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PRATT John Henry Pratt (c. 1811-1871), English clergyman and mathematician, 'spent many years in India as archdeacon of Calcutta. His observations and deductions laid the foundation for the later development of the principle of isostasy. THE ATTRACTION OF THE HIMALAYA MOUNTAINS UPON THE PLUMBLINE IN INDIA From Philosophical Transactions of the Royal Society of London, Vol. CXLV, pp. 53-100, 1855. It is now well known that the attraction of the Himalaya Mountains, and of the elevated regions lying beyond them, has a sensible influence upon the plumb-line in North India. This circumstance has been brought to light during the progress of the great trigonometrical survey of that country. It has been found by triangulation that the difference of latitude between the two extreme stations of the northern division of the arc, that is, between Kalianpur and Kaliana, is 523'42".294, whereas astronomical observations show a difference of 523'37".058, which is 5".236* less than the former. That the geodetic operations are not in fault appears from this; that two bases, about seven miles long, at the extremities of the arc having been measured with the utmost care, and also the length of the northern base having been computed from the measured length of the southern one, through a chain of triangles stretching along the whole arc, about 370 miles in extent, the difference between the measured and the computed lengths of the northern base was only 0.6 of a foot, an error which would produce, even if wholly lying in the meridian, a difference of latitude no greater than 0".006. The difference 5".236 must therefore be attributed to some other cause than error in the geodetic operations. This is the difference as stated by Colonel Everest in his work on the Measurement of the Meridional Arc of India, published in 1847. See p.clxxviii. A very probable cause is the attraction of the superficial matter which lies in such abundance on the north of the Indian arc. This disturbing cause acts in the right direction; for the tendency of the mountain mass must be to draw the lead of the plumb-line at the northern extremity of the arc more to the north than at the southern extremity, which is further removed from the attracting mass. Hence the effect of the attraction will be to lessen the difference of latitude, which is the effect observed. Whether this cause will account for the error in the difference of latitude in quantity, as well as in direction, remains to be considered, and is the question I propose to discuss in the present paper. To dissect and actually to calculate the attraction of the masses of which the Himalayas, and the regions beyond, are composed, appears, at the very thought of it, to be an herculean undertaking next to impossible. I am fully convinced, however, that no other method will succeed. It is upon this plan that the solution of the problem is conducted in this paper. It will be seen, that by selecting a peculiar law of dissection the calculation is very greatly simplified, and made to depend entirely and solely upon a knowledge of the elevations and depressions, in fact, the general contour of the surface. This information for some part of the mass is already supplied by the maps of the Trigonometrical Survey. In the following pages I propose, in the first place, to develop my method of calculation, and to deduce a

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formula by which the attraction can be determined with a precision corresponding to the degree of accuracy to which the contour of the surface is known. In the second place, I propose to reduce the formula to numbers, and so arrive at such an approximate value of the attraction as the data I have been able to collect will allow. This approximate value is, as will be seen, larger than 5".236, the error brought to light by the Survey. I make various suppositions with a view, if possible, to reduce my result to this, but without effect. This leads me to look in another direction for an explanation of the cause of discordance, and I arrive at a conclusion which clears up the discrepancy, confirms the calculations of this paper, and illustrates the importance of not disregarding the influence of mountain attraction.

Adding together the results of the last article, we have Deflection of plumb-line in meridian at A . . . = 27".853 Deflection of plumb-line in meridian at B . . . = 11".968 Deflection of plumb-line in meridian at C . . . = 6".909 . .Difference of meridian deflections at A and B = 15".885 Difference of meridian deflections at A and C = 20".944 Difference of meridian deflections at B and C 2 5~.059 The quantities is first of these considerably greater than 5".236, the quantity brought to light by the Indian Survey. And the values of the deflections at B and C bear a far higher ratio to those at A than has been generally supposed.... The conclusion, then, to which I come is, that there is no way of reconciling the difference between the error in latitude deduced in Colonel Everest's work and the amount I have assigned to the deflection of the plumb-line arising from attraction--and which, after careful re examination, I am decidedly of opinion is not far from the truth, either in defect or excess--but by supposing, that the ellipticity which Colonel Everest uses in his calculations, although correct as a mean of the whole quadrant, is too large for the Indian arc. This hypothesis appears to account for the difference most satisfactorily. The whole subject, however, deserves careful examination; as no anomaly should, if possible, remain unexplained in a work conducted with such care, labour, and ability, as the measurement of the Indian arc has exhibited. THE DEFLECTION OF THE PLUMB-LINE IN INDIA AND THE COMPENSATORY EFFECT OF A DEFICIENCY OF MATTER BELOW THE HIMALAYA MOUNTAINS

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From Philosophical Transactions of Abe Royal Society of London, Vol. CXLIX, pp. 745-778, 1858. The Astronomer Royal in a paper published in the Transactions for 1855, suggested that immediately beneath the mountain-mass there was most probably a deficiency of matter, which would produce, as it were, a negative attraction and so counteract the effect of the plumb-line. This hypothesis appears, however, to be untenable for three reasons:--(1) It supposes the thickness of the earth's solid crust to be considerably smaller than that assigned by the only satisfactory physical calculations made on the subject --those by Mr. Hopkins of Cambridge. He considers the thickness to be about 800 or 1000 miles at least. (2) It assumes that this thin crust is lighter than the fluid on which it is supposed to rest. But we should expect that in becoming solid from the fluid state, it would contract by the loss of heat and become heavier. (3) The same reasoning by which Mr. Airy makes it appear that every protuberance outside this thin crust must be accompanied by a protuberance inside, down into the fluid mass, would equally prove that wherever there was a hollow, as in deep seas, in the outward surface, there must be one also in the inner surface of the crust corresponding to it; thus leading to a law of varying thickness which no process of cooling could have produced. It is nevertheless to this source--I mean a Deficiency of Matter below--that we must look, I feel fully assured, for a compensatory cause, if any is to be found. My present object is to propose another hypothesis regarding the deficiency of matter below the mountain-mass, as first suggested by Mr. Airy; and to reduce my hypothesis to the test of calculation.... I will now state the hypothesis on which my present calculation proceeds. At the time when the earth had just ceased to be u holly fluid, the form must have been a perfect spheroid, with no mountains and valleys nor ocean-hollows. As the crust formed, and grew continually thicker, contractions and expansions may have taken place in any of its parts, so as to depress and elevate the corresponding portions of the surface. If these changes took place chiefly in a vertical direction, then at any epoch a vertical line drawn down to a sufficient depth from any place in the surface will pass through a mass of matter which has remained the same in amount all through the changes. By the process of expansion the mountains have been forced up, and the mass thus raised above the level has produced a corresponding attenuation of matter below. This attenuation is most likely very trifling, as it probably exists through a great depth. Whether this cause will produce a sufficient amount of compensation can be determined only by submitting it to calculation, which I proceed to do. The Tables thus calculated furnish the following results:-At Kaliana

At Kalianpur

At Damargida

Deflections in meridian, caused by a mass beyond of the Himmalayas and the Mountain region

27".978

12".047

6".790

Ditto, by the same mass distributed through a depth of 100 miles

26.440

12.111

6.855

Ditto

300 miles

21.106

11.678

6.866

Ditto

500 miles

17.066

9.622

6.670

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1000 miles

11.199

7.386

5.220

It will be seen how much the Deflections are reduced by this hypothesis, especially in the case where the attenuation extends through only 100 miles. In fact, in this case the upheaval of the mountains and the consequent attenuation below produce a slight deviation the other way at the two further stations. The success of the hypothesis may therefore, thus far, be considered to be established, although it remains an hypothesis still; and we must always be in uncertainty, not as to its answering this end, but as to its being true in nature. The existence of the mountainmass is a fact indisputable. Not so the compensating cause, which is simply conjectural as to its existence, and altogether uncertain as to its extent, if it exist. We have no certain and independent method of determining this; nor of ascertaining even if the hypothesis be valid, how far down the attenuation extends, or what law it follows. SPECULATIONS ON THE CONSTITUTION OF THE EARTH S CRUST From Proceedings of the Royal Society of London. Vol.Xiii, pp. 253-276, 1864 In fact the density of the crust beneath the mountains must be less than that below the plains, and still less than that below the ocean-bed. If solidification from the fluid state commenced at the surface, the amount of contraction in the solid parts beneath the mountain-region has been less than in the parts beneath the sea. In fact, it is this unequal contraction which appears to have caused the hollows in the external surface which have become the basins into which the waters have flowed to form the ocean. As the waters flowed into the hollow thus created, the pressure on the ocean-bed would be increased, and the crust, so long as it was sufficiently thin to be influenced by hydrostatic principles of floatation, would so adjust itself that the pressure on any coucbe de niveau of the fluid should remain the same. At the time that the crust first became sufficiently thick to resist fracture under the strain produced by a change in its density--that is, when it first ceased to depend for the elevation or depression of its several parts upon the principles of floatation, the total amount of matter In any vertical prism, drawn down into the fluid below to a given distance from the earth's centre, had been the same through all the previous changes. After this, any further contraction or any expansion in the solid crust would not alter the amount of matter in the vertical prism, except where there was an ocean; in the case of greater contraction under an ocean than elsewhere, the ocean would become deeper and the amount of matter greater, and in case of a less contraction or of an expansion of the crust under an ocean, the ocean would become shallower, or the amount of matter In the vertical prism less than before. It is not likely that expansion and contraction in the solid crust would effect the arrangement of matter in any other way. That changes of level do take place, by the rising and sinking of the surface, is a well-established fact, which rather favours these theoretical considerations. But they receive, I think, great support from the other fact, that the large effect of the ocean at Punnoe and of the mountains at Kaliana almost entirely disappear from the resultant defections brought out by the calculations. This theory, that the wide ocean has been collected on parts of the earth's surface where hollows have been made by the contraction and therefore increased density of the crust below, is well illustrated by the existence of a whole hemisphere of water, of which New Zealand is the pole, in stable equilibrium. Were the crust beneath only of the same density as that beneath the surrounding continents, the water would be drawn off by attraction and not allowed to stand in the undisturbed position it now occupies. I have, in what goes before, supposed that, in solidifying, the crust contracts and grows denser, as this appears to be most natural, though, after the solid mass is formed, it may either expand or contract, according as an accession or diminution of heat may take place. If, however, in the process of

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solidifying, the mass becomes lighter, the same conclusion will follow--the mountains being formed by a greater degree of expansion of the crust beneath them, and not by a less contraction, than in the other parts of the crust. It may seem at first difficult to conceive how a crust could be formed at all, if in the act of solidification it becomes heavier than the fluid on which it rests; for the equilibrium of the heavy crust floating on a lighter liquid would be unstable, and the crust would sooner or later be broken through, and would sink down into the fluid, which would overflow it. If, however, this process went on perpetually, the descending crust, which was originally formed by a loss of heat radiated from the surface into space, would reduce the heat of the fluid into which it sank, and after a time a thicker crust would be formed than before, and the difficulty of its being broken through would become greater every time a new one was formed. The least that can be gathered from the deflections of these coast-stations is, that they present no obstacle to the theory so remarkably suggested by the facts brought to light in India, viz. that mountainregions and oceans on a large scale have been produced by the contraction of the materials, as the surface of the earth has passed from a fluid state to a condition of solidity-- the amount of contraction beneath the mountain-region having been less than that beneath the ordinary surface, and still less than that beneath the ocean-bed, by which process the hollows have been produced into which the ocean has flowed. In fact the testimony of these coast-stations is in some degree directly in favour of the theory, as they seem to indicate, by excess of attraction towards the sea, that the contraction of the crust beneath the ocean has gone on increasing in some instances still further since the crust became too thick to be influenced by the principles of floatation, and that an additional flow of water into the increasing hollow has increased the amount of attraction upon stations on its

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