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The Life of Sir William Fairbairn, Bart
Chapter XVII - Mr Hopkins's Earth Experiements


Mr. Fairbairn was engaged for some years on an experimental investigation of great scientific interest, in regard to which, although the results were not published in his own name, he was entitled to much credit. This was an enquiry into certain physical properties of the materials of the earth's crust, undertaken at the instance of the late Mr. William Hopkins, of Cambridge.

Mr. Hopkins was an eminent mathematician and physicist; but he had chiefly made himself celebrated for studies of a novel and peculiar character, involving the application of high mathematical and mechanical principles to the science of geology.

The study of the structure of the earth, although from the time of Hutton and Werner it had occupied the earnest attention of scientific men, had involved only deductions and reasonings of a comparatively simple character. Mr. Hopkins had set himself to investigate, in a much deeper and more comprehensive manner, the nature of the mechanical forces and conditions which had been at work in order to produce the observed appearances; and he had shown that they were as capable of being reduced to rule and law as the phenomena of astronomy, although of course the processes were more obscure and the demonstrations more difficult to obtain. He had published many papers, for example, on the mechanism of glacier motion; on the influence of mechanical forces on the conformation of rocks, their elevation, denudation, &c.; on the theories of volcanoes and earthquakes; on the temperature of the earth; on climate; and many other subjects involving mathematical reasoning.

In the course of investigation it occurred to him that it would be possible to extend mathematical enquiry to the problem of the share that igneous action had had in the formation of the crust of the earth. There had always been a leaning in the minds of cosmical philosophers to the hypothesis that our planet had originally been a globe of matter in a state of fusion, on which a crust had become formed by the gradual cooling of the exterior, leaving the interior in all probability still a molten igneous mass. In support of this hypothesis were brought the well-known phenomena of volcanoes, earthquakes, and hot springs, as well as the established fact of the gradual increase of temperature in descending below the surface of the ground.

In January and March 1839, Mr. Hopkins laid before the Royal Society two papers, i On the Phenomena of Precession and Nutation, assuming the Fluidity of the Interior of the Earth,' in which were some profound speculations- and calculations as to the refrigeration and internal heat of the globe, and their effects on astronomical phenomena. These were followed by another paper in January 1842, 011 the ' Thickness and Constitution of the Earth's Crust>' ill which he pointed out that the problems would be materially affected by the eject of pressure on the temperature of fusion of the different matters forming the earth's crust, which were supposed to have been in a liquid state. He added, 'With the aid of a proper series of experiments on this point, a direct method of arriving at an approximation to the thickness of the crust of the globe, or rather to its least limit, might be easily explained.'

At the meeting of the British Association at Oxford, in June 1847, Mr. Hopkins presented a long and elaborate report 'On the Geological Theories of Elevation and Earthquakes,' in which the problems of the fluidity, solidification, form, and thickness of the earth's crust, were largely treated of, and he again urged (p. 52) the importance of the experimental determination of the influence of pressure in the process of solidification. To show in what a remarkable manner this would bear on the theory of the earth, he said :—

If this influence can be detected at all by experiment, it is probably considerably greater than stated above, as sufficient to justify the conclusion of the earth's solidity to a great depth; and there could, I conceive, in such case be little doubt as to the earth's entire solidity. If, on the contrary, it should appear that pressure exerts no such influence, or that it tends to retard solidification, we must conclude that the interior temperature of the earth cannot be due to its original heat. Whatever, then, may be the results of experiment on this subject, they must probably lead us, should they be sufficiently determinate, to conclusions of the first importance in speculative geology respecting the state of the interior of the globe.

To obtain these data by experiment, it became necessary to consult a mechanical engineer; for the means of producing and resisting the enormous pressures required were far beyond the scope of any ordinary laboratory arrangements. Mr. Fairbairn was known to Mr. Hopkins, not only as a practical engineer, but as a man devoted to science, and Mr. Hopkins, early in 1851, wrote to him as follows :—

Cambridge, April 25, 1851.

My dear Sir,—I am very anxious to get some experiments made for the purpose of determining whether great pressure has any sensible effect on the temperature of fusion of any proposed substance (a metallic substance for instance), or what will probably be found to be the same thing, on the temperature at which any substance, in a previous state of fusion, will become solid.

For this purpose I want the means of producing an enormous pressure on a cylinder of perhaps an inch or rather more in diameter, such as Mr. Hodgkinson produced on similar cylinders in his experiments on the crushing forces for them. My friend, Professor Willis, informs me that the lever which Mr. Hodgkinson made use of for this purpose is still, as he believes, in your hands at Manchester. And ray object in now writing to you is to ask whether you could allow me the use of it, supposing the experiments to be made under my own superintendence, at Manchester. I have no doubt of being able to pio-cure considerable pecuniary1 assistance from the committee for disposing of the annual grant made by (xovernme.nt for scientific purposes, but I should not like to apply to them till I can see my way clearly to the means of performing the experiments effectively. With the exception of the lever, the apparatus required would be of very small magnitude.

If you would have the kindness to give me an answer as soon as may be perfectly convenient to you, I shall feel very much obliged to you, as my application for pecuniary aid must be made during the present year.

Yours very truly,

W. Hopkins.

Io this Mr. Fairbairn replied :—

Manchester, April 29, 1851.

My dear Sir,—I have a lever such as you describe, with ail the requisite apparatus, the whole of which is very much at your service. The strength of the lever is computed to a pressure of about fifty tons, but this may be doubled by an additional apparatus if required.

It will afford me great pleasure to render any assistance towards the completion of your interesting experiments, and I shall be glad if you will inform me when you can visit Manchester for that purpose. In the interval you will perhaps inform me further of the nature of your experiments, and the preparations you will require to render tliem effective and satisfactory.

I am, My dear Sir,

Yours sincerely,

W. Fairbairn.

Mr. Hopkins then applied for the Government grant, and obtained an allowance of 250. 'for investigations on the effect of pressure on the temperature of fusion of certain substances.'

It was stipulated in the terms of the grant that the expenditure of the money should be under the superintendence of a committee, in which the name of Mr. Joule was inserted. This gentleman had, as is well known, identified himself especially with the study of the mechanical action of heat, and he took, thenceforward, an active share in the investigations.

In July Mr. Hopkins gave some further explanations, of which a few extracts may be inserted, as illustrating the nature of some of the difficulties Mr. Fairbairn had subsequently to overcome.

One of the most important, and perhaps difficult points, w ill be the determination of the time when the solidification of the matter experimented 011 (concealed from sight) takes place, and its temperature at that time. It has occurred to me that this may be done by carefully observing the change of temperature, as the matter is allowed to cool from a temperature which maintains it in a state of perfect fluidity. The temperature will decrease pretty uniformly till the solidification begins, but will remain nearly stationary, I conceive, till the solidification is completed, after which it will again regularly decrease. This is the first point I wish to have clearly tested, to ascertain with what degree of exactness the stationary temperature can be determined. If it can be done with accuracy I anticipate no serious difficulty in the experiments. He then went on to describe certain preliminary experiments on easily fusible substances, and added suggestions as to how these might be extended further, recommending Mr. Fairbairn to consult with Mr. Joule on the subject generally.

After some further correspondence, Mr. Hopkins, in the middle of December, visited Manchester, and conferred fully with Mr. Fairbairn and Mr. Joule; the nature of the apparatus was settled, and it was put in hand, Mr. Hopkins paying another visit in January 1852, to examine what was being done.

The construction appears to have occupied some months, for in April, Mr. Fairbairn, in writing an account of what he was doing to his friend Dr. Robinson, of Armagh, remarked that he had some difficulty in f procuring vessels sufficiently strong at an increased temperature, to retain the substances on which the experiments were to be made.'

Constant discussions went on between the parties, and on May 8 Mr. Fairbairn wrote:— it. If, however, you can overcome them, I believe it will be the best arrangement possible. [This was done.]

On June 26 Mr. Fairbairn wrote from London:—

I had no time to write you on the subject of our experiments, which in some respects were highly satisfactory, in others not so. The apparatus is now completely insulated and perfectly tight, but we had some difficulty in reading off the temperature, &c., &c.

The earlier experiments were directed to the behaviour of a substance easily fusible—namely, spermaceti, the object being to make very exact observations on the temperature of fusion; and for a long time the aim was simply to verify by careful observation the suggestions in Mr. Hopkins's letter of July 1851 as to the temperature remaining stationary for a time at the point of solidification. When this was settled the spermaceti was put under heavy pressure, with the object of observing what effect this had in varying the point at which the congelation occurred. The experiments appear to have been conducted by all three of the persons mentioned. Mr. Fairbairn and Mr. Joule were living at Manchester, but Mr. Hopkins paid, as appears from the papers, ' long and frequent visits,' during which he was generally a guest at Mr. Fairbairn's house.

Writing to Baron von Humboldt on August 23, 1852, Mr. Fairbairn said :—

I am at present engaged, in conjunction with Mr. Hopkins, of Cambridge, on a series of experiments to determine the laws of the solidification of bodies under severe pressure. It is a subject in which I am sure you take a deep interest, as it involves a question in physics most difficult to solve ; namely, under what circumstances solidification is effected at great depths under the surface of the earth, andl how nature works under superincumbent pressure. I have a powerful apparatus for the purpose, and can give a pressure of nearly 6,000 lbs. upon the square inch; but we have many difficulties to encounter, and considerable trouble in preventing the radiation of heat from the-' vessel which contains the substances under pressure. I have got the apparatus so far complete as to indicate with certainty the progressive changes of temperature during the progress of crystallisation in passing from the fluid to the solid state; nevertheless, we have still much to do.

In September Mr. Hopkins was again at Manchester, arranging further contrivances for increasing the accuracy of the experiments, which it still took two months to carry out; and on November 23 Mr. Fairbairn wrote to Mr. Hopkins :—

Enclosed you ba^e the results of our experiments on Saturday last, which on examination you will find a nearer approach to the stationary temperature than any of those yet made.

Od a consultation with my friend, Mr. Joule, we have come to the decision to let the matter stand over for a time, till we hear from, or rather till we have the pleasure of seeing you either here or in London. At our next meeting something must be determined upon, and I think it may be desirable to vary the form and character of our proceedings, in order to arrive at conclusions, that will enable you to deduce your laws.

Some further experiments were made, and Mr. Hopkins replied on December 21:—

I thank you for the account of your last experiments. I have no doubt whatever of the temperature of solidification having been obtained very approximately in both of the last experiments under pressure. We are manifestly approximating to unquestionable results.

After this, new apparatus was prepared according to the plans jointly agreed on.

In March 1853, Professor (now Sir) William Thomson, who had been previously consulted on the subject by Mr. Hopkins and Mr. Joule, devised an improvement in the apparatus, so elegant and ingenious as to deserve a brief mention. It had been difficult to find out, while the heat was increasing, the exact point of time at which the fusion took place. As the only feasible mode thought of, the spermaceti was enclosed in a glass tube, through which it could be observed, and the fusion determined by its loss of opacity. Professor Thomson suggested that a small piece of magnetised steel wire should be put into the spermaceti before it was enclosed m the tube, and so placed as to be at the upper part of it when operated on. A small compass was then placed outside the vessel, in such a position that its needle might be acted on by the magnetised wire inside. When fusion took place, the wire, being no longer supported by the solid material, fell to the bottom, and the moment of its doing so was made evident by the motion of the compass outside. This was tried in July, and answered admirably, allowing the containing tube to be made of brass, and so avoiding the danger of the use of glass under such great heat and pressure.

On August 12, 1853, Mr. Joule wrote to Mr. Fairbairn :—

Seiford, August 12, 1853.

My dear Sir,—Our experiment this morning was satisfactory, the needle having fallen at 373, the exact temperature expected by Mr. Hopkins, and which shows that the temperature of fusion rises with the pressure in arithmetic progression. The lead box answered capitally. I have sent a line to Mr. H. to communicate the result.

I am yours truly,

James P. .Jodle.

Wm Fairbairn.

Mr. Hopkins, remarking on this in a letter dated August 22, said :—

I had previously heard from Mr. Joule of his completely successful experiment, for such it has manifestly been. Its agreement with my calculated result is most satisfactory. In this case the law is clear, that the increase of the temperature of the fusion is proportional to the pressure.

With respect to the conductive power of the substances pressed, we had better leave those experiments till my next visit to Manchester, or at least till after the meeting at Hull.

Could you send to Professor Phillips a drawing (it does not signify how rough) of our apparatus? It may be as small, too, as you please. He will get an enlarged drawing of it made for exhibition at Hull [British Association meeting] if I should find it expedient, as I think I shall, to exhibit it at the time of my address.

The subject was brought forward at the. Hull meeting, and the nature of the experiments and apparatus was explained; but no written paper upon it was presented, and therefore no record of it appeared in the published report for the year.

The following letter may be put on record on scientific grounds

Salford, August 24, 18,33.

My dear Sir,—I transmitted to Mr. Hopkins yesterday, an account of some experiments on the physical properties of beeswax, which may perhaps serve to throw some light on the experiments on the alteration of the point of liquefaction by pressure. The results arrived at are as follow :—

The wax softened gradually until the point of absolute fluidity, 54° Cent., was reached. The increase of the specific heat at high temperatures was owing to the heat due to a change of state being mixed therewith.

I find the specific heat of wax in the perfect fluid condition to be .506, and another experiment gave -.501.

Taking the specific heat both at perfect solidity and perfect fluidity to be -5, I find the heat absorbed in changing the state of one grain of wax from perfect solidity to perfect fluidity to be 33-2° Cent, per one grain of water.

Professor Thomson's formula gives, with the above data, 96 division of the thermometer used in the pressure experiments, or 24° Cent, as the theoretical elevation for our greatest pressure, the actual result being 68 divisions, or 17° Cent. The difference is not great under the circumstances.

I am afraid I shall not be able to get to Hull, unless, indeed, I contrive to get off for one day.

Believe me, dear Sir,

Yours very truly,

J. P. Joule.

W. FAIkBAlRN, Esq.

To this time the experiments had only been preliminary —i.e., on substances which had no immediate connection with the enquiry, but were used to obtain general laws. J-iut, emboldened by the success of these trials, Mr. Hopkins now proposed to carry them out on a large scale, to apply them to other substances, and to make use of greater pressures and higher temperatures. He accordingly, on November 7, 1853, gave Mr. Fairbairn suggestions for the necessary alterations and additions to the apparatus, and requested his advice and co-operation thereon. At the beginning of 185 i he again spent some days at Manchester, but the new arrangements took some time. In April thermometers were still in construction (extending to 610° Fahr.), and it was the middle of the year before Mr. Hopkins could get the new experiments fairly in hand.

At this time the second element was brought into the investigation. Mr. Hopkins desired to ascertain the capabilities of the various substances for the conduction of heat, and the influence of compression on this property. Mr. Fairbairn had accordingly to prepare specimens, in the form of small cubes, which were compressed under pressures sometimes reaching to 80,000 lbs. on the square inch.

At the meeting of the British Association at Liverpool, in September 1854, Mr. Hopkins presented to the Physical Section ' An Account of some Experiments on the Eifect of Pressure on the Temperature of Fusion of different Substances.'1 In this he stated ' his great obligations to Mr. Fairbairn for the promptitude with which, iu the first instance, he proffered his assistance and cooperation ; and the manner in which he had since afforded the aid of his great practical knowledge, and the ample means which his establishment afforded for conducting experiments of this nature.'

Mr. Hopkins described the apparatus, and the causes of the failures which had occurred successively, till by degrees apparatus had been devised and constructed which was likely to prove successful. He then gave the results obtained, which showed that the temperature of fusion increased in regular ratio with the pressure. The following were the substances tried, and the melting points (Fahrenheit) at different pressures :—

 

At Atmospheric Pressure

At 7.790 Its. fer ».oi re ill.

Atll,88»lbsi pel fcq-jare in.

 

o

o

0

Spermaceti .

124

140

176-5

Was .

148-5

106-5

176-5

Sulphur

255

275-5

285

Stearine

138

155

165

On October 20, 1854, Mr. Fairbairn wrote to Mr. Hopkins:—

The tubes, cylinder and furnace, and other parts of the apparatus for the compression of substances, are now complete, excepting only the electric wires and the float for measuring the amount of compression. Altogether it is a complete apparatus, and may be used in a laboratory or elsewhere, with tolerable certainty as to the results. It is rather an expensive piece of machinery, something above 20/., but it is very complete, and I make no doubt will effect good and satisfactory results. The only difficulty will be the working of the wires and the float, but that can only be determined by a few experiments.

It was decided to make the first trial of the new machine at Manchester; but Mr. Hopkins could not get there till the Easter vacation of 1855.

On June 16 of that year, Mr. Fairbairn, writing to Sir David Brewster, said :—

I am the more anxious to see you, as I wish to consult you upon the experiments on densities, which I mentioned to you some time since. Some of them are very curious and interesting, and I make no doubt, with the powerful apparatus I have at command, that some new facts are almost sure to present themselves. You shall see them, and at the same time give me your advice, when you come down.

Mr. Hopkins spent some further time at Manchester in the long vacation, and afterwards, on October 8, 1855, he wrote Mr. Fairbairn a letter from which the following are extracts:—

I was prevented writing to you as I had intended, at Glasgow, by the difficulties which continued to beset me in my experiments till the last moment of my being at Manchester. It was only on the last day of my sojourn there that I considered myself to have overcome, as I believe, the last difficulty, and to have obtained results which I could rely upon with the more difficult substances, such as tin and bismuth. With respect to the latter, there is clearly no increase, but probably a decrease of the temperature of fusion resulting from pressure. According to our new theory of heat, this ought to he the case, provided there he no increase of volume while the substance passes from the solid to the fluid state. I had just time before I left to try the experiment, and assure myself that bismuth in a fluid state probably occupies tes volvrae than in its solid state, while such substances as wax, spermaceti, &c., of which the temperature of fusion is so much increased by pressure, occupy much larger space in a fluid than in a solid state. This J» all accordant with theory ; but requires s.till to be worked out with accuracy, which there will be no difficulty now in doing. This, with some other things, must remain for iny Christmas visit.

But this Christmas visit never took place; Mr. Hopkins's health began to fail, and he was obliged to give up any further active labour in the experiments. In August, 1864, he wrote to Mr. Fairbairn as follows :—

During the winter I have repeatedly formed the intention of writing to you. My old enemy, the bronchial cough, attacked me again in the summer of 1863.....I became very feeble and ill. I was sure also that my memory for abstractions, and my power of continued application to that kind of mental effort which, during the latter and best part of my life has afforded me the most intellectually active and agreeable employment, was in danger of being affected.

I understand that there is 100/. with which the Royal Society has accredited me over and above what I have drawn on account of our experiments. I will see, whatever it may be, that it be paid to yourself. I wish you also to keep all the instruments, about which T 1hink I spent myself some 501, or 60?. All this, in addition to what the Royal Society has advanced to you before, will, I fear, be but a very poor compensation for all the expense and trouble you have undertaken for me. My age now numbers too many years to allow me to bark as I have done, and for the last eighteen mouths or more I believe that I have injured my health by too close application. I am not strong enough at present to carry on the experiments, and from what I have stated above you will understand that I am not sanguine of ever being able to do so. They have already enabled me to produce two memoirs, which perhaps will hereafter be found of some value to those interested in the subject; but I fear now that I shall not have sufficient strength to finish the final memoir -which I had contemplated, though I have obtained a certain amount of materials for it. But it would require still much labour to make it complete enough for publication, except as an abstract.

Mr. Hopkins's prognostications were but too well founded. Soon after this, his powerful mind succumbed to the great strain he had put upon it, and he died in October 1866.

In December, 1865, the Eoyal Society wrote to Mr. Fairbairn on the subject of the balance of money ; but he declined to receive anything further.

The results of the whole matter were given, in a scientific form, in a paper read by Mr. Hopkins before the Eoyal Society, June 18, 1857,2 entitled ' Experimental Eesearches on the Conductive Powers of various Substances, with the Application of the Eesults to the Problem of Terrestrial Temperature.'

In the opening paragraph he says :—

I am likewise bound to express in the strongest terms my obligations to my friends Mr. Fairbairn and Mr. Joule. Without the aid of the former of these gentlemen I should have been unable even to commence the series of experiments which I have now nearly concluded; and among the many ways in which this assistance has been so promptly rendered, I may mention his having constantly placed at my disposal the invaluable services of one of his principal workmen, William Ward, without whose untiring activity and mechanical resources I should have utterly despaired of bringing my experiments to any successful issue.

This paper contains an elaborate mathematical discussion of the subject; but a more popular account of the results arrived at may be gathered from a lecture given by Mr. Hopkins before the Royal Institution, on May 13, 1859.

After stating the facts, showing a gradual increase of temperature in descending below the surface of the earth, which (excluding local anomalies) he estimates at 1° Fahr. for every sixty feet depth, he formulates the inference from it as follows :—

If a sphere of very large dimensions, like the earth, were heated, and left to cool in surrounding space, it is shown by accurate investigation, that after a sufficient and very great length of time, the law according to which the temperature would increase in descending beneath the earth's surface, would be that the increase of temperature would be proportional to the increase of depth, which coincides with the observed law. Now, according to this law, the temperature at the depth of sixty or seventy miles would probably be sufficient to reduce to fusion nearly all the materials which constitute the earth's external solid envelope; and hence it had been concluded that the earth probably consists of a central molten mass, or a fluid nucleus, and an external solid shell, of not more than sixty or seventy miles in thickness, or even less.

This has been the ordinary supposition, not only popularly, but also generally among scientific men. But Mr. Hopkins goes on to show that the experiments, of which it has been the object of this chapter to give an account, throw doubt on the conclusiveness of the reasoning on which this opinion is founded.

He points out that an important element of the argument is wanting. It involves the hypothesis that the conductive power of the rocks which constitute the lower portions of the earth's crust is the same as that of the rocks which form its upper portion. For if the conductive power of the lower portions of the earth's solid crust be greater than that of the thin upper portion of it through which man has been able to penetrate, the depth to which we must proceed to arrive at a certain temperature (as that of fusion for the lower rocks) will be proportionately greater.

He then shows that the experiments in question lead to the conclusion that the conductivity of the inferior portions of the earth's solid crust, which are consolidated under very heavy pressure, must be much greater, and may be very much greater, than that of the less consolidated and more superficial sedimentary beds.

Moreover, the temperature of fusion under heavy pressure is another element in the argument. The experiments show that in regard to certain substances that also is much increased by great pressure; and by analogy, it may be concluded that such will, at least in some considerable degree, be the case with the mineral matter of the earth's crust.

Judging by the data obtained, Mr. Hopkins infers that the actual thickness of the solid crust of the earth must probably be at least about 200 miles, and may be considerably greater, even if we admit no other source of terrestrial heat than the central heat here contemplated.

Mr. Hopkins then goes on to explain another kind of argument, of a mathematical nature, bearing on the same subject, derived from the phenomenon of the precession of the equinoxes, which brings out a similar result; and he concludes:—

Thus, both the modes of investigation described lead to like conclusions respecting the least thickness which can he assigned to the solid envelope of our globe. It must be much greater than geologists have frequently imagined it to be.

The following paragraph from the Royal Society paper may be added :—

After the preceding investigations, it appears to me extremely difficult, if not impossible, to avoid the conclusion that a part at least of the heat now existing in the superficial crust of our globe is due to superficial and not to central causes. It should be remarked, however, that the argument thus afforded is not directly against the theory of a primitive heat, but only against the manifestation of the remains of such heat as the sole cause of the existing terrestrial temperature at depths beyond the direct influence of solar heat.

The conclusion that the earth's solid crust is so thin as many geologists have believed it to be, as well as those theories resting on that conclusion, whether of volcanic action or of elevation or depression of the earth's surface, at least in more recent geological times, must be in a great degree invalidated.

Mr. Hopkins stated in this paper his intention of following it with another, in which a further portion of the experiments, not included here, would be given and reasoned on ; but this he had not strength to do.

It will be gathered from the above account what great and difficult questions these experiments were directed to; and although of course it is not intended to claim for Mr. Fairbairn any of the more abstruse portions of the researches, there is no doubt that his excellent practical skTl contributed largely to the success of the investigation.


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