Monday, 11 November 2013

Lecture 4: Ascertaining the Figure of the Earth

Lecture 4


 Ascertaining the Figure of the Earth


            We have now arrived by a gradual progress at the discovery of the relative immobility of the stars. We have seen that they all apparently revolve together round the Earth with a uniform velocity. This was merely an hypothesis assumed for the purpose of connecting together the various facts. It will now become necessary for our astronomer to examine its truth and to endeavour to discover whether it accords with other facts which gradually present themselves.

            It has already been remarked that the rotation of the stars round the Earth afford proof that this body is isolated in space. The investigation of its figure and magnitude will now become not merely an object of curiosity but one of the greatest importance. It will soon be perceived that the appearance of the heavens may be accounted for on two hypotheses. One has already been mentioned, the other is that the Earth itself revolves on its axis. It is evident that either of these will account equally for the phenomena; only if the Earth moves it must turn in a contrary direction to the apparent motion of the stars. Before we survey the proofs by which this latter hypothesis is supported it will be necessary to ascertain in a rough manner the figure of the Earth we inhabit. For this purpose we may have recourse to some very familiar appearances which afford a ready solution of the question.

A person standing on the sea shore and viewing a ship approaching towards him will observe that the masts and rigging become visible a considerable time before the hull of the vessel. If the Earth were a plane surface this could not take place or rather the contrary would be [the] case, for the body of the vessel being so much larger than the slender mast would, as is well-known from optical principles, be visible much sooner. If the vessel be viewed through a telescope it will be very evident that the hull is prevented from being seen by the elevation of the sea between the observer and the object. This observation indicates a roundness in the figure of the Earth, and if it be repeated in different parts of the globe the result will always be the same. Another proof of the rotundity of the Earth is afforded by the practice of engineers in the construction of canals: they are obliged to make an allowance for the Earth's convexity since the true level is not a straight line but a curve which falls below it about 8 inches in every mile. This deviation is nearly the same in every part of the globe.

From these two arguments it clearly follows that the Earth is, if not perfectly spherical, very nearly so. This is still further confirmed by observations on the height of the pole at different places in the same meridian. The farther northward we travel the higher the pole appears to be elevated. For every 70 miles its altitude is increased one degree. Calculation will inform us that this could not take place if the Earth were a flat surface. But its spherical shape accounts for these appearances.

            If Man had confined himself solely to the collection of facts science would have presented a barren detail of arbitrary names; and he would never have attained the knowledge of the great laws of Nature. It is by comparing phenomena together and by endeavouring to trace their mutual connection, by gradually correcting his theory that he has succeeded in discovering these laws, the existence of which may be perceived in their most complicated effects.

            When we reflect on the diurnal motion to which all the heavenly bodies are subject, we are naturally led to infer the existence of some one general cause which moves or which appears to move them round the axis of the Earth. When we consider that these bodies are insulated with respect to each other and are apparently placed at various distances form the Earth the simplicity of the two theories stands strikingly contrasted, and it seems much more natural to admit this latter motion and to regard that of the heavens as only apparent.

Many objections have been raised against the motion of the Earth but these may be by attentive consideration of its attendant circumstances be easily removed. It has been urged that this motion would, if it existed, be perceptible to the senses. But this is not the fact. In a similar case the passengers in the cabin of a vessel sailing on a smooth sea are not aware of the motion of the ship. Every thing near them with which they can compare it moves likewise. If however they look at objects situated of the land from which they are departing these will appear to recede and it is only by a process of reasoning that they discover that it the vessel which moves. That this is the case is obvious from the remarks of children in these circumstances who always believe that the land and the objects with connected with it are in motion. The more evenly the ship moves the stronger is this deception. Is it then suprising that the Earth which meets with no obstacles and no resistance, whose motion is perfectly equal should seem to its inhabitants at rest?

It has been objected that this theory would assign to the inhabitants of the equator an immensely rapid motion but this objection is of vastly greater weight against the other hypothesis. If the Earth revolves on its axis the equatorial parts will move some few hundred miles in an hour. But if the starry heavens move round their axis in the space of 24 hours these luminaries must fly with a velocity of which it is impossible for the human mind to form any adequate conception. It were easy to multiply millions by millions. I might assign to figures a name which should be said to measure this inconceivable velocity. The powers of numbers are unlimited but the finite capacity of Man must forbear to apply his diminutive scale estimate the magnitude of the Earth.

            These, it is true, are but probable reasons for the rotation of the Earth. There are, however others which rest on stronger evidence. Newton has established three laws to which all matter is subject and all succeeding philosophers have acknowledged their truth. From these it follows by a strict train of demonstrative reasoning that two bodies acting on each other will not revolve round the centre of one of them but will move round the common centre of gravity of both. If this be applied to the stars, which are immensely larger than the Earth, it will follow that it is impossible for them to perform their revolutions round this globe. This is a proof derived entirely from theory. It is not on that account the less conclusive. I shall only at present mention one other of a mixed nature. It is found from theoretical calculations that if a sphere covered with any fluid revolve round its axis it will change its spherical shape and become spheroidal or flattened at the poles, and this compression will be greater in proportion as the swiftness of its rotation increases. The globe we inhabit is precisely in this situation. It is nearly a sphere, is partly covered with a fluid and revolves on its axis. It ought therefore from theory to be flattened at the poles, and we shall presently find on investigation that this is the fact. It must be observed in justice to the illustrious Newton that his hypothesis of gravity, from which this follows as a necessary consequence, was published long before those measurements were undertaken which subsequently confirmed the fact.

The first among the moderns who openly maintained the rotation of the Earth, an opinion alike repugnant to the vanity and prejudices of Mankind, was undoubtedly Copernicus. Galileo quickly embraced it and contributed greatly by his writings and discoveries to spread its belief over Europe, but an opposition arose from a quarter from which it was little to be expected. Religion was alarmed and the power of the Inquisition was called in to arrest the progress of reason and of truth. The history of this persecution is too remarkable to be omitted and forms a singular era in the progress of philosophy. It arose from this circumstance. A carmelite monk, Father Toscarini, who was converted by the writings of Galileo to the opinion of Copernicus was the innocent cause of it. In 1615 he published a letter addressed to the general of his order where he examined the sense in which appeared the sense in which several passages of scripture which appeared contrary to Copernicus ought to be understood. And without deviating in the least from that respect which was due to the sacred writings he proposed a method of reconciling them equally wise and ingenious. Some time antecedent to this a Spanish theologian in a commentary on the book of Job, had embraced the system of Copernicus, and had remarked that in matters of philosophical discussion the holy writings always expressed themselves conformably to the language and opinions of the common herd of Mankind. This same doctrine had been taught before him by many learned doctors and commentators much respected in the church. But these authorities were insufficient to preserve Galileo and Toscarini from censure. Their works were presented to the tribunal of cardinals, whose office it was to inspect the different books which were published. They were condemned and the work of Copernicus, which had occasioned them, was also involved in

the condemnation. It was also ordered that in all new editions certain parts should be omitted, particularly those which treated this system as a reality, and also two chapters in which the opinions of those who maintained that the holy writings were to be understood literally was treated with a sort of contempt. Finally this tribunal came to the following resolution: the opinion of those who place the Sun immovable in the centre of the Universe was declared to be heretical, false and absurd, and that which placed the Earth in this centre but gave it rotation on its axis was qualified as being erroneous in point of faith and a dangerous tendency. Galileo's reputation was too great and his discoveries had contributed too much credit the system of Copernicus for him to escape the censure of the Inquisition. No sooner was this new heresy of the Earth's motion brought before the consideration of the tribunal that this great man was cited to appear before it as one of the greatest promoters. He did not think fit to expose himself to a long imprisonment or perhaps to some worse punishment by too obstinate an attachment to his opinions. He therefore disadvowed them and they suffered him to depart about the beginning of 1616.

Galileo, however, meditated a piece of revenge which he put in execution a few years after. He laboured in retirement at his Dialogues on the three celebrated systems of the world which is a complete apology for that of Copernicus considered in a physical point of view. His next difficulty was to get it printed a licence was necessary but how was it to be procured. For this purpose he wrote a preface in which he explained that several foreigners had thought and even published their opinions that the condemnation of the Copernican system was the work of a tribunal which was ignorant of the reasons that might be alleged in its favour and that he wished to show that the Italian doctors were not less conversant with the reasons for and against it than the most learned strangers. By this artful representation he was permitted to print his book: it appeared in 1632 and consists of a dialogue between three interlocutors. The first is Sagredo a Venetian senator, another is himself under the name of Salviati, and the third is Simplicius a peripatetic. Of course the unfortunate Simplicius is only introduced to be beaten and confuted in the clearest manner, although he is furnished by Galileo with the strongest arguments ever adduced by the Aristotelian school.

It was impossible that the object of these dialogues could for a long time be concealed. The success which they had and the ridicule they cast on the adversaries of Copernicus re-awoke the Inquisition. Galileo had had several disputes on hydrostatical questions about comets with a certain Father Grassi, a Jesuit, and it is asserted that the good father contributed not a little to animate the rage of the inquisitors. Doubtless Galileo considered himself secure from the resentment of this tribunal under the protection of the Grand Duke of Tuscany, but this prince either through weakness or from political motives dared not support him: and Galileo cited a second time before the holy office was obliged to make his appearance at Rome. On his arrival he was thrown into prison and detained until his sentence was pronounced. They threatened him with the severest punishments if he did not a second time recant his opinions and if he should ever again presume to teach by word or writing the heretical doctrine of the Earth's motion.

By these means they obtained from him that humiliating recantation which was published all over Europe and which furnished matter of  triumph to the enemies of Copernicus and himself. Part of the abjuration he was compelled to sign runs thus "I Galileo, in the seventieth year of my age brought personally to justice and being on my knees with a sincere heart and faith I abjure and detest the absurdity error and heresy of the motion of the Earth". What a spectacle must this have been. What a contrast between the venerable sage and his intolerable persecutors. A philosopher respectable for his age, illustrious from his attachment to science, whose discoveries had exalted our idea of the Creator from a wider acquaintance with His works, compelled by an ignorant tribunal of bigots to assert his belief in doctrines contradicted by the evidence of his senses.

Posterity has in some measure compensated the misfortunes of Galileo, if posthumous fame can be considered in this light. His name is ever joined with his brilliant discoveries while those of his uncharitable judges loaded with the contempt of the wise and good have faded from the pages of history. This, however, was not sufficient to satisfy the tyranny of the Inquisition; the rest of his sentence was that he should repeat a certain number of prayers daily and be imprisoned for life. This latter part of it was mitigated at the intercession of the Grand Duke of Tuscany and, after the expiration of a twelvemonth, Galileo was liberated, but forbidden to leave the territory of Florence lest he should withdraw himself from the power of the Inquisition. He devoted the remainder of his life to those pursuits which had occupied his youth and terminated his illustrious career in 1642 regretted by all Europe.

If curiosity alone were interested in the measure of the Earth it would be a sufficient reason for undertaking the enquiry. What can be more natural to Man than the desire of becoming acquainted with the magnitude of the globe which has been assigned him for an habitation? But there are other motives which amply justify the anxiety that has been displayed particularly during the two last centuries to arrive at the knowledge of this measure. A slight acquaintance with geography will convince us that it is of the greatest importance and that it would be impossible to estimate the errors which would be committed in the distances of a vast number of places are only determined by astronomical observations, if we did not know what length on the Earth corresponded to a certain number of degrees. The art of navigation relies constantly on this measure. We have already seen that several ineffectual attempts were made for completing this object by the Greeks and Arabs, and that from the numerous errors to which their methods were subject that little reliance can be placed on their results.

The celebrated Fernel, a physician and mathematician of the 16th century, is the first among the moderns who undertook to determine the magnitude of the Earth. He went from Paris to Amiens which is nearly in the same meridian and measured the distance by the number of revolutions made by the wheel of his carriage. He travelled in this manner until the height of the pole was altered one degree and determined the length of a degree on the Earth's surface at 56,746 toises, which does not differ from its real length by one part in eighty. This accuracy would have done much credit to Fernel if it could be ascribed to the method he made use of but it is obvious that a philosopher travelling in a carriage is ill-prepared for operations in which the greatest precision is required and that it was only by a fortunate chance that he approach so near the truth.

Snellius [Snell] is the next who attempted a more accurate measure. He is the author of an excellent method of measuring a large arc of the meridian. As it is the foundation of this operation and is the only method that has been used by astronomers during the last half century some account of it will be necessary.

            If at the two ends of a base line of known length the angles, which some distant object forms with the other end be measured, the distance of the observed object from either end may be found by calculation. If two lines of known length form an angle, and if this angle be observed, the distance between the two ends may be found without the trouble of measuring it. It is on these two principles that the determination of a terrestrial arc depends. Some convenient level spot must be chosen on which a base of considerable length must be measured; from the two ends of this the angles with some distant object must be found. From the principles already mentioned the distances of these objects from each end of the base may be ascertained and consequently their mutual distance. This line whose length is thus determined may be used as a base, and other objects must be chosen whose distances are to be determined in the same manner. These operations are to be continued until we arrive at the end of the arc proposed to be measured. We have thus a series of triangles from which by trigonometrical methods it is easy to determine the distance in a straight line of the first from the last point.

This is but an outline of the plan usually pursued in such undertakings. There are numerous little niceties made use of for avoiding even the minutest cause of error. These however will be better understood in the account of each particular operation. Snellius was the first who made use of this method; he measured a degree in Holland between the towns of Alcmaer and Bergen-op-Zoom. Finding his measurement incorrect he revised it and observed all the angles a second time. From the calculations resulting from this second attempt he deduced the length of a degree which corresponds much more accurately with [the] modern result.

            Shortly after this Richard Norwood, an Englishman, undertook the task of measuring the distance between London and York. The method he pursued was different from Snellius. He measured with a chain the length of the road and by means of the compass he determined how much it deviated from the meridian. When he came to a hill he observed the angle which it formed with the horizon and made allowances for it in his calculations. At each of the two stations which determined the length of his arc he observed the altitude of the pole, and thus determined the number of degrees he had measured.

The next astronomer who undertook the difficult task of assigning the magnitude of the Earth was Riccioli. It would be uninteresting to detail the means he made use of and the numerous errors to which they were subject. It is sufficient to remark that he commenced his undertaking with a conviction that the ancient measures were perfectly accurate and consequently used every means to make his own coincide with them, and to this may be probably be attributed the enormous error which occurs in the value he assigned to the length of a degree.

            The diameter of the Earth is, as it were, the scale by which we measure the distance of the heavenly bodies; it is in some respects the first element of astronomy and its importance naturally led Men to  undertake operations on a large scale to determine it. It must however be confessed that notwithstanding the labours already mentioned it still remained a matter of considerable uncertainty.

The two most accurate measures yet recorded differed from each other more than 7,000 fathoms in the length of a degree. The Academy of Sciences [of France] considering that the art of observing had lately made considerable advances and wishing to determine so important a point selected Abbe Picard for the purpose  of measuring a new degree in the neighbourhood of Paris. In this new attempt the greatest pains were taken to ensure accuracy, but in these delicate operations there are so many precautions to be taken the greater number of which are only suggested by time and by the errors of others that it is no reflection on the accuracy of Picard that the most scrupulous examination of his observations has only caused an alteration of about 30 toise in the result of his measure.

            About this time a voyage was undertaken by several French astronomers for the purpose of observing some important points. It is only mentioned at present from the discovery to which it gave rise. It was observed by Richer that a pendulum clock, which he had brought from Paris where it had kept regular time, on being set in motion at Cayenne [French Guiana], which is situated near the equator, lost nearly two minutes and a half during 24 hours. This obliged him to shorten the pendulum [by] about ?th [of an] inch, the quantity by which it had been shortened while he was at Cayenne.

This singular fact excited great astonishment. It was impossible to explain it by the effect of heat on the pendulum for it [also] took place on the summits of the Andes, where the temperature of the air is the same as in Europe, or even colder. The first who gave a satisfactory explanation of it was Newton. He attributed it to the spheroid figure of the Earth and proved that its two diameters were not equal. If the Earth is flattened at the poles the length of a degree at the equator will be shorter than that of one at the pole. The results of the degrees already measured could not be reconciled to the hypothesis of the Earth being flattened at the poles, but it must be confessed that they were very unfavourably situated for determining the question. The learned world was at this time much divided. Newton and all the philosophers who relied on physical enquiries maintained that the Earth was flattened at the poles, while all the followers of Descartes and a multitude of foreigners assigned to it an elongated figure.

It is a very singular circumstance that the first operation undertaken with a view to determine this point should have been decidedly unfavourable to the Newtonians. From the results of 8 or 9 degrees measured by Cassini in France it appeared that they increased as they approached the equator. The only plan which now remained was to decide the question by the measurement of two degrees, one near the pole and the other at the equator. For this purpose two expeditions were undertaken which do infinite credit to the country which gave birth to them. Maupertuis, the President of the French Academy, accompanied by Clairaut , Camms and Lemonnier undertook a voyage to the polar circle. The spot they selected for their operations was situated near the town of Torneo in Lapland.

            It is impossible sufficiently to admire the zeal and ardour with which these philosophers surmounted the greatest difficulties. They traversed the thick forests of Lapland which had never yet been penetrated. They climbed the steepest mountains and remained whole weeks on their summits exposed to all the inclemencies of the weather. By such means, after nearly 3 months labour, they were in possession of an excellent series of triangles, which extended from one end of the arc to the other. This however was not the only labour. A base must be measured, but the circumstances of the country which were adverse to every other part of the operations were favourable to this. A line of 7,500 fathoms in length was measured on the ice of the river which flows near Torneo and by a second measurement there only appeared the slight difference of four inches.

The expedition to the equator was undertaken by Godin, Bouguer and La Condamine. They assembled at Quito in South America and were joined by two Spanish astronomers appointed to assist them. They commenced their undertaking by measuring a base, but in a country covered with mountains it was difficult to discover a piece of ground sufficiently flat for their purpose. They were fortunate in finding a spot of ground of sufficient length near Quito. This they measured twice and the difference of the two measures only amounted to 2 inches. But the difficulties they met with in the determination of the base were but a slight prelude to those which they afterwards experienced. If we imagine a lofty chain of mountains whose summits though situated in  the torrid zone are covered with perpetual snow and whose less elevated parts are continually involved in rain and fogs we shall have a faint idea of the places in which these philosophers were obliged to fix their stations. Here they were compelled to stay sometimes for whole months waiting for some fortunate interval of fine weather in order to observe their signals placed on other distant mountains.

These local inconveniences prolonged their stay during two years. The work was at last completed in 1739 and fixed the length of 3 degrees. Such was the termination of one of the grandest expeditions ever undertaken for the purposes of science. Our philosophers now separated each to return to Europe by a different route. The adventures they met with are rather curious. Bouguer was the first who arrived in France. He pursued the shortest course and crossed the Atlantic. La Condamine possessed of the greatest intrepidity and an insatiable curiosity boldly traversed the vast continent of South America and descended the River Amazon. Of this interesting voyage he published a separate account which by the elegance of its style and the animated picture which it presents of the dangers he escaped and of the manners and customs of the countries he traversed, excites all the interest of fiction while it possesses the higher recommendation of truth and information.

The two Spanish officers returned round Cape Horn, the southernmost point of America. They arrived in Spain in 1746, the first without any accident, the second was captured by an English cruiser. He however pays a grateful tribute to the hospitality he experienced in this country. His books and papers were immediately restored [to him] and he was elected a member of the Royal Society.

            Godin another of the party was detained in Peru by various circumstances until 1748 and witnessed the horrible catastrophe which destroyed the towns of Gallao and Lima. A brother of Godin, who had accompanied him as far as Paraguay, remained there to be joined by his wife and family whom he had desired to meet him by descending the River Amazon. They had the misfortune to be lost in the vast woods of the interior of America. This circumstance gave rise to a pathetic letter of La Condamine in which he relates the fate of the various astronomers who had participated in the measure of the Earth. He there details the sufferings she experienced in wandering those vast deserts after seeing seven of her companions perish until by accident she regained the bank of the river.

The surgeon who accompanied the expedition was assassinated at a bull feast at Cuenca. La Condamine travelled 500 leagues to obtain the punishment of the assassin, who was transported to the island of Chiloe, but soon after obtained his liberty.

            The result of the operations we have detailed left no doubt respecting the figure of the Earth. It was decided that the degrees diminish as we approach the equator and consequently the Earth is a flattened spheroid.


 Bouguer (1749). La Figure de la Terre: déterminée par les observations de messieurs Bouguer, & de La Condamine . chez Charles-Antoine Jombert.