 places of figures, without any further multiplication. So much for the time and trouble saved, which is still greater in questions of division ; but by means of logarithms many questions can be worked, and of the most important kind, which no time or labour would otherwise enable us to resolve. Geometry teaches the properties of figure, or particular portions of space, and distances of points PLEASURES OF SCIENCE. 19 from each other. Thus, when you see a triangle^ or three-sided figure, one of whose sides is perpen- dicular to another side, you find, by means of geo- metrical reasoning respecting this kind of triangle, that if squares be drawn on its three sides, the large square upon the slanting side opposite the two perpendiculars, is exactly equal to the smaller squares upon the perpendiculars, taken together ; and this is absolutely true, whatever be the size of the triangle, or the proportions of its sides to each other. Therefore, you can always find the length of any one of the three sides by knowing the lengths of the other two. Suppose one perpen- dicular side to be 3 feet long, the other 4, and you want to know the length of the third side opposite to the perpendicular ; you have only to find a number such, that if, multiplied by itself, it shall be equal to 3 times 3, together with 4 times 4, that is 25.* (This number is 5.) Now only observe the great advantage of know- ing this property of the triangle, or of perpendicu- lar lines. If you want to measure a line passing over ground which you cannot reach — to know. * It is a propei'ty of numbers, that every number -what- ever, whose last place is either 5 or 0, is, when multiplied into itself, equal to two others which are square numbers, and divisible by 3 and 4 respectively : — thus, 45 X 45 ^2025= 729+1298, the squares of 27 and 36; and 60X60 = 3600= 1296-1-2304, the squares of 36 and 48. 20 OBJECTS, ADVANTAGES, AND for instance, the length of one side, covered with water, of a field, or the distance of one point on a lake or bay from another point on the opposite side — you can easily find it by measuring two lines perpendicular to one another on the dry land, and running through the two points ; for the line wished to be measured, and which runs through the water, is the third side of a perpendicular-sided triangle, the other two sides of which are ascer- tained. But there are other properties of tri- angles, which enable us to know the length of two sides of any triangle, whether it has perpendicular sides or not, by measuring one side, and also mea- suring the inclinations of the other two sides to this side, or what is called the two angles made by those sides with the measured side. Therefore you can easily find the perpendicular line drawn, or supposed to be drawn, from the top of a moun- tain through it to the bottom, that is, the height of the mountain ; for you can measure a line on level ground, and also the inclination of two lines, sup- posing them drawn in the air, and reaching from the two ends of the measured line to the mountain's top ; and having thus found the length of the one of those lines next the mountain, and its inclination to the ground, you can at once find the perpendi- cular, though you cannot possibly get near it. In the same way, by measuring lines and angles on the ground, and near, you can find the length of PLEASURES OF SCIENCE. 21 lines at a great distance, and wliich you cannot approach : for instance, the length and breadth of a field on the opposite side of a lake or sea ; the distance of two islands ; or the space between the tops of two mountains. Again, there are curve-lined figures as well as straight, and geometry teaches the properties of these also. The best known of all the curves is the circle^ or a figure made by drawing a string round one end which is fixed, and marking w^here its other end traces, so that every part of the circle is equally distant from the fixed point or centre. From this fundamental property, an infinite variety of others follow by steps of reasoning more or less numerous, but all necessarily arising one out of another. To give an instance ; it is proved by geometrical reasoning, that if from the two ends of any diameter of the circle you draw two lines to meet in any one point of the circle whatever, those lines are perpendicular to each other. Another property, and a most useful one, is, that the sizes, or areas, of all circles whatever, from the greatest to the smallest, from the sun to a watch-dialplate, are in exact proportion to the squares of their distances from the centre ; that is, the squares of the strings they are drawn with : so that if you draw a circle with a string 5 feet long, and another with a string 10 feet long, the large circle is four times the size of the small one, as far 22 OBJECTSj ADVANTAGES, AND as the space or area inclosed is concerned ; the square of 10 or 100 being four times the square of 5 or 25. But it is also true, that the lengths of the circumferences themselves, the number of feet over which the ends of the strings move, are in proportion to the lengths of the strings ; so that the curve of the large circle is only twice the length of the curve of the lesser. But the circle is only one of an infinite variety of curves, all having a regular formation and fixed properties. The oval or ellipse is, perhaps, next to the circle, the most familiar to us, although we more frequently see another curve, the line formed by the motion of bodies thrown forward. When you drop a stone, or throw it straight up, it goes in a straight line ; when you throw it forward, it goes in a curve line till it reaches the ground ; as you see by the figure in which water runs when forced out of a pump, or from a fire-pipe, or from the spout of a kettle or teapot. The line it moves in is called a parabola ; every point of which bears a certain fixed relation to a certain point within it, as the circle does to its centre. Geometry teaches various properties of this curve : for example, if the direction in which the stone is thrown, or the bullet fired, or the water spouted, be half the per- pendicular to the ground, that is, half way be- tween being level with the ground and being up- right, the curve will come to the ground at a PLEASURES OF SCIENCE. 23 greater distance than if any other direction what- ever were given, with the same force. So that, to make the gun carry farthest, or the fire-pipe play to the greatest distance, they must be pointed, not, as you might suppose, level or point blank, but about half way between that direction and the per- pendicular. If the air did not resistj and so some- what disturb the calculation, the direction to give the longest range ought to be exactly half perpen- dicular. The ovalf or ellipse, is drawn by taking a string of any certain length, and fixing, not one end as in drayving the circle, but both ends to different points, and then carrying a point round inside the string, always keeping it stretched as far as pos- sible. It is plain, that this figure is as regularly drawn as the circle, though it is very diflTerent from it ; and you perceive that every point of its curve must be so placed, that the straight lines drawn from it to the two points where the string was fixed, are, when added together, always the same ; for they make together the length of the string. Among various properties belonging to this curve, in relation to the straight lines drawn within it, is one which gives rise to the construction of the trammels, or elliptic compasses, used for making figures and ornaments of this form ; and 24 OBJECTS, ADVANTAGES, AND also to the construction of lathes for turning oval frames, and the like. If you wish at once to see these three curves, take a pointed sugar-loaf, and cut it any where clean through in a direction parallel to its base or bottom ; the outline or edge of the loaf where it is cut will be 2i circle. If the cut is made so as to slant, and not be parallel to the base of the loaf, the outline is an ellipse, provided the cut goes quite through the sides of the loaf all round, or is •in such a direction that it would pass through the sides of the loaf were they extended ; but if it goes slanting and parallel to the line of the loaf's side, the outline is a parabola ; and if you cut in any direction, not through the sides all round, but through the sides and base, and not parallel to the line of the side, being nearer the perpendicular, the outline will be another curve of which we have not yet spoken, but whf h is called an hyper- bola. You will see another instance of it, if you take two plates of glass, and lay fchem on one another ; then put their edge in water, holding them upright and pressing them together; the water, which, to make it more plain, you may colour with a few drops of ink or strong tea, rises to a certain height, and its outline is this curve ; which, how- ever much it may seem to differ in form from a circle or ellipse, is found by mathematicians to PXEASURES OF SCIENCE. 25 resemble them very closely in many of its most remarkable properties. These are the curve lines best known and most frequently discussed ; but there are an infinite number of others all related to straight lines and other curve lines by certain fixed rules : for ex- ample, the course which any point in the circum- ference of a circle, as a nail in the felly of a wheel rolling along, takes through the air, is a curve called the cycloid^ which has many remarkable properties ; and, among others, this, that it is, of all lines possible, the one in which any body, not falling perpendicularly, will descend from one point to another the most quickly. Another curve often seen is that in which a rope or chain hangs when supported at both ends : it is called the Ca- tenary, from the Latin for chain ; and in this form some arches are built. The form of a sail filled with wind is the same curve. II. DIFFERENCE BETWEEN MATHEMATICAL AND PHYSICAL TRUTHS. You perceive, if you reflect a little, that the science which we have been considering, in both its branches, has nothing to do with matter ; that is to say, it does not at all depend upon the properties or even upon the existence of any bodies or sub- 26 OBJECTS, ADVANTAGES, AND stances whatever. The distance of one point or place from another is a straight line ; and whatever is proved to be true respecting this line, as, for instance, its proportion to other lines of the same kind, and its inclination towards them, what we call the angles it makes with them, would be equally true whether there were anything in those places, at those two points, or not. So if you find the number of yards in a square field, by measuring one side, 100 yards, and then, multiplying that by itself, which makes the whole area 10,000 square yards, this is equally true whatever the field is, whether corn, or grass, or rock, or water ; it is equally true if the solid part, the earth or water, be removed, for then it will be a field of air bounded by four walls or hedges ; but suppose the walls or hedges were removed, and a mark only left at each corner, still it would be true that the space inclosed or bounded by the lines supposed to be drawn between the four marks, w^as 10,000 square yards in size. But the marks need not be there ; you only want them v/hile measuring one side : if they were gone, it would be equally true that the lines, supposed to be drawn from the places where the marks had been, inclose 10,000 square yards of air. But if there were no air, and conse- quently a mere void, or empty space, it would be equally true that this space is of the size you had found it to be by measuring the distance of one PLEASURES OF SCIENCE. 27 point from another, of one of the space's corners or angles from another, and then multiplying that distance by itself. In the same way it would be true, that, if the space were circular, its size, compared with another circular space of half its diameter, would be four times larger : of one-third its diameter nine times larger, and of one-fourth sixteen times, and so on always in proportion to the squares of the diameters ; and that the length of the circumference, the number of feet or yards in the line round the surface, would be twice the length of a circle whose diameter was one half, thrice the circumference of one whose diameter was one-third, four times the circumference of one whose diameter was one-fourth, and so on, in the simple proportion of the diameters. Therefore, every property which is proved to belong to figures belongs to them without the smallest relation to bodies or matter of any kind, although we are accustomed only to see figures in connection with bodies ; but all those properties would be equally true if no such thing as matter or bodies existed ; and the same may be said of the properties of number, the other great branch of the mathematics. When we speak of twice two, and say it makes four, we affirm this without thinking of two horses, or two balls, or two trees ; but we assert it concerning two of any thing and every thing equally. Nay, this branch of matliematics may be said to apply still more ex- 28 OBJECTS, ADVANTAGES, AND tensively than even the other ; for it has no relation to space, which geometry has ; and, therefore, it is applicable to cases where figure and size are wholly out of the question. Thus you can speak of two dreams, or two ideas, or two minds, and can calcu- late respecting them just as you would respecting so many bodies ; and the properties you find be- longing to numbers, will belong to those numbers when applied to things that have no outward or visible or perceivable existence, and cannot even be said to be in any particular place, just as much as the same numbers applied to actual bodies which may be seen and touched. It is quite otherwise with the science which we are now going to consider. Natural Philosophy, This teaches the nature and properties of actually existing substances, their motions, their connections with each other, and their influence on one another. It is sometimes also called Physics, from the Greek word signifying Nature, though that word is more frequently, in common speech, confined to one particular branch of the science, that which treats of the bodily health. ^We have mentioned one distinction between Mathematics and Natural Philosophy, that the former does not depend on the nature and existence of bodies, which the latter entirely does. Another distinction, and one closely connected with this, is, that the truths which Mathematics teach are PJLEASUKES OF SCIENCE. 29 necessarily such, — they are truths of themselves, and wholly independent of facts and experiments, — they depend only upon reasoning- ; and it is utterly impossible they should be otherwise than true. This is the case vvith all the properties which we find belong to numbers and to figures — 2 and 2 must of necessity, and through all time, and in every place, be equal to 4: those numbers must necessarily be always divisible by 3, without leav- ing any remainder over, which have the sums of the figures they consist of divisible by 3 ; and circles must necessarily^ and for ever and ever, be to one another in the exact proportion of the squares of their diameters. It cannot be otherwise ; we cannot conceive it in our minds to be otherwise. No man can in his own mind suppose to himself that 2 and 2 should ever be more or less than 4 ; it would be an utter impossibility — a contradiction in the very ideas ; and if stated in words, those words would have no sense. The other propertiest of number, though not so plain at first sight as this, are proved to be true by reasoning, every one step of which follows from the step immediately before, as a matter of course, and so clearly and unavoid- ably, that it cannot be supposed, or even imagined, to be otherwise ; the mind has no means of fancying how it could be otherwise: the final conclusion, from all the steps of the reasoning or demonstration, as it is called, follows in the same v/ay from the c so OBJECTS, ADVANTAGES, AND last of the steps, and is therefore just as evidently and necessarily true as the first step, which is always something self-evident ; for instance, that 2 and 2 make 4, or that the whole is greater than any of its parts, but equal to all its parts put together. It is through this kind of reasoning, step by step, from the most plain and evident things, that we arrive at the knowledge of other things which seem at first not true, or at least not generally true ; but when we do arrive at them, we perceive that they are just as true, and for the same reasons, as the first and most obvious matters ; that their truth is absolute and necessary, and that it would be as absurd and self-contradictory to suppose they ever could, under any circumstances, be not true, as to suppose that 2 added to 2 could ever make 3, or 5, or 100, or anything but 4; or, which is the same thing, that 4 should ever be equal to 3, or 5, or 100, or anything but 4. To find out these Teasonings, to pursue them to their consequences, and thereby to discover the truths which are not immediately evident, is what science teaches us : but when the truth is once discovered, it is as certain and plain by the reasoning, as the first truths themselves from which all the reasoning takes its rise, on which it all depends, and which require no proof, because they are self-evident at once, and must be assented to the instant they are understood. PLEASURES OF SCIENCE. 31 But it is quite different with the truths which Natural Philosophy teaches. All these depend upon matter of fact ; and that is learnt by observa- tion and experiment, and never could be discovered by reasoning at all. If a man were shut up in a room with pen, ink, and paper, he might by thinking discover any of the truths in arithmetic, algebra, or geometry ; it is possible at least ; there would be nothing absolutely impossible in his dis- covering all that is now known of these sciences ; and if his memory were as good as we are supposing his judgment and conception to be, he might dis- cover it all without pen, ink, and paper, and in a dark room. But we cannot discover a single one of the fundamental properties of matter without ob- serving what goes on around us, and trying experi- ments upon the nature and motion of bodies. Thus, the man whom we have supposed shut up, could not possibly find out beyond one or two of the very first properties of matter, and those only in a very few cases ; so that he could not tell if these were general properties of all matter or not. He could tell that the objects he touched in the dark were hard and resisted his touch ; that they were ex- tended and were solid : that is, that they had three dimensions, length, breadth, and thickness. He might guess that other things existed besides those he felt, and that those other things resembled what he felt in these properties; but he could know c2 32 OBJECTS, ADVANTAGES, AND nothing for certain, and could not even conjecture mucli beyond this very limited number of qualities. He must remain utterly ignorant of what really exists in nature, and of what properties matter in general has. These properties, therefore, we learn by experience ; they are such as we know bodies to have ; they happen to have them — they are so formed by Divine Providence as to have them — but they might have been otherwise formed ; the great Author of Nature might have thought fit to make all bodies diiferent in every respect. "We see that a stone dropped from our hand falls to the ground ; this is a fact which we can only know by ex- perience ; before observing it, we could not have guessed it, and it is quite conceivable that it should be otherwise : for instance, that when we remove our hand from the body it should stand still in the air ; or fly upward, or go forward, or backward, or sideways ; there is nothing at all absurd, con- tradictory, or inconceivable in any of these sup- positions; there is nothing impossible in any of them, as there would be in supposing the stone equal to half of itself, or double of itself ; or both falling down and rising upwards at once ; or going to the right and to the left at one and the same time. Our only reason for not at once thinking it quite conceivable that the stone should stand still in the air, or fly upwards, is that we have never seen it do so, and have become accustomed to see PLEASURES OF SCIENCE. 33 it do otherwise. But for that, we should at once think it as natural that the stone should fly upwards or stand still, as that it should fall down. But no degree of reflection for any length of time could accustom us to think 2 and 2 equal to anything but 4, or to believe the whole of any thing equal to a part of itself. After we have once, by observation or experi- ment, ascertained certain things to exist in fact, we may then reason upon them by means of the mathematics ; that is, we may apply mathematics to our experimental philosophy, and then such reason- ing becomes absolutely certain, taking the funda- mental facts for granted. Thus, if we find that a stone falls in one direction when dropped, and we further observe the peculiar way in which it falls, that is, quicker and quicker every instant ^11 it reaches the ground, we learn the rule or the proportion by which the quickness goes on increas- ing ; and we further find, that if the same stone is pushed forward on a table, it moves in the direction of the push, till it is either stopped by something, or comes to a pause by rubbing against the table and being hindered by the air. These are facts which we learn by observing and trying, and they might all have been different if matter and motion had been otherwise constituted ; but supposing them to be as they are, and as we find them, we can, by reasoning mathematically from them, find 34 OBJECTS, ADVANTAGES, AND out many most curious and important truths de- pending upon those facts, and depending upon them not accidentally, but of necessity. For example, we can find in what course the stone will move, if, instead of being dropped to the ground, it is thrown forward : it will go in the curve already mentioned, the parabola, somewhat altered by the resistance of the air, and it will run through that curve in a peculiar way, so that there will always be a certain proportion between the time it takes and the space it moves through, and the time it would have taken, and the space it would have moved through, had it dropped from the hand in a straight line to the ground. So we can prove, in like manner, what we before stated of the relation between the distance at which it will come to the groufid, and the direction it is thrown in; the distance being greatest of all when the direction is half way between the level or horizontal and the upright or perpendicular. These are mathematical truths, derived by mathematical reasoning upon physical grounds ; that is, upon matter of fact found to exist by actual observation and experiment. The result, therefore, is necessarily true, and proved to be so by reasoning only, provided we have once ascertained the facts; but taken altogether, the result depends partly on the facts learned by ex- periment or experience, partly on the reasoning from these facts. Thus it is found to be true by PLEASURES OF SCIENCE. 35 reasoning, "and necessarily true, that if the stone falls in a certain way when unsupported, it must, when thrown forward, go in the curve called a parabola, provided there be no air to resist : this is a necessary or mathematical truth, and it cannot possibly be otherwise. But when we state the matter without any supposition, — without any " ?"/*," — and say, a stone thrown forward goes in a curve called a parabola, we state a truth, partly fact, and partly drawn from reasoning on the fact ; and it might be otherwise if the nature of things were different. It is called a proposition or truth in Natural Philosophy ; and as it is discovered and proved by mathematical reasoning upon facts in nature, it is sometimes called a proposition or truth in the Mixed Mathematics^ so named in contradis- tinction to the Pure Mathematics^ which are employed in reasoning upon figures and numbers. The man in the dark room could never discover this truth unless he had been first informed, by those who had observed the fact, in what way the stone falls when unsupported, and moves along the table when pushed. These things he never could .have found out by reasoning : they are facts, and he could only reason from them after learning them by his own experience, or taking them on the credit of other people's experience. But having once so learnt them, he could discover by reasoning merely, and with as much certainty as if he lived 36 OBJECTS, ADVANTAGES, AND in daylight, and saw and felt the moving body, that the motion is a parabola, and governed by certain rules. As experiment and observation are the great sources of our knowledge of Nature, and as the judicious and careful making of experiments is the only way by which her secrets can be known, ^Natural and Experimental Philosophy mean one and the same thing ; mathematical reasoning being applied to certain branches of it, particularly those which relate to motion and pressure. III. NATURAL OR EXPERIMENTAL SCIENCE. Natural Philosophy, in its most extensive sense, has for its province the investigation of the laws of matter ; that is, the properties and the motions of matter ; and it may be divided into two great branches. The first and most important (which is sometimes, on that account, called Natural Philosophy by way of distinction, but more properly Mechanical Philosophy) investi- gates the sensible motions of bodies. The second investigates the constitution and qualities of all bodies, and has various names, according to its different objects. It is called Chemistry, if it teaches the properties of bodies with respect to heat, mixture with one another, weight, taste, appearance, and so forth ; Anatomy and Animal PLEASURES OF SCIENCE. 37 Physiology^ (from the Greek word signifying to speak of the nature of any thing,) if it teaches the structure and functions of living bodies, especially the human ; for, when it shows those of other animals, we term it Comparative Anatomy; Medicine^ if it teaches the nature of diseases, and the means of preventing them and of restoring health ; Zoology, (from the Greek words signifying to speak of animals^ if it teaches the arrangement or classification and the habits of the different lower animals ; Botany, (from the Greek word for herbage,^ including Vegetable Physiology^ if it teaches the arrangement or classification, the structure and habits of plants ; Mineralogy, includ- ing Geology, (from the Greek words meaning to speak of the earth,) if it teaches the arrangement of minerals, the structure of the masses in which they are found, and of the earth composed of those masses. The term Natural History is given to the three last branches taken together, but chiefly as far as they teach the classification of different things, or the observation of the resemblances and differences of the various animals, plants, and inanimate and ungrowing substances in nature. But here we may make two general observations. The^r^^ is, that every such distribution of the sciences is necessarily imperfect ; for one runs un- avoidably into another. Thus, Chemistry shows the qualities of plants with relation to other sub- c 3 38 OBJECTS, ADVANTAGES, AND stances, and to each other ; and Botany does not overlook those same qualities, though its chief object be arrangement. So Mineralogy, though principally conversant with classifying metals and earths, yet regards also their qualities in respect of heat and mixture. So, too, Zoology, beside arranging animals, describes their structures, like Comparative Anatomy. In truth, all arrangement and classifying depends upon noting the things in which the objects agree and differ ; and among those things, in which animals, plants, and minerals agree, or differ, must be considered the anatomical qualities of the one and the chemical qualities of the other. From hence, in a great measure, fol- lows the second observation, namely, that the sciences mutually assist each other. We have seen how Arithmetic and Algebra aid Geometry, and how both the purely Mathematical Sciences aid Mechanical Philosophy. Mechanical Philosophy, in like manner, assists, though, in the present state of our knowledge, not very considerably, both Chemistry and Anatomy, especially the latter ; and Chemistry very greatly assists both Piiysiology, Medicine, and all the branches of Natural History. The first great head, then, of Natural Science, is Mechanical Philosophy ; and it consists of various subdivisions, each forming a science of great importance. The most essential of these, PLEASURES OF SCIENCE. 39 and which is indeed fundamental, and applicable to all the rest, is called Dynamics^ from the Greek word signifying j^oz^^er or force ^ and it teaches the laws of motion in all its varieties. The case of the stone thrown forward, which we have already mentioned more than once, is an example. Ano- ther, of a more general nature, but more difficult to trace, far more important in its consequences, and of which, indeed, the former is only one par- ticular case, relates to the motions of all bodies, which are attracted (or influenced, or drawn) by any power towards a certain point, while they are, at the same time, driven forward, by some push given to them at first, and forcing them onwards, at the same time that they are drawn towards the point. The line in which a body moves while so drawn and so driven, depends upon the force it is pushed with, the direction it is pushed in, and the kind of power that draws it towards the point ; but at present, we are chiefly to regard the latter circumstance, the attraction towards the point. If this attraction be uniform, that is, the same at all distances from the point, the body will move in a circle, if one direction be given to the forward push. The case with which we are best acquainted is when the force decreases as the squares of the distances, from the centre or point of attraction, increase ; that is, when the force is four times less at twice the distance, nine times less at thrice tlie 40 OBJECTS, ADVANTAGES, AND distance, sixteen times less at four times the dis- tance, and so on. A force of this kind acting on the body, will make it move in an oval, a parabola, or an hyperbola, according to the amount or direc- tion of the impulse, or forward push, originally given ; and there is one proportion of that force, Avhieh, if directed perpendicularly to the line in which the central force draws the body, will make it move round in a circle, as if it were a stone tied to a string and whirled round the hand. The most usual proportions in nature, are those which deter- mine bodies to move in an oval or ellipse, the curve described by means of a cord fixed at both ends, in the way already explained. In this case, the point of attraction, the point towards which the body is drawn, will be nearer one end of the ellipse than the other, and the time the body will take to go round, compared with the time any other body would take, moving at a different dis- tance from the same point of attraction, but drawn towards that point with a force which bears the same proportion to the distance, will bear a certain proportion, discovered by mathematicians, to the average distances of the two bodies from the point of common attraction. If you multiply the num- bers expressing the times of going round, each by itself, the products will be to one another in the proportion of the average distances multiplied each by itself, and that product again by the dis- PLEASURES OF SCIENCE. 41 tance. Thus, if one body take two hours, and is five yards distant, the other, being ten yards off, will take something less than five hours and forty minutes.* jSTow, this is one of the most important truths in the whole compass of science ; for it does so happen, that the force with which bodies fall towards the earth, or what is called their gravity, the power that draws or attracts them towards the earth, varies with the distance from the Earth's centre, exactly in the proportion of the squares, lessening as the distance increases : at two diame- ters from the Earth's centre, it is four times less than at one ; at three diameters, nine times less ; and so forth. It goes on lessening, but never is destroyed, even at the greatest distances to which we can reach by our observations, and there can be no doubt of its extending indefinitely beyond. But, by astronomical observations made upon the motion of the heavenly bodies, upon that of the Moon for instance, it is proved that her movement is slower and quicker at different parts of her course, in the same manner as a body's motion on the earth would be slower and quicker, according to its distance from the point it was drawn towards, * This is expressed mathematically by saying, that the squares of the times are as the cubes of the distances. Mathematical language is not only the simplest and most easily understood of any, but the shortest also. 42 OBJECTS, ADVANTAGES, AND provided it was drawn by a force acting in the pro- portion to the squares of the distance, which we have frequently mentioned ; and the proportion of the time to the distance is also observed to agree with the rule above referred to. Therefore, she is shown to be attracted towards the Earth by a force that varies according to the same proportion in which gravity varies ; and she must consequently move in an ellipse round the Earth, which is placed in a point nearer the one end than the other of that curve. In like manner, it is shown that the Earth moves round the Sun in the same curve line, and is drawn towards the sun by a similar force ; and that all the other planets in their courses, at various distances, follow the same rule, moving in ellipses, and drawn towards the Sun by the same kind of power. Three of them have moons like the Earth, only more numerous, for Jupiter has four, Saturn seven, and Herschel six, so very distant, that we cannot see them without the help of glasses ; but all those moons move round their principal planets, as ours does round the Earth, in ovals or ellipses ; while the planets, with their moons, move in their ovals round the Sun, like our own Earth with its moon. But this power, which draws them all towards the sun, and regulates their path and their motion round him, and which draws the moons towards the principal planets, and regulates their motion PLEASURES OF SCIENCE. 43 and path round those planets, is the same with the gravity by which bodies fall towards the earth, being attracted by it. Therefore, the whole of the heavenly bodies are kept in their places, and wheel round the sun, by the same influence or power that makes a stone fall to the ground. It is usual to call the sun, and the planets which with their moons move round him (eleven in num - ber, including the four lately discovered, and the one discovered by Herschel), the Solar System, because they are a class of the heavenly bodies far apart from the innumerable fixed stars, and so near each other as to exert a perceptible influ- ence on one another, and thus to be connected together. The Comets belong to the same system, accord- ing to this manner of viewing the subject. They are bodies which move in elliptical paths, but far longer and narrower than the curves in which the earth and the other planets and their moons roll. Our curves are not much less round than circles ; the paths of the comets are long and narrow, so as, in many places, to be more nearly straight lines than circles. They differ from the planets and their moons in another respect ; they do not depend on the sun for the light they give, as our moon plainly does, being dark when the earth comes be- tween her and the sun ; and as the other planets do, those of them that are nearer the sun than we 44 OBJECTS, ADVANTAGES, AND are, being dark when they come between us and him, appearing to pass across his surface. But the comets give light always of themselves, being appa- rently vast bodies heated red-hot by coming in their course far nearer the sun than the nearest of the planets ever do. Their motion, when near the sun, is much more rapid than that of the planets ; they both approach him much nearer, retreat from him to much greater distances, and take much longer time in going round him than any of the planets do. Yet even these comets are subject to the same great law of gravitation which regulates the motions of the planets. Their year, the time they take to revolve, is in some cases 75, in others 135, in others 300 of our years ; their distance is a hundred times our distance when farthest off, and not a hundred and sixtieth of our distance when nearest the sun ; their swiftest motion is above twelve times swifter than ours, although ours is a hundred and forty times swifter than a cannon ball's ; yet their path is a curve of the same kind with ours, though longer and flatter, differing in its formation only as one oval differs from another by the string you draw it with having the ends fixed at two points more distant from each other : consequently the sun, being in one of those points, is much nearer the end of the path the comet moves in, than he is near the end of our path. Their motion, too, follows the same rule, being PLEASURES OP SCIENCE. 45 swifter the nearer the sun : the attraction of the sun for them varies according to the squares of the distances, being four times less at twice the distance, nine times less at thrice, and so on; and the proportion between the times of revolv- ing and the distances is exactly the same, in the case of those remote bodies, as in that of the moon and the earth. One law prevails over all, and regulates their motions as well as our own ; it is the gravity of the comets towards the sun, and they, like our own earth and moon, wheel round him in boundless space, drawn by the same force, acting by the same rule, which makes a stone fall when dropped from the hand. The more full and accurate our observations are upon those heavenly bodies, the better we find all their motions agreeing with this great doctrine ; although, no doubt, many things are to be taken into the account besides the force that draws them to the different centres. Thus, while the moon is drawn by the earth, and the earth by the sun, the moon is also drav/n directly by the sun ; and while Jupiter is drawn by tlie sun, so are his moons ; and both Jupiter and his moons are drawn by Saturn : nay, as this power of gravitation is quite universal, and as no body can attract or draw another without being itself drawn by that other, the earth is drawn by the moon, while the moon is drawn by the earth ; and the sun is attracted by 46 OBJECTS, ADVANTAGES, AND the planets which he draws towards himself. These mutual attractions give rise to many devia- tions from the simple line of the ellipse, and pro- duce many irregularities in the simple calculation of the times and motions of the bodies that com- pose the system of the universe. But the extraor- dinary powers of investigation applied to the sub- ject by the modern improvements in mathematics, have enabled us at length to reduce even the greatest of the irregularities to order and system ; and to unfold one of the most wonderful truths in all sciences, namely, that by certain necessary con- sequence of the simple fact upon which the whole fabric rests, the proportion of the attractive force to the distances at which it operates, — all the irre- gularities which at first seemed to disturb the order of the system, and to make the appearances depart from the doctrine, are themselves subject to a cer- tain fixed rule, and can never go beyond a par- ticular point, but must begin to lessen when they have slowly reached that point, and must then lessen until they reach another point, when they begin again to increase ; and so on, for ever. Nay, so perfect is the arrangement of the whole system, and so accurately does it depend upon mathe- matical principles, that irregularities, or rather apparent deviations, have been discovered by ma- thematical reasoning before astronomers had ob- served them, and then their existence has been TLEASURES OF SCIENCE. 47 ascertained by observation, and found to agree precisely with the results of calculation.* Thus, the planets move in ovals, from gravity, the power that attracts them towards the sun, combined with the original impulse they received forwards ; and the disturbing forces are continually varying the course of the curves or ovals, making them bulge out in the middle, as it were, on the sides, though in a very small proportion to the whole length of the ellipse. The oval thus bulging, its breadth in- creases by a very small quantity yearly and daily ; and after a certain large number of years, the bulging becomes as great as it ever can be : then the alteration takes a contrary direction, and the curve gradually flattens as it had bulged ; till, in the same number of years which it took to bulge, * The application of mathematics to chemistry has already produced a great change in that science, and is calculated to produce still greater improvements. It may be almost cer- tainly reckoned upon as the source of new discoveries, made by induction after the mathematical reasoning has given the suggestion. The learned reader -will perceive that we allude to the beautiful doctrine o^ Definite or Multiple Proportions. To take an example ; the probability of an oxide of arsenic being discovered is impressed upon us, by the composition of arsenious and arsenic acids, in which the oxygen is as 2 to 3 ; and therefore we may expect to find a compound of the same base, with the oxygen as unity. The extraor- dinary action of chlorine and its compounds on light leads us to expect some further discovery respecting its composi- tion, perhaps respecting the matter of light. 48 OBJECTS, ADVANTAGES, AND it becomes as flat as it ever can be, and tlien it begins to bulge again, and so on for ever. And so, too, of every other disturbance and irregularity in the system : what at first appears to be some departure from the rule, when more fully examined, turns oat to be only a consequence of it, or the result of a more general arrangement springing from the principle of gravitation ; an arrangement of which the rule itself, and the apparent or sup- posed exception, both form parts. The power of gravitation, which thus regulates the whole system of the universe, is found to rule each member or branch of it separately. Thus, it is demonstrated that the tides of the ocean are caused by the gravitation which attracts the water towards the sun and moon ; and the figure both of our earth and of such of the other bodies as have a spinning motion round their axis, is determined by gravitation combined with that motion : they are all flattened towards the ends of the axis they spin upon, and bulge out towards the middle. The great discoverer of the principle on which all these truths rest, Sir Isaac Newton, certainly by far the most extraordinary man that ever lived, concluded by reasoning upon the nature of motion and matter, that this flattening must take place in our globe ; every one before his time had believed the earth to be a perfect sphere or globe, chiefly from observing the round shadow which it casts on TLEASUEES OP SCIENCE. 49 the moon in eclipses ; and it was many years after his death that the accuracy of his opinion was proved by measurements on the earth's surface, and by the different weight and attraction of bodies at the equator, where it bulges, and at the poles, where it is flattened. The improvement of tele- scopes has enabled us to ascertain the same fact with respect to the planets Jupiter and Saturn. Besides unfolding the general laws which re- gulate the motions and figures of the heavenly bodies forming our Solar System, Astronomy con- sists in calculations of the places, times, and eclipses of those bodies, and their moons ov satellites (from a Latin word signifying an attendajit), and in ob- servations of the Fixed Stars, which are innume- rable assemblages of bodies, not moving round the Sun as our Earth and the other planets do, nor re- ceiving the light they shine with from his light ; but shining, as the Sun and the Comets do, with a light of their own, and placed, to all appearance, immoveable, at immense distances from our world, that is, from our Solar System. Each of them is probably the sun of some other system like our own, composed of planets and their moons or satel- lites ; but so extremely distant from us, that they all are seen by us like one point of faint light, as you see two lamps placed a few inches asunder, only like one, when you view them a great way off. The number of the Fixed Stars is prodigious : even 50 OBJECTS, ADVANTAGES, AND to the naked eye they are very numerous, about 3000 being thus visible ; but when the heavens are viewed through the telescope, stars become visible in numbers wholly incalculable : 2000 are dis- covered in one of the small collections of a few visible stars called Coiistellations ; nay, what ap- pears to the naked eye only a light cloud, as the Milky Way, when viewed through the telescope, proves to be an assemblage of innumerable Fixed Stars, each of them in all likelihood a sun and a system like the rest, though at an immeasurable distance from ours. The size, and motions, and distances of the heavenly bodies are such as to exceed the power of ordinary imagination, from any comparison with the smaller things we see around us. The Earth's diameter is nearly 8000 miles in length ; but the Sun's is above 880,000 miles, and the bulk of the Sun is above 1,300,000 times greater than that of the Earth. The planet Jupiter, which looks like a mere speck, from his vast distance, is nearly 1300 times larger than the Earth. Our distance from the Sun is above 95 millions of miles ; but Jupiter is 490 millions, and Saturn 900 millions of miles distant from the Sun. The rate at which the Earth moves round the Sun is 68,000 miles an hour, or 140 times swifter than the motion of a cannon-ball ; and the planet Mercury, the nearest to the Sun, moves still quicker, nearly 110,000 miles an hour. PLEASURES OF SCIENCE. 51 We, upon the Earth's surface, besides being carried round the Sun, move round the Earth's axis by the rotatory or spinning motion which it has ; so that every 24 hours we move in this manner near 24,000 miles, beside moving round the Sun above 1,600,000 miles. These motions and distances, however, prodigious as they are, seem as nothing compared to those of the comets, one of which, when farthest from the Sun, is 11,200 millions of miles from him ; and, when nearest the Sun, flies at the amazing rate of 880,000 miles an hour. Sir Isaac Newton calculated its heat at 2000 times that of red-hot iron ; and that it would take thousands of years to cool. But the distance of the Fixed Stars is yet more vast : they have been supposed to be 400,000 times farther from us than we are from the Sun, that is 38 millions of millions of miles ; so that a cannon-ball would take nearly nine millions of years to reach one of them, supposing there was nothing to hinder it from pursuing its course thither. As light takes about eight minutes and a quarter to reach us from the Sun, it would be above six years in coming from one of those stars ; but the calculations of later astronomers prove some stars to be so far distant, that their light must take centuries before it can reach us ; so that every particle of light which enters our eyes left the star it comes from three or four hundred years ago. 52 Astronomers have, by means of their excellent glasses, aided by Geometry and calculations, been able to observe not only stars, planets, and their satellites, invisible to the naked eye, but to mea- sure the height of mountains in the Moon, by ob- servations of the shadows which those eminences cast on her surface ; and they have discovered vol- canoes, or burning mountains, in the same body. The tables, which they have by the like means been enabled to form of the heavenly motions, are of great use in navigation. By means of the eclipses of Jupiter's satellites, and by the tables of the Moon's motions, we can ascertain the position of a ship at sea ; for the observation of the Sun's height at mid-day gives the latitude of the place, that is, its distance from the equinoctial or equator, the line passing through the middle of the Earth's sur- face equally distant from both poles ; and these tables, with the observations of the satellites, or moons, give the distance east and west of the observatory for which the tables are calculated — called the longitude of the place : consequently the mariner can thus tell nearly in what part of the ocean he is, how far he has sailed from his port of departure, and how far he must sail, and in what direction, to gain the port of his destination. The advantage of this knowledge is therefore manifest in the common affairs of life ; but it sinks into insignificance com- pared with the vast extent of those views which the PLEASURES OF SCIENCE. 53 contemplations of the science afford, of numberless worlds filling the immensity of space, and all kept in their places, and adjusted in their prodigious motions by the same simple principle, under the guidance of an all-wise and all-powerful Creator. We have been considering the application of Dynamics to the motions of the heavenly bodies^ which forms the science of Physical Astronomy, The application of Dynamics to the calculation, production, and direction of motion, forms the science of Mechanics, sometimes called Practical Mechanics, to distinguish it from the more general use of the word, which comprehends every thing that relates to motion and force. The fundamental principle of the science, upon which it mainly de- pends, flows immediately from a property of the circle already mentioned, and which, perhaps, ap- peared at the moment of little value, — that the lengths of circles are in proportion to their di- ameters. Observe how upon this simple truth nearly the whole of those contrivances are built by which the power of man is increased as far as solid matter assists him in extending it ; and nearly the whole of those doctrines, too, by which he is en- abled to explain the voluntary motions of animals, as far as these depend upon their own bodies. There can be nothing more instructive in showing the importance and fruitfulness of scientific truths, however trivial and forbidding they may at first D 54 OBJECTS, ADVAJJTAGES, AND sight appear. For it is an immediate consequence of this property of the circle, that if a rod of iron, or beam of wood, or any other solid material, be placed on a point, or pivot, so that it may move as the arms of a balance do round its centre, or a see- saw board does round its prop, the two ends will go through parts of circles, each proportioned to that arm of the beam to which it belongs : the two circles will be equal if the pivot is in the centre or middle point of the beam; but if it is nearer one end than the other, say three times, that end will go through a circular space, or arch, three times shorter than the circular space the other end goes through in the same time. If, then, the end of the long beam goes through three times the space, it must move with three times the swiftness of the short beam's end, since both move in the same time ; and therefore any force applied to the long end must overcome the resistance of three times that force applied at the opposite end, since the two ends move in contrary directions : hence one pound placed at the long end would balance three placed at the short end. The beam we have been supposing is called a Lever, and the same rule must evidently hold for all proportions of the lengths of its arms. If, then, the lever be seventeen feet long, and the pivot, or fulcrum (as it is called, from a Latin word signifying support), be a foot from one end, an ounce placed on the other end will balance a PLEASURES OF SCIEXCE. 55 pound placed on the near end ; and the least addi- tional weight, or the slightest push or pressure on the far end, so loaded, will make the pound weight on the other move upwards. If, instead of an ounce, we place upon the end of the long arm the short arm of a second beam or lever supported by a fulcrum, one foot from it, and then place the long arm of this second lever upon the short arm of a third lever, whose fulcrum is one foot from it ; and if we put on the end of this third lever's long arm an ounce weight, that ounce will move upwards a pound on the second lever's long arm, and this moving upwards will cause the short arm to force downwards sixteen pounds at the long end of the first lever, which will make the short end of the first lever move upwards, though two hundred and fifty- six pounds be laid on it : the same thing continu- ing, a pound on the long arm of the third lever will move a ton and three-quarters on the short arm of the first lever ; that is, will balance it, so that the slightest pressure with the finger, or a touch from a child's hand, will move as much as two horses can draw. The lever is called, on this ac- count, a mechanical power; and there are five other mechanical powers, of most of which its pro- perties form the foundation ; indeed they have all been resolved into combinations of levers. The pulley seems the most difficult to reduce under the principle of the lever. Thus the wheel and axle is D 2 56 OBJECTS, ADVANTAGES, AND only a lever moving round an axle, and always re- taining the effect gained during every part of the motion, by means of a rope wound round the butt end of the axle ; the spoke of the wheel being the long arm of the lever, and the half diameter of the axle its short arm. By a combination of levers, wheels, pulleys, so great an increase of force is ob- tained, that, but for the obstruction from friction, and the resistance of the air, there could be no bounds to the effect of the smallest force thus mul- tiplied ; and to this fundamental principle Archi- medes, one of the most illustrious mathematicians of ancient times, referred, when he boasted, that if he only had a pivot or fulcrum whereon he might rest his machinery, he could move the Earth. Upon so simple a truth, assisted by the aid derived from other sources, rests the whole fabric of me- chanical power, whether for raising weights, or cleaving rocks, or pumping up rivers from the bowels of the earth ; or, in short, performing any of those works to which human strength, even augmented by the help of the animals whom Pro- vidence has subdued to our use, would prove alto- gether inadequate. The application of Dynamics to the pressure and motions of fluids, constitutes a science which re- ceives different appellations according as the fluids are heavy and liquid like water, or light and in- visible like air. In the former case it is called PLEASURES OF SCIENCE. 57 Hydrodynamics, from the Greek words signifying water, and power or force ; in the latter Pneu- matics, from the Greek word signifying breath or air; and Hydrodynamics is divided into Hydro- statics, which treats of the weight and pressure of liquids, from the Greek words for balancing of water; and Hydraulics, which treats of their motion, from the Greek name for certain musical instruments played with water in pipes. The discoveries to which experiments, aided by mathematical reasoning, have led, upon the pressure and motion of fluids, are of the greatest importance, whether we regard their application to practical purposes, or to their use for explaining the ap- pearances in nature, or their singularity as the subjects of scientific contemplation. When it is found that the pressure of water or any other liquid upon the surface that contains it, is not in the least degree proportioned to its bulk, but only to the height at which it stands, so that a long small pipe, containing a pound or two of the fluid, will give the pressure of twenty or thirty tons ; nay, of twice or thrice as much, if its length be in- creased and its bore lessened, without the least regard to the quantity of the liquid, we are not only astonished at so extraordinary and unexpected a property of matter, but we straightway perceive one of the great agents employed in the vast operations of nature, in which the most trifling 58 OBJECTS, ADVANTAGES, AND means are used to work the mightiest effects. We likewise learn to guard against many serious mis- chiefs in our own works, and to apply safely and usefully a power calculated, according as it is directed, either to produce unbounded devastation, or to render the most beneficial service. Nor are the discoveries relating to the Air less interesting in themselves, and less applicable to important uses. It is an agent, though invisible, as powerful as Water, in the operations both of nature and of art. Experiments of a simple and decisive nature show the amount of its pressure to be between 14 and 15 pounds on every square inch ; but, like all other fluids, it presses equally in every direction : so that though, on one hand, there is a pressure downwards of above 250 pounds, yet this is exactly balanced by an equal pressure upwards, from the air pressing round and getting below. If, however, the air on one side be removed, the whole pressure from the other acts unbalanced. Hence the ascent of water in pumps, which suck out the air from a barrel, and allow the pressure upon the water to force it up 32 or 33 feet, that body of water being equal to the weight of the atmosphere. Hence the ascent of the mercury in the barometer is only 28 or 29 inches, mercury being between 13 and 14 times heavier than water. Hence, too, the motion of the steam-engine ; the piston of which, until the direct force of steam was PLEASURES OP SCIENCE. 59 applied, used to be pressed downwards by the weight of the atmosphere from above, all air being re- moved below it by first filling it with steam, and then suddenly cooling and converting that steam into water, so as to leave nothing in the space it had occupied. Hence, too, the power which some animals possess of walking along the perpendicular surfaces of walls, and even the ceilings of rooms, by squeezing out the air between the inside of their feet and th« wall, and thus being supported by the pressure of the air against the outside of their feet. The science of Optics, (from the Greek word for seeing,) which teaches the nature of light, and of the sensation conveyed by it, presents, of itself, a field of unbounded extent and interest. To it the arts, and the other sciences, owe those most useful instruments which have enabled us at once to examine the minutest parts of the structure of animal and vegetable bodies, and to calculate the size and the motions of the most remote of the heavenly bodies. But as an object of learned curiosity, nothing can be more singular than the fundamental truth discovered by the genius of Newton, — that the light, which we call white, is in fact composed of all the colours, blended in certain proportions ; unless, perhaps, it be that astonishing conjecture of his unrivalled sagacity, by which he descried the inflammable nature of the 60 OBJECTS, ADVANTAGES, AND diamond, and its belonging, against all appearance of probability, to the class of oily substances, frona Laving observed, that it stood among them, and far removed from all crystals, in the degree of its action upon light ; a conjecture turned into cer- tainty by discoveries made a century afterwards. To a man who, for original genius and strong natural sense, is not unworthy of being named after this illustrious sage, we owe the greater part of Electrical science. It treats of the peculiar sub- stance, resembling both light and heat, which, by rubbing, is found to be produced in a certain class of bodies, as glass, wax, silk, amber; and to be conveyed easily or conducted through others, as "wood, metals, water ; and it has received the name of Electricity^ from the Greek word for amber. Dr. Franklin discovered that this is the same matteJ which, when collected in the clouds, and conveyed from them to the earth, we call lightning, and whose noise, in darting through the air, is thunder. The observation of some movements in the limbs of a dead frog gave rise to the discovery oi Animal Electricity, or Galvanism, as it was at first called from the name of the discoverer ; and which has of late years given birth to improvements that have changed the face of chemical philosophy ; affording a new proof how few there are of the processes of nature incapable of repaying the labour we bestow in patiently and diligently examining them. It is PLEASURES OF SCIENCE. 61 to the results of the remark accidentally made upon the twitching in the frog's leg, not, however, hastily dismissed and forgotten, but treasured up and pursued through many an elaborate experiment and calculation, that we owe our acquaintance with the extraordinary metal, liquid like mercury, lighter than water, and more inflammable than phosphorus, which forms, when it burns by mere exposure to the air, one of the salts best known in commerce, and the principal ingredient in salt- petre. In order to explain the nature and objects of those branches of Natural Science more or less connected with the mathematics, some details were necessary, as without them it was difficult imme- diately to perceive their importance, and, as it were, relish the kind of instruction which they afford. But the same course needs not be pursued with respect to the other branches. The value and the interest of chemistry is at once perceived, when it is known to teach the nature of all bodies ; the relations of simple substances to heat and to one another, or their combinations together; the composition of those which nature produces in a compound state ; and the application of the whole to the arts and ma- nufactures. Some branches of philosophy, again, are chiefly useful and interesting to particular classes, as surgeons and physicians. Others are easily un- derstood by a knowledge of the principles of d3 62 OBJECTS, ADVANTAGES, AND Mechanics and Chemistry, of which they are appli- cations and examples ; as those which teach the structure of the earth and the changes it has under- gone ; the motions of the muscles, and the structure of the parts of animals ; the qualities of animal and vegetable substances ; and that department of Agriculture which treats of soils, manure, and machinery. Other branches are only collections of facts, highly curious and useful indeed, but which any one who reads or listens, perceives as clearly, and comprehends as readily, as the professed student. To this class belongs Natural History, in so far as it describes the habits of animals and plants, and its application to that department of Agriculture which treats of cattle and their IV. APPLICATION OF NATURAL SCIENCE TO THE ANIMAL AND VEGETABLE WORLD. But, for the purpose of further illustrating the advantages of Philosophy, its tendency to enlarge the mind, as well as to interest it agreeably, and afford pure and solid gratification, a few instances may be given of the singular truths brought to light by the application of Mathematical, Mechani- cal, and Chemical knowledge to the habits of animals and plants ; and some examples may be PLEASURES OP SCIENCE. 63 added of the more ordinary and easy, but scarcely less interesting* observationSj made upon those habits, without the aid of the profounder sciences. We may remember the curve line which mathe- maticians call a Cycloid. It is the path which any point of a circle, moving along a plane, and round its centre, traces in the air ; so that the nail on the felly of a cart-wheel moves in a Cycloid, as the cart goes along, and as the wheel itself both turn« round its axle and is carried along the ground. Now this curve has certain properties of a peculiar and very singular kind with respect to motion. One is, that if any body whatever moves in a cycloid by its own weight or swing, together with some other force acting upon it all the while, it will go through all distances of the same curve in exactly the same time ; and, accordingly, pendu- lums have sometimes been contrived to swing in such a manner, that they shall describe cycloids, or curves very near cycloids, and thus move in equal times, whether they go through a long or a short part of the same curve. Again, if a body is to descend from any one point to any other, not in the perpendicular, by means of some force acting on it together v/ith its weight, the line in which it will go the quickest of all will be the cycloid ; not the straight line, though that is the shortest of all 64 OBJECTS, ADVANTAGES, AND lines which can be drawn between the two points ; nor any other curve whatever, though many are much flatter, and therefore shorter than the cycloid — but the cycloid, which is longer than many of them, is yet, of all curved or straight lines which can be drawn, the one the body will move through in the shortest time. Suppose, again, that the body is to move from one point to another, by its weight and some other force acting together, but to go through a certain space, — as a hundred yards, — the way it must take to do this, in the shortest time possible, is by moving in a' cycloid ; or the length of a hundred yards must be drawn into a cycloid, and thpn the body will descend through the hundred yards in a shorter time than it could go the same distance in any other path whatever. Now, it is believed thai Birds, as the Eagle, which build in the rocks, drop or fly down from height to height in this course. It is impossible to make very accurate observations of their flight and path ; but there is a general resemblance between the course they take and the cycloid, which has led ingenious men to adopt this opinion. If we have a certain quantity of any substance, a pound of wood, for example, and would fashion it in the shape to take the least room, we must make a globe of it ; it will in this figure have the PLEASURES OF SCIENCE. 65 smallest surface. But suppose we want to form the pound of wood, so that in moving through the air or water it shall meet with the least possible resistance ; then we must lengthen it out for ever, till it becomes not only like a long-pointed pin, but thinner and thinner, longer and longer, till it is quite a straight line, and has no perceptible breadth or thickness at all. If we would dispose of the given quantity of matter, so that it shall have a certain length only, say a foot, and a certain breadth at the thickest part, say three inches, and move through the air or water with the smallest possible resistance which a body of those dimen- sions can meet, then we must form it into a figure of a peculiar kind called the Solid of least resist- ance, because, of all the shapes that can be given to the body, its length and breadth remaining the same, this is the one which will make it move with the least resistance through the air, or water, or other fluid. A very difficult chain of mathe- matical reasoning, by means of the highest branches of algebra, leads to a knowledge of the curve Avhich, by revolving on its axis, makes a solid of this shape, in the same way that a circle, by so re- volving, makes a sphere or globe ; and the curve certainly resembles closely the face or head part of a fish. Nature, therefore, (by which we always mean the Divine Author of nature,) has fashioned these fishes so, that, according to mathematical 66 OBJECTS, ADVANTAGES, AND principles, they swim the most easily through the element they live and move in.* Suppose upon the face part of one of these fishes a small insect were bred, endowed with faculties sufficient to reason upon its condition, and upon the motion of the fish it belonged to, but never to have discovered the whole size and shape of the face part ; it w^ould certainly complain of the form as clumsy, and fancy that it could have made the fish so as to move with less resistance. ' Yet if the whole shape were disclosed to it, and it could discover the principle on which that shape was preferred, it would at once perceive, not only that what had seemed clumsy was skilfully con- trived, but that, if any other shape whatever had been taken, there would have been an error com- mitted ; nay, that there must of necessity have been an error ; and that the very best possible arrange- ment had been adopted. So it may be with man in the universe, where, seeing only a part of the great system, he fancies there is evil ; and yet, if he w^ere permitted to survey the whole, what had seemed imperfect might appear to be necessary for the general perfection, insomuch that any other arrangement, even of that seemingly imperfect part, must needs have rendered the wdiole less perfect. * The feathers of the wings of birds are found to be placed at the best possible angle for helping on the bird by their action on the air. PLEASURES OF SCIENCE. 67 The common objection is, that what seems evil might have been avoided ; but in the case of the fish's shape, it could not have been avoided. It is found by optical inquiries, that the particles or rays of light, in passing through transparent substances of a certain form, are bent to a point Avhere they make an image or picture of the shining bodies they come from, or of the dark bodies they are reflected from. Thus, if a pair of spectacles be held between a candle and the wall, they make two images of the candle upon it ; and if they be held between the window and a sheet of paper when the sun is shining, they make a picture on the paper of the houses, trees, fields, sky, and clouds. The eye is found to be composed of seve- ral natural magnifiers which make a picture on a membrane at the back of it, and from this mem- brane there goes a nerve to the brain, conveying the impression of the picture, by means of which we see. Now, white light was discovered by Newton to consist of differently-coloured parts, which are differently bent in passing through transparent sub- stances, so that the lights of several colours come to a point at different distances, and thus create an indistinct image at any one distance. This was long found to make our telescopes imperfect, inso- much that it became necessary to make them of reflectors or mirrors, and not of magnifying glasses, the same difference not being observed to affect the 68 OBJECTS, ADVANTAGES, AND reflection of light. But another discovery was, about fifty years afterwards, made by Mr. DoUond, — that, by combining different kinds of glass in a compound magnifier, the difference may be greatly corrected; and on this principle he constructed his telescopes. It is found, too, that the different natural magnifiers of the eye are combined upon a principle of the same kind. Thirty years later, a third discovery was made by Mr. Blair, of the greatly superior effect which combinations of differ- ent liquids have in correcting the imperfection ; and, most wonderful to think, when the eye is ex- amined, we find it consists of different liquids, acting naturally upon the same principle which was thus recently found out in optics by many in- genious mechanical and chemical experiments. Again, the point to which any magnifier collects the light is more or less distant as the magnifier is flatter or rounder, so that a small globe of glass or any transparent substance makes a microscope. And this property of light depends upon the na- ture of lines, and is purely of a mathematical nature, after we have once ascertained by experi- ment, that light is bent in a certain way when it passes through transparent bodies. Now birds flying in the air, and meeting with many obstacles, has brances and leaves of trees, require to have their eyes sometimes as flat as possible for protec- tion ; but sometimes as round as possible, that they PLEASURES OF SCIENCE. 69 may see the small objects, flies and other insects, which they are chasing through the air, and which they pursue with the most unerring certainty. This could only be accomplished by giving them a power of suddenly changing the form of their eyes. Accordingly, there is a set of hard scales placed on the outer coat of their eye, round the place where the light enters ; and over these scales are drawn the muscles or fibres by which motion is communicated ; so that, by acting with these muscles, the bird can press the scales, and squeeze the natural magnifier of the eye into a round shape when it wishes to follow an insect through the air, and can relax the scales, in order to flatten the eye again, when it would see a distant object, or move safely through leaves and twigs. This power of altering the shape of the eye is possessed by birds of prey in a very remarkable degree. They can thus see the smallest objects close to them, and can yet discern larger bodies at vast distances, as a carcass stretched upon the plain, or a dying fish afloat on the water. A singular provision is made for keeping the surface of the bird's eye clean — for wiping the glass of the instrument, as it were— and also for protecting it, while rapidly flying through the air and through thickets, without hindering the sight. Birds are, for these purposes, furnished with a third eyelid, a fine membrane or skin, which is con- 70 OBJECTS, ADVANTAGES, AND stantly moved very rapidly over the eyeball by two muscles placed in the back of the eye. One of the muscles ends in a loop, the other in a string which goes through the loop, and is fixed in the corner of the membrane, to pull it backward and forward. If you wish to draw a thing towards any place with the least force, you must pull directly in the line between the thing and the place ; but if you wish to draw it as quickly as possible, and with the most convenience, and do not regard the loss of force, you must pull it obliquely, by drawing it in two directions at once. Tie a string to a stone, and draw it straight towards you with one hand ; then, make a loop on another string, and running the first through it, draw one string in each hand, not towards you, but sideways, till both strings are stretched in a straight line : you will see how much more easily the stone moves quickly than it did before when pulled straight forward. Again, if you tie strings to the two ends of a rod, or slip of card, in a running groove, and bring them to meet and pass through a ring or hole, fQr every inch in a straight line that you draw both together below the ring, the rod will move onward two. Now this is proved, by mathematical reason- ing, to be the necessary consequence of forces ap- plied obliquely : there is a loss of power, but a great gain in velocity and convenience. This is the thing required to.be gained in the third eyelid, PLEASUHES OF SCIENCE. 71 and the contrivance is exactly that of a string and a loop, moved each by a muscle, as the two strings are by the hands in the cases we have been supposing. A third eyelid of the same kind is found in the horse, and called the haw ; it is moistened with a pulpy substance (or mucilage) to take hold of the dust on the eyeball, and wipe it clear off; so that the eye is hardly ever seen with anything upon it, though greatly exposed from its size and posture. The swift motion of the haw is given to it by a gristly elastic substance placed between the eyeball and the socket, and striking obliquely, so as to drive out the haw with great velocity over the eye, and then let it come back as quickly. Ignorant persons, when this haw is inflamed from cold, and swells so as to appear, which it never does in a healthy state, often mistake it for an imperfection, and cut it off: so nearly do ignorance and cruelty produce the same mischief If any quantity of matter, as a pound of wood or iron, is fashioned into a rod of a certain length, say one foot, the rod will be strong in proportion to its thickness ; and, if the figure is the same, that thickness can only be increased by making it hol- low. Therefore hollow rods or tubes, of the same length and quantity of matter, have more strength than solid ones. This is a principle so well under- stood now, that engineers make their axles and other parts of machinery hollow, and therefore stronger 72 OBJECTS, ADVANTAGES, AND with the same weight than they would be if thinner and solid. Now the bones of animals are all more or less hollow ; and are therefore stronger with the same weight and quantity of matter than they otherwise would be. But birds have the largest bones in proportion to their weight ; their bones are more hollow than those of animals which do not fly ; and therefore they have the needful strength without having to carry more weight than is absolutely necessary. Their quills derive strength from the same construction. They possess another peculiarity to help their flight. No other animals have any communication between the air-vessels of their lungs and the hollow parts of their bodies ; but birds have it ; and by this means they can blow out their bodies as we do a bladder, and thus be- come lighter when they would either make their flight towards the ground slower, or rise more swiftly, or float more easily in the air ; while, by lessening their bulk and closing their wings, they can drop more speedily if they wish to chase or to escape. Fishes possess a power of the same kind,^ though not by the same means. They have air- bladders in their bodies, and can puff" them out, or press them closer, at pleasure : when they want to rise in the water, they fill out the bladder, and this lightens them ; when they would sink, they squeeze the bladder, pressing the air into a smaller space, and this makes them heavier. If the bladder PLEASURES OF SCIENCE. 73 breaks, the fish remains at the bottom, and can be held up only by the most laborious exertions of the fins and tail. Accordingly, flat fish, such as skaits and flounders, which have no air-bladders, seldom rise from the bottom, but are found lying on banks in the sea, or at the bottom of rivers. If you have a certain space, as a room, to fill up with closets or little cells, all of the same size and shape, there are only three figures which will an- swer, and enable you to fill the room without losing any space between the cells ; they must either be squares, or figures of three equal sides, or figures of six equal sides. With any other figures what- ever, space would be lost between the cells. This is evident upon considering the matter ; and it is proved by mathematical reasoning. The six-sided figure is by far the most convenient of those three shapes, because its corners are flatter, and any round body placed in it has therefore more space, less room being lost in the corners. This figure, too, is the strongest of the three ; any pressure from without or from within will hurt it least, as it has something of the strength of an arch. A round figure would be still stronger, but then room would be lost between the circles, whereas with the six-sided figure none is lost. Now, it is a most remarkable fact, that Bees build their cells exactly in this shape, and thereby save both room and materials beyond what they could save if 74 OBJECTS, ADVANTAGES, AND they built in any other shape whatever. They build in the very best possible shape for their pur- pose, which is to save all the room and all the wax they can. So far as to the shape of the walls of each cell ; but the roof and floor, or top and bot- tom, are built on equally true principles. It is proved by mathematicians, that, to give the greatest strength, and save the most room, the roof and floor must be made of three square planes meeting in a point ; and they have further proved, by a dem.on- stration belonging to the highest parts of Algebra, that there is one particular angle or inclination of those planes to each other where they meet, which makes a greater saving of materials and of work than any other inclination whatever could possibly do. Now, the Bees actually make the tops and bottoms of their cells of three planes meeting in a point ; and the inclinations or angles at v/hich they meet are precisely those found out by the mathematician to be the best possible for saving wax and work.* * Koenig, pupil of Bernoulli, and Maclaurin, proved by very refined investigations, carried on with the aid of the. fluxional calculus, that the obtuse angle naust be 109° 28', and the acute 70° 32', to save the most wax and work pos- sible. Maraldi found by actual measurement, that the angles are about 110<=* and 70°. These angles never vary in any place ; and it is scarcely less singular, that the breadth of all bees' cells are everywhere precisely the same, the drone or male cells being ^|ths and the worker or female cells i^ths of an inch in breadth, and this in all countries and times. PLEASURES OF SCIENCE. 75 Who would dream of the bee knowing the highest branch of the Mathematics — the fruit of Newton's most wonderful discovery— a result, too, of which he was himself ignorant, one of his most celebrated followers having found it out in a later age ? This little insect works with a truth and correctness which are perfect, and according to the prin- ciples at which man has arrived only after ages of slow improvement in the most difficult branch of the most difficult science. But the Mighty and All-wise Creator, who made the insect and the phi- losopher, bestowing reason on the latter, and giving the former to m ork without it — to Him all truths are known to all eternity, with an intuition that mocks even the conceptions of the sagest of human kind. It may be recollected, that when the air is ex- hausted or sucked out of any vessel, there is no longer the force necessary to resist the pressure of the air on the outside ; and the sides of the vessels are therefore pressed inwards with violence : a flat glass would thus be broken, unless it were very thick ; a round one, having the strength of an arch, would resist better ; but any soft substance, as leather or skin, would be crushed or squeezed to- gether at once. If the air was only sucked out slowly, the squeezing would be gradual ; or, if it were only half sucked out, the skin would only be partly squeezed together. This is the process by 76 OBJECTS, ADVANTAGES, AND which Bees reach the fine dust and juices of hollow- flowers, like the honeysuckle, and some kinds of long fox-glove, which are too narrow for them to enter. They fill up the mouth of the flower with their bodies, and suck out the air, or at least a large part of it ; this makes the soft sides of the flower close, and squeezes the dust and juice towards the insect as well as a hand could do, if applied to the outside. We may remember this pressure or weight of the atmosphere as shown by the barometer and the suck- ing-pump. Its weight is near fifteen pounds on every square inch, so that if we could entirely squeeze out the air between our two hands, they would cling together with a force equal to the pressure of double this weight, because the air would press upon both hands ; and if we could contrive to suck or squeeze out the air between one hand and the wall, the hand would stick fast to the wall, being pressed on it with the weight of above two hundredweight, that is, near fifteen pounds on every square inch of the hand. Now, by a late most curious discovery of Sir Everard Home, the distinguished anatomist, it is found that this is the very process by which Flies and other insects of a similar description are enabled to walk up perpendicular surfaces, however smooth, as the sides of walls and panes of glass in windows, and to walk as easily along the ceiling of a room with their bodies downwards and their feet over PLEASURES OF SCIENCE. 77 head. Their feet, when examined by a microscope, are found to have flat skins or flaps, like the feet of web-footed animals, as ducks and geese ; and they have by means of strong folds the power of drawing the flap close down upon the glass or wall the fly walks on, and thus squeezing out the air completely, so as to make a vacuum between the foot and the glass or wall. The conse- quence of this is, that the air presses the foot on the wall with a very considerable force compared to the weight of the fly ; for if its feet are to its body in the same proportion as ours are to our bo- dies, since we could support by a single hand on the ceiling of the room (provided it made a vacuum) more than our whole weight, namely, a weight of above fifteen stone, the fly can easily move on four feet in the same manner by help of the vacuum made under its feet. It has likewise been found that some of the larger Sea-animals are by the same construction, only upon a greater scale, enabled to climb the perpendicular and smooth surfaces of the ice hills among which they live. Some kinds of Lizard have a like power of climbing, and of creeping with their bodies downwards along the ceiling of a room ; and the means by which they are enabled to do so are the same. In the large feet of those animals, the contrivance is easily observed, of the toes and muscles, by which the skin of the foot is 78 OBJECTS, ADVANTAGES; AND pinned down, and the air excluded in the act of walking or climbing ; but it is the very same, only upon a larger scale, with the mechanism of a fly's or a butterfly's foot; and both operations, the climbing of the sea-horse on the ice, and the creep- ing of the fly on the window or the ceiling, are performed exactly by the same power, the weight of the atmosphere, v/hich causes the quicksilver to stand in the weather-glass, the wind to whistle through a key-hole, and the piston to descend in an old steam-engine. Although philosophers are not agreed as to the peculiar action which light exerts upon vegetation, and there is even some doubt respecting the decom- position of air and water during that process, one thing is undeniable, — the necessity of light to the growth and health of plants : without it they have neither colour, taste, nor smell ; and accordingly they are for the most part so formed as to receive it at all times when it shines on them. Their cups, and the little assemblages of their leaves before they sprout, are found to be more or less affected by the light, so as to open and receive it. In several kinds of plants this is more evident than in others; their flowers close entirely at night, and open in the day. Some constantly turn round towards the light, following the sun, as it were, while he makes or seems to make his revolution, so that they receive the greatest quantity possible PLEASURES OF SCIENCE. 79 of his rays. Thus clover in a field follows the apparent course of the sun. But all leaves of plants turn to the sun, place them how you will, light being essential to their thriving. The lightness of inflammable gas is well known. When bladders of any size are filled with it, they rise upwards, and float in the air. Now, it is a most curious fact, ascertained by Mr. Knight, that the fine dust, by means of which plants are im- pregnated one from another, is composed of very small globules, filled with this gas — in a word, of small air-balloons. These globules thus float from the male plant through the air, and striking against the females, are detained by a glue pre- pared on purpose to stop them, which no sooner moistens the globules than they explode, and their substance remains, the gas flying off which enabled them to float. A provision of a very simple kind is also, in some cases, made to prevent the male and female blossoms of the same plant from breed- ing together, this being found to hurt the breed of vegetables, just as breeding in and in spoils the race of animals. It is contrived that the dust shall be shed by the male blossom before the female of the same plant is ready to be affected by it ; so that the impregnation must be performed by the dust of some other plant, and in this way the breed be crossed. The light gas with which the globules are filled is most essential to the operation, as it e2 80 OBJECTS, ADVANTAGES, AND conveys them to great distances. A plantation of yew-trees has been known, in this way, to impreg- nate another several hundred yards off. The contrivance by which some creeper plants are enabled to climb walls, and fix themselves, deserves attention. The Virginia creeper has a small tendril, ending in a claw, each toe of which has a knob, thickly set with extremely small bristles ; they grow into the invisible pores of the wall, and swelling, stick there as long as the plant grows, and prevent the branch from falling ; but when the plant dies, they become thin again, and drop out, so that the branch falls down. The Vanilla plant of the West Indies climbs round trees likewise by means of tendrils ; but when it has fixed itself, the tendrils drop off, and leaves are formed. It is found by chemical experiments, that the juice which is in the stomachs of animals (called the gas- tric ^ulce, from a Greek word signifying the belly) has very peculiar properties. Though it is for the most part a tasteless, clear, and seemingly a very simple liquor, it nevertheless possesses extraor- dinary powers of dissolving substances which it touclies or mixes with ; and it varies in different classes of animals. In one particular it is the same in all animals ; it will not attack living matter, but only dead ; the consequence of which is, that its powers of eating away and dissolving are perfectly P1.EASURES OF SCIENCE. 81 safe to the animals themselves, in whose stomachs it remains without ever hurting them. This juice differs in different animals according to the food on which they subsist ; thus, in birds of prey, as kites, hawks, owls, it only acts upon animal matter, and does not dissolve vegetables. In other birds, and in all animals feeding on plants, as oxen, sheep, hares, it dissolves vegetable matter, as grass, but will not touch flesh of any kind. This has been ascertained by making them swallow balls with meat in them, and several holes drilled through to let the gastric juice reach the meat : no effect was produced upon it. We may further observe, that there is a most curious and beau- tiful correspondence between this juice in the stomach of different animals and the other parts of their bodies, connected with the important opera- tions of eating and digesting their food. The use of the juice is plainly to convert what they eat into a fluid, from which, by various other processes, all their parts, blood, bones, muscles, &c., are after- wards formed. But the food is first of all to be obtained, and then prepared by bruising, for the action of the juice. Now birds of prey have in- struments, their claws and beaks, for tearing and devouring their food (that is, animals of various kinds), but those instruments are useless for picking up and crushing seeds ; accordingly they have a gastric juice which dissolves the animals they eat ; 82 OBJECTS, ADVANTAGES, AND while birds which have only a beak fit for pecking, and eating seeds, have a juice that dissolves seeds, and not flesh. Nay more, it is found that the seeds must be bruised before the juice will dissolve them : this you find by trying the experiment in a vessel with the juice ; and accordingly the birds have a gizzard, and animals which graze have flat teeth, which grind and bruise their food, before the gas- tric juice is to act upon it. We have seen how wonderfully the Bee works, according to rules discovered by man thousands of years after the insect had been following them with perfect accuracy. The same little animal seems to be acquainted with principles of which we are still ignorant. We can, by crossing, vary the forms of cattle with astonishing nicety; but we have no means of altering the nature of an animal once born, by means of treatment and feeding. This power, however, is undeniably possessed by the bees. When the queen bee is lost by death or otherwise, they choose a grub from among those which are born for workers ; they make three cells into one, and placing the grub there, they build a tube round it ; they afterwards build another cell of a pyramidal form, into which the grub grows ; they feed it with peculiar food, and tend it with extreme care. It becomes, when transformed from the worm to the fly, not a worker, but a queen bee. These singular insects resemble our own species PLEASURES OF SCIENCE. 83 in one of our worst propensities, the disposition to war; but their attention to their sovereign is equally extraordinary, though of a somewhat ca- pricious kind. In a few hours after their queen is lost, the whole hive is in a state of confusion. A singular humming is heard, and the bees are seen moving ail over the surface of the combs with great rapidity. The news spreads quickly, and when the queen is restored, quiet immediately suc- ceeds. But if another queen is put upon them, they instantly discover the trick, and, surrounding her, they either suffocate or starve her to death. This happens if the false queen is introduced within a few hours after the first is lost or removed ; but if twenty-four hours have elapsed, they will receive any queen, and obey her. The labours and the policy of the Ants are, when closely examined, still more wonderful, per- haps, than those of the Bees. Their nest is a city consisting of dwelling-places, halls, streets, and squares into which the streets open. The food they principally like is the honey which comes from another insect found in their neighbourhood, and which they, generally speaking, bring home from