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ON THE SCIENCE OF WEIGHING AND MEASURING, AND THE STANDARDS OF WEIGHT AND MEASURE*

VIII.

*T* HE ordinary method of commercial weighing by putting -*- the weights in one scale and the commodity to be weighed in the other, and then observing when a sufficient equilibrium is produced, is inadmissible forscientific weighings, as it is subject to errors arising from defects in the balance itself. To avoid any such errors, and obtain scientific precision in the results, a check is required which is found in a system of double weighing. There are two methods of double weighing for the comparison of two standard weights. One method, known as Borda's, and generally used in France, is that of substitution, or weighing first one of the standard weights to be compared, and then the other substituted for it, against a counterpoise placed in the other pan. The difference between the mean resting points of the index needle in these two weighings shows the difference of the two weights in divisions of the scale. The second method, known as Gauss's, but which was first invented by Le Pere Amiot, and is now generally used in England and Germany, except for hydrostatic weighings, is that of alternation, or first weighing the two standards against each other, and then repeating the weighings, after interchanging the weights in the pans. By this second method no counterpoise weight is required, and half the difference between the mean resting points of the index needle shows the difference of the two weights, in divisions of the scale. In all scientific weighings of standards with balances of precision, it is necessary that the weights to be compared should be so nearly equal that neither pan shall absolutely weigh down the other. The balance must merely oscillate so that the pointer does not exceed the limits of the index scale. In order to obtain an equipoise within this limit, it is requisite to provide small balance weights, most accurately verified, to be added to either pan, as may be found necessary.

The mode of reading adopted by the'best authorities in the process of weighing by Gauss's method is as follows: —The comparing standard being in the left-hand pan, and the compared standard in the right-hand pan, and sufficient equipoise being obtained by adding small balance weights, if requisite, the balance is put in action, and the movement of the needle observed through a telescope. The reading at the first turn of the pointer is disregarded. The three next turns are noted, and the reading at the third turn of the pointer, and half the sum of the readings at the second and fourth turns are taken as the highest and lowest readings. Their mean is the resting point of the balance, or the reading of its position of equilibrium. The balance is then stopped, and the weights interchanged, when similar readings are taken and dealt with in the same manner. These two observations constitute one comparison. In cases where great accuracy is required, several successive comparisons are taken, in order to obtain a mean result. Some additional weighings are taken after adding a small balance weight to either pan, in order to ascertain the value of a division of the index scale. And if this balance-weight be added successively to each pan the weighings may be used as additional comparisons.

In using Gauss's method of weighing, it is very' desirable to be able to transfer the pans and the weights contained in them from one end of the beam to the other without opening the balance case, and thus to avoid sudden changes of temperature of air within the balance case and consequent production of currents of air. For this pur

* Continued from p. 555.

pose, the following plan is adopted. A grooved brass rod is fixed inside the balance case over and a little behind the beam. Upon this rod a brass slider is made to traverse by being attached to a slender brass rod drawn backwards or forwards from the outside of the case. A descending wire with a hook at the end is attached to the slider. For changing the weights, the slider and hook are brought to the right-hand end of the beam, when the pan and weight are lifted from the beam and transferred to the hook by means of a brass rod curved at the end and introduced through a small hole at the side of the balance case. The pan and weight are then slid to the other end of the beam, when the left-hand pan and weight are lifted in a similar manner from the beam and the right-hand pan and weight substituted. It only remains then to transfer the left-hand pan and weight to the right-hand end of the beam.

This method possesses a further advantage. In making a great number of comparisons between two standard weights, they are exposed to some risk of being injured

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Fig. 18.—Mode af hydrostatic weighing (one-third size).

by wear, if they are taken up in the ordinary way with a piir of tongs. This risk is obviated by their being kept in the pans when lifted. Two light pans are used of as nearly as possible equal weight, each of which has a loop of wire forming an arch with the ends attached to the opposite sides of the pan, so that it can be easily lifted with the curved end of a brass rod. The pans are marked X and Y respectively. By interchanging the weights in the pans after a series of comparisons, and making a second series and taking the mean result, it gives the difference between the two weights, unaffected by any possible difference in the weight of the two pans. This contrivance is especially useful, when either of the weights to be compared consists of several separate weights. It was used by Prof. Miller for all his more important weighings during the construction of the imperial standard pound.

The advantage possessed by Gauss's method of alternation over Borda's method of substitution has been proved by Prof. Miller as follows :—

Let P and Q be two standard weights of the same denomination to be compared, and C the counterpoise of each.

For Borda's method, let the readings of the index be denoted by (C, P), when C is in the left pan and P in the right pan, and by (C, Q), when C is in the left pan, and Q in the right pan.

For Gauss's method, let (Q, P) denote the readings when Q is in the left pan and P in the right, and (P, Q), when P is in the left pan and Q in the right pan.

Let e be the probable difference between the recorded and the true position of equilibrium, that is to say, the probable error of a single weighing (not of a comparison, which requires two weighings).

Then by Borda's method, (C, P) has a probable error e, and (C, Q) has a probable error c; and the two weighings give the value of P — Q with a probable error of ,/(«■ + **) - e>/2.

By- Gauss's method, (Q, P) has a probable error <?, and (P, Q) has a probable trror e; and the two weighings give the value of P - Q with a probable error of

Thus the probable error of the result of two weighings by Borda's method is twice as great as by Gauss's method.

To obtain a value of P — Q by Borda's method with a probable error of — J2, we must make four comparisons of

two weighings each. Therefore one comparison by the method of Gauss gives as good a result as four comparisons by Borda's method.

The result of this weighing of two standard weights against each other gives only their apparent difference when weighed in air. In crder to ascertain their true difference, it becomes necessary to determine the weight of air displaced by each, from the data which have been already mentioned, and to allow for any difference of weight of air displaced, according to the following formula :—

If the weights P and Q appear to be equal in air, the weight of P — weight of air displaced by P is equal to the weight of Q — weight of air displaced by Q.

■In determining the weight of ordinary atmospheric air in rooms where standard weights are compared, and containing a certain quantity of aqueous vapour and carbonic acid, the practice has been to take, as the unit of weight of air, a litre of dry atmospheric air free from carbonic acid, = 1-2932327 gramme, at o°C, as determined by Ritter from the observations of M. Regnault in Paris, lat. 480 50' 14", and 60 metres above the level of the sea, under the barometric pressure of 760 millimetres of mercury. Assuming that atmospheric air contains, on an average, carbonic acid equal to o-ooo4 of its volume, and the density of carbonic acid gas being 1-529 of that of atmospheric air, the weight of a litre of dry atmospheric air containing its average amount of carbonic acid, under the stated circumstances, is 1-2934963 gramme.

Allowance should be made for the difference of the force of gravity in latitudes other than Paris, as well as for the difference of height of the place of observation above the mean level of the sea. Although the absolute weight varies with the latitude and with the height above or below the mean level of the sea, yet this variation is not felt in the comparison of standard weights in a vacuum, because the weights are equally affected on both sides of the beam. But in all weighings of standards in air re

quiring special accuracy, such variation must be taken into account in computing the weight of air displaced by each standard weight.

Mr. Baily has shown from his pendulum experiments * that if we take G to denote the force of gravity at the mean level of the sea in lat 45°, the force of gravity in lat. X, at the mean level of the sea

= G (1 - o-oo25659 cos 2 X).

And Poisson f has proved that the force of gravity in 1 given latitude at a place on the surface of the earth at the height z above the mean level of the sea—

j _/2_3p'\£_I x (force of gravity at the mean ~ }' \ ~ 2p ) r ) level of the sea in the same lat.;

where r is the radius of the earth, p its mean density, and p' the density of that part of the earth which is above the mean level of the sea. If as is probable,—

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3P =132 nearly; r= 636619Smetre,

2p

it follows that the weight in grammes of a litre of dry atmospheric air containing the average amount of carbonic acid, at 0°, and under the pressure of 760 millimetres of mercury at 0°, at the height s above the mean level of the sea in lat. X is—

1-2930693 (1 - 1-32 - ) (1 — 00025659 cos 2 X).

At Cambridge, where Prof. Miller's observations for determining the weight of the new standard pound were made, in lat. 52" 12' 18", about 8 metres above the mean level of the sea (and for which place his tables were computed,) the weight of a litre of dry air containing ibc average quantity of carbonic acid was found by him to be 1-293893 gramme. This weight of air is therefore a little greater than at Paris. From similar data, after taking a further correction by Lasch of the weight of a litre of doair at Paris = 1-293204 gramme, the weight of a litre of dry air at Berlin (lat. 52" 30', and 40 metres above mean sea level) has been computed to be 1-29388 gramme.

The co-efficient of expansion of air under constant pressure between o° and 50° C. is taken from Regnaulr's determination to be 0-003656 for i° C, in other words between o° and 500 C, the ratio of the density of air at o" to its density at f is I + 0003656 /.

With regard to the barometric pressure of the air and the allowance to be made for the pressure of vapour present in it, the density of the vapour of water is determined to be 0-622 of that of air ; that is to say, the ratio of the density of the vapour of water to that of air is 1 — 0-378.

Hence, if/be the temperature of the air, b the barometric pressure, v the pressure of the vapour present in the air, b and v being expressed in millimetres of mercury at o° C, the weight of a litre of air at Cambridge becomes

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The ratio of the density of air to the maximum density of water is found by dividing the above expression by 1,000, as a litre of water is the volume of 1,000 grammes of water at its maximum density. Prof. Miller's Tabic I. gives the logarithms of this ratio at the normal barometric pressure of 760 millimetres, at the several degrees of temperature from to 300. These logarithms require to be diminished only by 0-000026 for weighings at the Standards Office, Westminster, lat. 51° 30', and about 5 metres above the mean sea-level; and when dimi

* "Memoir* of the Astronomical Society," vol. vu, p. 04.
t "Memoires de l'lnstitut," tome xxi. pp. 91, 338.

nished by o-oooi32, they may be used for the reductions of weighings at Paris.

The values of the pressure of vapour at the same temperatures in millimetres of mercury at o', according to Regnault's observations, are stated by Prof. Miller in a separate Table II. These values are given on the assumption that the pressure of vapour in rooms that are not heated artificially is two-thirds of the maximum pressure of vapour due to the temperature, as shown by the results of experiments on the authority of Biot, Regnault, and Bianchi.

The actual mode of ascertaining the weight of air displaced by two standard weights may now be described.

For determining the temperature of the air and of the two standard weights during the weighings, two standard thermome'.ers are placed in' the balance case, and their readings noted at the beginning and end of the weighings. The weight of air displaced by each of two standard weights is to be ascertained by the following formula:

Log weight in grains of air displaced by P = log. /; -+log. AJ + log. (1 + eVt) + log. weight of P in grains log. AP

Here / denotes the temperature of the air by the Centigrade thermometer;

b the barometric pressure of the air in millimetres of mercury at o° C.;

v the maximum pressure of aqueous vapour contained in the air, also in millimetres of mercury;

h = b - 0-378 X § -';

At the ratio of density of air at to the maximum density of water;

ePt the allowance for expansion in volume of P, or the ratio of its density at o5 to its density at /;

AP the ratio of density of P at o° to the maximum density of water.

By this formula, the required result is to be obtained. The logarithms of the three first terms may be found in Prof. Miller's tables, pp. 785-791 of his account of the construction of the new standard pound, Phil. Trans., part iii. of 1856.

Reference has already been made to the mode of ascertaining the volume or density of a standard weight by determining the difference of its weight in air and in water. The following practice for all such hydrostatic weighings was adopted by Prof. Miller when determining the densities of all the standard weights constructed under the sanction of the Commission for restoring the Imperial Standards, and is also followed in the Standards Department. In this process it is requisite to employ pure distilled water, and with this object the water used in the Standards Department is twice distilled in a still of the best construction, erected in the office, and the best chemical tests are employed for ascertaining that the water is free from any foreign substances.

The vessel for containing the distilled water is a glass jar, rather more than 6 inches in internal height and diameter. A stout copper wire is stretched across the mouth of the jar (see Fig. 18) in such a manner as to leave a circular space in the middle, large enough to admit the passage of the standard weight P, the density of which is to be ascertained. This copper wire supports two thermometers, adjustable as to their height, for determining the temperature of the water at the mean height of B during the weighings. It also serves to sustain a glass tube, open at both ends, and placed close to the side of the jar. A small glass funnel is inserted in the upper part of the tube, and in the lower part are one or two pieces of clean sponge.

The standard weight P is suspended from a hook under the right pan of the balance, specially constructed for hydrostatic weighings. A fine copper wire, the weight of which per inch is known, is attached to the hook by a loop, and has another loop at the other end. To this lower loop is attached a stout wire, bent and terminating

I in a double hook, which fits round P, and holds it securely.

I The counterpoise of P is next placed in the left pan of the

i balance. The glass jar is placed under the right pan of the balance, P being suspended in it, and the water is gently poured into the funnel and the jar filled to the

I requisite height above P. The bubbles of air are arrested by the pieces of sponge, and, ascending up the glass tube, are thus prevented from entering the jar. It is of import

1 ance to ascertain that no bubble of air is attached to P, and if so, it may generally be removed by the feather of a quill. But it sometimes happens that the weight P has an irregular surface, and air attaching to it cannot be thus dislodged. In such cases a small bell-shaped glass jar just large enough to hold P and its supporting wire, is used. This vessel is filled with water sufficient to cover P, and is suspended over the flame of a spirit lamp by a stout wire, bent at its lower end into a ring, into which the jar descends to its rim, and the water is allowed to boil until it is seen that the air has been entirely expelled. When cooled, the small jar containing P is immersed iu the water, which nearly fills the large jar, and the small jar, with its wire, is then disengaged and lowered till P hangs clear of it, when it is removed. The transfer of P from the small to the large jar is thus effected without taking it out of the water.

For the actual weighing of P in water, after it has been counterpoised in air, weights equal to the difference of weight of P in water and in air, are placed in the right pan till equilibrium is produced, when the readings of the scale are observed. P is next removed, leaving its hook suspended in the water, and a volume of water equal to the volume of P is added to the water in the jar, so as to leave the same quantity of wire immersed as before. The requisite weights are then added to the right pan, until the equilibrium, which has been disturbed by the removal of P, is again produced, when the reading of the scale is observed and noted. This gives the actual weight in water of P.

.The thermometers in the water are so placed as to give the temperature of the water at the centre of gravity of P. Another thermometer is placed in the balance case to give the temperature of the air during the weighings. The reading of the barometer is also noted.

Having determined the weight of P in air of ascertained density, its volume and density are calculated according to the following formula, the unit of volume being the volume of a grain weight of water at its maximum density :—

Let P in water at I" appear to weigh as much as Q in air. Then the weight ot water at tD displaced by P = weight of P — weight of Q -f- weight of air displaced by

Q

Log. volume of P = weight in grains of the water displaced by P + log. VV, - log. (1 + ePt); where VVt is the ratio of the maximum density of water to its density at /, and ePt is the expansion in volume of P at /. (The logarhhms of these values are given in tables.)

Log. density of P = log. weight of P in grains — log. volume of P.

The actual weight of air displaced is to be ascertained by the method already stated.

As the true weight of P in air cannot be ascertained until its volume or density is known, an approximate value of the volume of P may be found by assuming the weight of P to be equal to its apparent weight in air ; and this value of the volume of P may be used in reducing the weight of P, and thus a more accurate value of the volume of P obtained, by means of which a closer approximation to the values of the absolute weight of P, and of its density may be found. This process should be repeated when greater exactness is required.

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EARTH-SCULPTURE *

AMONG the questions which may be treated as matters of strict science, and which yet cannot be wholly divested of the strong human, one might almost say personal, interest which belongs to them, is the birth of mountains and valleys. The familiar outlines of his dwelling-place have fixed the attention of man from the infancy of the race up to the present day. Long before science arose to deal with them they had become inwoven with his history, his habits, and his creed. The great mountains had been to him emblems of majesty and eternity, lifting up their fronts to heaven as they had done from the beginning, and would no doubt do to the end. They rose before him as monuments of the power of that great Being who had heaved them out of chaos. It was enough for him in that early time to feel their mighty influences ; he had then no questions or doubts as to how or when they first appeared upon the earth.

Happily, in spite of questioning, exacting Science, these first natural and instinctive feelings are not yet dead within us. A knowledge even of all the laws of mountain-making cannot, if our minds are healthy and our hearts beat true, deprive us wholly of that first genuine child-like awe and wonder in presence of noble mountains,—crag and cliff sweeping in rugged and colossal massiveness above dark waves of pine, far into the keen and clear blue air ;—the vast mantle of snow, so cloudlike in its brightness, yet thrown in many a solid fold over crest and shoulder; the dark spires and splintered peaks, half snow, half stone, rising into the sky, like very pillars of heaven; and then the verdure of the valleys below, the dash of waterfalls, the plenteous gush of springs, the laugh and dance of brook and river as they one and all hurry down to the plains—who can see these things for the first time, nay, for the hundredth time, without at least some sparkle of the simple child-like emotion of the olden time, or without appreciating, even if he cannot fully share, the feeling of the poet to whom they bring " dim eyes suffused with tears "?

These great dominant features of the land must indeed ever rivet our imagination, and yet when the questioning spirit of modern science asks to know ho«v they cair.c into being, we are no longer permitted to content ourselves with the early belief that they were but parts of the prim;cval outlines of the earth. The progress of inquiry and knowledge has destroyed that belief. We find, too, that both labour and patience are needed ere we can understand what has been put in its place. But the task of learning this is well repaid. However grandly the mountains rose when they were gazed at only in awe and wonder, they gain an added sublimity when the eyes which look upon them can trace some of the steps whereby their grim magnificence has been achieved.

We naturally associate the more lofty and rugged parts of the land with the operations of former earthquakes and convulsions by which the solid earth has been broken and ridged into these picturesque forms. This obvious inference was early adopted in geology, and though in many cases a mere belief rather than a legitimate deduction from observation, and springing from a conviction of what ought to be, rather than what has been proved to be the case, it has sturdily maintained its hold alike on the popular mind, and also to a very considerable extent in the orthodox geological creed.

Towards the end of last century, however, Hutton and Playfair, names never to be mentioned in Edinburgh without gratitude and pride, proclaimed views of a very different character. They maintained that the rocks of the land, originally accumulated under the sea, have been upheaved by underground movements, and without pretending to know in what external forms these

• The Opening Address for the Session 1873-4 to the Edinburgh Geological Society, delivered Thursday, Nov. 6, by the President, Prof. Geikic, F.R.S.

rocks first appeared above the sea, they contended that the present contours of the land had arisen mainly from a process of sculpture,—the valleys having been carved out by rains, streams, and other superficial agents, while the hills were left standing up as ridges between. So satisfied were these bold and clear-sighted men that their idea was essentially true, that they gave themselves 110 concern in gathering detailed proofs in its support They were content with general appeals to the face of nature everywhere as their best and irrefragable witness. But, as events proved, they were in advance of their time. The views which they promulgated on this subject were first opposed, then laid aside and forgotten. In the subsequent literature of the science for fully half a century they almost wholly disappear. An occasional reference to them may be met with, where, however, they are cited only to be dismissed, as if the writer seemed hardly able to restrain some expression of his wonder that men could ever have been found so Quixotic as to vent such notions, or that others could have been so gullible as to believe them.

Apart altogether from the truth or error of the Huttonian teaching regarding the origin of the earth's soperficial features, no one who has the progress of geology at heart can regard without regret this almost contemptuous dismissal of the question from the range of scientific inquiry. For together with that teaching went all interest in, and even all intelligent appreciation of, the problem which Hutton had set himself to solve. Men turned back to vague notions about cataclysms, earthquakes, subterranean convulsions and ^fractures, of which they spoke, and sometimes still speak, with a boldness in inverse proportion to their knowledge of the actual conditions of the problem. They studied with praiseworthy assiduity and success the working of the various natural agents whereby the surface of the land is affected, but it was with the view rather of showing how the materials of new continents are gathered together, than of learning how the outlines of existing continents have been produced. The study of the origin of mountain and valley went out of fashion, and from the time of Playfair's Illustrations, published at the beginning of this century, received in this country but scant and haphazard attention until in recent years the subject has gradually revived, and has become one of the most prominent and interesting subjects of geological research.

It is not my purpose to give any historical sketch of the progress of inquiry on this question, although I ought not even to refer to it without an allusion to the names of Scrope, Ramsay, Jukes, Ruskin, Dana, Topley, Whitaker, Greenwood, the Duke of Argyll, Mackintosh, and others, who, though often differing widely in their views, have done so much to renew an interest in what will probably always prove one of the most alluring aspects of geology. Thoroughly convinced of the essential truth on which the Huttonian doctrines were based I wish, on the present occasion, first to define and illustrate some of the leading features of these doctrines as I hold them myself, and as I believe them to be held by the great body of active field geologists in Britain, and secondly, to review certain objections which have recently been reiterated against them.

At the outset it is necessary to ascertain what relation the internal arrangements of the rocks bear to the external forms of the land, in other words, the influence of what is called Geological Structure. It is obvious, as Hutton showed, that since the rocks have been formed as a whole under the sea, they must have been raised out of that original position into land, so that the first point we settle beyond dispute is that the mass of the land owes its existence to upheaval from below. But though we fix securely enough this starting point in our inquiry, it by no means follows that we thereby settle what was the original outline of the land so upheaved. The nonrecognition of this fact has involved not a few of the writers on this subject in great confusion and error.

Among the geologists of the present day there is a growing conviction that upheaval and subsidence are concomitant phenomena, and that viewed broadly they both arise from the effects of the secular cooling and consequent contraction of the mass of the earth. The contraction has not been uniform, as if the globe had been a cooling ball of solid iron. On the contrary, owing to very great differences in the nature and condition of the various parts of our planet and perhaps to features of the interior with which we are yet but imperfectly acquainted, some portions have sunk much more than others. These, having to accommodate themselves into smaller dimensions would undergo vast compression and exert an enormous pressure on the more stable tracts which bounded them. It could not but happen that after long intervals of strain, some portions of the squeezed crust would at length find relief from this pressure by rising to a greater or less height, according to their extent and the amount of force from which they sought to escape. These upraised areas would no doubt tend to occur in bands or lines across the direction of the pressure, much as the folds we produce in the sheets of an unbound book are more or less nearly parallel with the two sides from which we squeeze the paper. They would sometimes be broad folds—huge wide swellings of the earth's surface. At other times they might be long, lofty, and comparatively sharp ridges. In the one case they would give rise to high plateaux or table-lands, in the other they would be recognised as mountain-chains.

This is a rough-and-ready statement of what seems the probable explanation of the origin of the elevated tracts upon the earth's surface. It is evident that the pressure would be vastly gi eater a few hundreds or thousands of feet underground than at the surface, and hence that though the rocks deep down might be squeezed and crumpled, as we could crumple brown paper, yet that at the surface they might show little or no contortion. Certainly without further proof we could never affirm that a contorted mass of rock which now forms the surface of the ground rose as part of the surface during the time of upheaval and contortion. Intensely crumpled rocks would rather suggest a deeper position, with the subsequent removal of the rocks under which they originally lay.

As the earth has been cooling and contracting ever since it had a separate existence as a planet, its surface must have been exposed to a long scries of such shrinkage movements as those we arc considering. Apart, therefore, from local evidence, we should expect that ridges and depressions must have been impressed upon that surface in a long succession from the earliest periods downwards, and hence that the present mountain-chains and basins of the earth must be of many different ages. We cannot tell what the first mountains were made of, nor where they lay, although some of the existing ridges of the earth's surface are undoubtedly, even in a geological sense, very old. In not a few cases the same mountainchain can be shown from its internal structure to be of many successive dates, as if it lay along a line of weakness which had served again and again as a line of relief from the severe earth-pressure.

These questions have been treated with much ability by Constant Prevost, Dana, Mallet, and others, to whose writings I refer for details. In stating them in this general way my object is to show that those geologists who, like myself, believe in the truth of the Huttonian doctrines of denudation, are most unfairly represented when they are said to ignore the influence of subterranean forces upon the exterior of the earth. None can recognise more clearly than they do how entirely have the great surface outlines of the globe been dependent upon the action of these forces, that is, upon the results which

flow from the contraction of the planet and from the reaction of the heated interior upon the surface.

But a block of marble is not a statue, nor would a part of the earth's crust heaved up into land form at once such a surface of ridge, and valley, and nicely adjusted water system as any country of which we know anything on the face of the globe. In each case it is a process of sculpture, and the result varies not only with the tools but with the materials on which they are used. You would not expect the same kind of caning upon granite as upon marble. And so, too, in the great process of earthsculpture, each chief class of rock has its own characteristic style. The tools by which this great work has been done are of the simplest and most everyday order—the air, rain, frost, springs, brooks, rivers, glaciers, icebergs, and the sea. These tools have been at work from the earliest times of which any geological record has been preserved. Indeed, it is out of the accumulated chips and dust which they have made, afterwards hardened into solid rock and upheaved, that the very framework of our continents has been formed. The thickness of these consolidated materials is to be measured, not by feet merely, but by miles. If the removed materials are so thick, they show what a vast mass of rock must have been carved away. And even before knowing anything of the way in which the various tools are used, we should be justified in holding it to be, at the least, extremely improbable that any land surface would long retain its original contour or even any trace of it.

But when we come to watch with attention how the tools really do their work, this improbability increases enormously. Adopting a method of inquiry suggested by Mr. Croll, I have elsewhere shown that even at their present state of progress the amount of geological change which they would accomplish in a comparatively small number of ages is almost incredible. On a moderate computation they would reduce the general mass of the British Islands down to the level of the sea in five or six millions of years, and might carve out valleys a thousand feet deep in a fourth part of that time. It is evident that though the upheaval of some parts of the continents may go back into the remotest geological antiquity, the forms of the present surface must be, comparatively speaking, modem.

There is reason to believe that many, if not most, of the great mountain chains of the globe are, in a geological sense, of recent origin. The Alps, for example, though they may have undergone many earlier movements, were ridged up into their existing mass long after the soft clays were laid down which cover so large an area of the low lands in the south of England, and on which London is built. It would require far more detailed work than has ever been bestowed upon these mountains to enable us even to approximate to what was the original form of the surface just after the upheaval, and before the array of sculpture-tools began their busy and ceaseless task upon these great masses of rock. We may believe that a scries of huge parallel folds of curved and broken rock rose for thousands of feet into the air, that when, after the earth-throes had ceased, rain and snow and frost first laid their fingers on the new-born summits, these agents of destruction would have a most uneven surface to work upon, and would necessarily be guided byit in their working; and hence that some, at least, of the dominant earliest ridges and hollows would be perpetuated. Such a belief would cany probability in its favour, but it would certainly not amount to a proof of the supposed perpetuation. That would require to be corroborated by the internal and external evidence of the mountains themselves. In some tracts,as, for instance, among the singularly symmetrical ridges and furrows of the Jura, it would not be difficult to restore the original outline, and to fix exactly how far the subterranean movements had determined the present external forms of the ground,

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