Jerome Cardan Part 5

[86] November 1536.

[87] Ferrari was one of Cardan's most distinguished pupils. "Ludovicus Ferrarius Bononiensis qui Mathematicas et Mediolani et in patria sua professus est, et singularis in illis eruditionis."--_De Vita Propria_, ch. x.x.xv. p. 111. There is a short memoir of Ferrari in _Opera_, tom. ix.

[88] _Opera_, tom. i. p. 66.

[89] Fra Luca's book, _Summa de Arithmetica Geometria Proportioni e Proportionalita_, extends as far as the solution of quadratic equations, of which only the positive roots were used. At this time letters were rarely used to express known quant.i.ties.

[90] The early writers on Algebra used _numerus_ for the absolute or known term, _res_ or _cosa_ for the first power, _quadratum_ for the second, and _cubus_ for the third. The signs + and - first appear in the work of Stifelius, a German writer, who published a book of Arithmetic in 1544.

Robert Recorde in his _Whetstone of Wit_ seems first to have used the sign of equality =. Vieta in France first applied letters as general symbols of quant.i.ty, though the earlier algebraists used them occasionally, chiefly as abbreviations. Aristotle also used them in the _Physics.--Libri. Hist.

des Sciences Mathematiques_. i. 104.

[91] _Opera_, tom. iv. p. 222.

[92] In the conclusion of the Treatise on Arithmetic, Cardan points out certain errors in the work of Fra Luca. Fra Luca was a pupil of Piero della Francesca, who was highly skilled in Geometry, and who, according to Vasari, first applied perspective to the drawing of the human form.

[93] Tartaglia, _i.e._ the stutterer.

[94] Papadopoli, _Hist. Gymn. Pata._ (Ven. 1724).

[95] "Balbisonem post relatam jurisprudentiae lauream redeuntem Brixiam Nicolaus secutus est, caepitque ex Mathematicis gloriam sibi ac divitias parare, aeque paupertatis impatiens, ac fortunae melioris cupidus, quam dum Brixiae tuetur, h.o.m.o morosae, et inurbanae rusticitatis prope omnium civium odia sibi conciliavit. Quamobrem alibi vivere coactus, varias Italiae urbes incoluit, ac Ferrariae, Parmae, Mediolani, Romae, Genuae, arithmeticam, geometricam, ceteraque quae ad Mathesim pertinent, docuit; depugnavitque scriptis accerrimis c.u.m Cardano ac sibi ex illis quaesivit nomen et gloriam. Tandem domicilium posuit Venetiis, ubi non a Senatoribus modo, ut mos Venetus habet eruditorum hominum studiosissimus, maximi habitus est, at etiam a variis Magnatum ac Principum legatis praemiis ac muneribus auctus sortem, quam tamdiu expetierat visus sibi est concilia.s.se. Ergo ratus se majorem, quam ut a civibus suis contemneretur, Brixiam rediit, ubi spe privati stipendii Euclidis elementa explanare coepit; sed quae illum olim a civitate sua austeritas, rustica, acerba, morosa, depulerat, eadem illum in eum apud omnes contemptum, et odium iterum dejicit, ut exinde horrendus ac detestabilis omnibus fugere, atque iterum Venetias confugere compulsus fuerit. Ibi persenex decessit."--Papadopoli, _Hist.

Gymn. Pata.,_ ii. p. 210.

[96] This work is the chief authority for the facts which follow. The edition referred to is that of Venice, 1546. There is also a full account of the same in Cossali, _Origine dell' Algebra_ (Parma, 1799). vol. ii. p.

96.

[97] _Quesiti et Inventioni_, p. 115.

[98] Cardan writes: "Vi supplico per l'amor che mi portati, et per l'amicitia ch'e tra noi, che spero durara fin che viveremo, che mi mandati sciolta questa questione. 1 cubo piu 3. cose egual a 10." Cardan had mistaken (1/3 _b_)^3 for 1/3 _b_^3, or the cube of 1/3 of the co-efficient for 1/3 of the cube of the co-efficient.--_Quesiti et Inventioni_ p. 124.

[99] _Quesiti et Inventioni_, p. 125.

[100] "Non ha datta fora tal opera come cose composto da sua testa ma come cose ellette raccolte e copiate de diverse libri a penna."--_Quesiti et Inventioni_, p. 127.

[101] Cardan repeats the remark in the first chapter of the _Liber Artis Magnae_ (_Opera_, tom. iv. p. 222). "Deceptus enim ego verbis Lucae Paccioli, qui ultra sua capitula, generale ullum aliud esse posse negat (quanquam tot jam antea rebus a me inventis, sub manibus esset) desperabam tamen invenire, quod quaerere non audebam." Perhaps he wrote them down as an apology or a defence against the storm which he antic.i.p.ated as soon as Tartaglia should have seen the new Algebra.

[102] Subsequently Tartaglia wrote very bitterly against Cardan, as the latter mentions in _De Libris Propriis_. "Nam etsi Nicolaus Tartalea libris materna lingua editis nos calumniatur, impudentiae tamen ac stult.i.tiae suae non aliud testimonium quaeras, quam ipsos illius libros, in quibus nominatim splendidiorem unumquemque e civibus suis proscindit: ade ut nemo dubitet insanisse hominem aliquo infortunio."--_Opera_, tom. i. p.

80.

[103] _Quesiti et Inventioni_, p. 129.

[104] Montucla, _Histoire de Math._ i. 596, gives a full account of Ferrari's process.

[105] In the _De Vita Propria_, Cardan dismisses the matter briefly: "Ex hoc ad artem magnam, quam collegi, dum Jo. Colla certaret n.o.bisc.u.m, et Tartalea, a quo primum acceperam capitulum, qui maluit aemulum habere, et superiorem, quam amic.u.m et beneficio devinctum, c.u.m alterius fuisset inventum."--ch. xlv. p. 175.

[106] Prefixed to the _De Vita Propria_.

[107] In a question of broken faith, Cardan laid himself open especially to attack by reason of his constant self-glorification in the matter of veracity.

[108] Leonardo knew that quadratic equations might have two positive roots, and Cardan pursued this farther by the discovery that they might also have negative roots.

[109] "Caput xxviii. De capitulo generali cubi et rerum aequalium numero, Magistri Nicolai Tartagliae, Brixiensis--Hoc capitulum habui a prefato viro ante considerationem demonstrationum secundi libri super Euclidem, et aequatio haec cadit in [Symbol: Rx]. cu v binomii ex genere binomii secundi et qunti [m~]. [Symbol: Rx]. cuba universali recisi ejusdem binomii."--_Opera_, tom. iv. p. 341.

[110] Montucla, who as a historian of Mathematics has a strong bias against Cardan, gives him credit for the discovery of the _fictae radices_, but on the other hand he attributes to Vieta Cardan's discovery of the method of changing a complete cubic equation into one wanting the second term.--Ed. 1729, p. 595.

[111] _Opera_, tom. i. p. 66.

CHAPTER VI

IT has been noted that Cardan quitted Pavia at the end of 1544 on account of the bankruptcy of the University, and that in 1546 a generous offer was made to him on condition of his entering the service of Pope Paul III.; an offer which after some hesitation he determined to refuse. In the autumn of this same year he resumed his teaching at Pavia, a fact which sanctions the a.s.sumption that this luckless seat of learning must have been once more in funds. In the year following, in 1547, there came to him another offer of employment accompanied by terms still more munificent than the Pope's, conveyed through Vesalius[112] and the amba.s.sador of the King of Denmark. "The emolument was to be a salary of three hundred gold crowns per annum of the Hungarian currency, and in addition to these six hundred more to be paid out of the tax on skins of price. This last-named money differed in value by about an eighth from the royal coinage, and would be somewhat slower in coming in. Also the security for its payment was not so solid, and would in a measure be subject to risk. To this was farther added maintenance for myself and five servants and three horses. This offer I did not accept because the country was very cold and damp, and the people well-nigh barbarians; moreover the rites and doctrines of religion were quite foreign to those of the Roman Church."[113]

Cardan was now forty-six years of age, a mathematician of European fame, and the holder of an honourable post at an ancient university, which he might have exchanged for other employment quite as dignified and far more lucrative. In dealing with a character as bizarre as his, it would be as a rule unprofitable to search deeply for motives of action, but in this instance it is no difficult matter to detect upon the surface several causes which may have swayed him in this decision to remain at Pavia.

However firmly he may have set himself to win fame as a physician, he was in no way disposed to put aside those mathematical studies in which he had already made so distinguished a name, nor to abandon his astrology and chiromancy and discursive reading of all kinds. At Pavia he would find leisure for all these, and would in addition be able to make good any arrears of medical and magical knowledge into which he might have fallen during the years so largely devoted to the production of the _Book of the Great Art_. Moreover, the time in question was one of the prime epochs in the history of the healing art. A new light had just arisen in Vesalius, who had recently published his book, _Corporis Humani Fabrica_, and was lecturing in divers universities on the new method of Anatomy, the actual dissection of the human body. He went to Pavia in the course of his travels and left traces of his visit in the form of a revived and re-organized school of Anatomy. This fact alone would have been a powerful attraction to Cardan, ever greedy as he was of new knowledge, but there was another reason which probably swayed him more strongly still, to wit, the care of his eldest son's education and training. Gian Battista Cardano was now in his fourteenth year, and, according to the usages of the time, old enough to make a beginning of his training in Medicine, the profession he was destined to follow. It is not recorded whether or not he chose this calling for himself; but, taking into account the deep and tender affection Jerome always manifested towards his eldest son, it is not likely that undue compulsion was used in the matter. The youth, according to his father's description, strongly favoured in person his grandfather Fazio.[114] He had come into the world at a time when his parents' fortunes were at their lowest ebb, during those terrible months spent at Gallarate,[115] and in his adolescence he bore divers physical evidences of the ill nurture--it would be unjust to call it neglect--which he had received. At one time he was indeed put in charge of a good nurse, but he had to be withdrawn from her care almost immediately through her husband's jealousy, and he was next sent to a slattern, who fed him with old milk, and not enough of that; or more often with chewed bread. His body was swollen and unhealthy, he suffered greatly from an attack of fever, which ultimately left him deaf in one ear. He gave early evidence of a fine taste in music, an inheritance from his father, and was, according to Cardan's showing, upright and honest in his carriage, gifted with talents which must, under happier circ.u.mstances, have placed him in the first rank of men of learning, and in every respect a youth of the fairest promise. The father records that he himself, though well furnished by experience in the art of medicine, was now and again worsted by his son in disputation, and alludes in words of pathetic regret to divers problems, too deep for his own powers of solution, which Gian Battista would a.s.suredly have mastered in the course of time. He does not forget to notice certain of the young man's failings; for he remarks that he was temperate of speech, except when he was angered, and then he would pour forth such a torrent of words that he scarce seemed in his right mind.

Cardan professes to have discerned a cause for these failings, and the calamities flowing therefrom, in the fact that Gian Battista had the third and fourth toes of his right foot united by a membrane; he declares that, if he had known of this in time, he would have counteracted the evil by dividing the toes.[116] Gian Battista eventually gained the _baccalaureat_ in his twenty-second year, and two years after became a member of the College.

The life which Cardan planned to lead at Pavia was unquestionably a full one. He had several young men under his care as pupils besides his son, amongst them being a kinsman of his, Gasparo Cardano, a youth of sterling virtue and a useful coadjutor in times to come. He was at this time engaged on his most important works in Medicine and Physical Science. He worked hard at his profession, practising occasionally and reading voraciously all books bearing on his studies. He wrote and published several small works during the four years--from 1547 to 1551--of his Professorship at Pavia; the most noteworthy of which were the Book of Precepts for the guidance of his children, and some Treatises on the Preservation of Health. He also wrote a book on Physiognomy, or as he called it Metoposcopy, an abstract of which appears as a chapter in _De Utilitate_ (lib. iii. c. 10), but the major part of his time must have been consumed in collecting and reducing to form the huge ma.s.s of facts out of which his two great works, _De Subtilitate_ and _De Varietate Rerum_, were built up.

A mere abstract of the contents of these wonderful books would fill many pages, and prove as uninteresting and unsuggestive as abstracts must always be; and a commentary upon the same, honestly executed, would make a heavy draft on the working life-time of an industrious student. In reference to each book the author has left a statement of the reasons which impelled him to undertake his task, the most cogent of which were certain dreams.[117] Soon after he had begun to write the _De Astrorum Judiciis_ he dreamt one night that his soul, freed from his body, was ranging the vault of heaven near to the moon, and the soul of his father was there likewise. But he could not see this spirit, which spake to him saying, "Behold, I am given to you as a comrade." The spirit of the father then went on to tell the son how, after various stages of probation, he would attain the highest heaven, and in the terms of this discourse Cardan professed to discern the scheme of his more important works.

The _De Subtilitate_ represents Cardan's original conception of a treatise dealing with the Cosmos, but during the course of its preparation a vast ma.s.s of subsidiary and contingent knowledge acc.u.mulated in his note-books, and rendered necessary the publication of a supplementary work, the _De Varietate_,[118] which, by the time it was finished, had grown to a bulk exceeding that of the original treatise. The seminal ideas which germinated and produced such a vast harvest of printed words, were substantially the same which had possessed the brains of Paracelsus and Agrippa. Cardan postulates in the beginning a certain sympathy between the celestial bodies and our own, not merely general, but distributive, the sun being in harmony with the heart, and the moon with the animal humours.

He considers that all organized bodies are animated, so that what we call the Spirit of Nature is present everywhere. Beyond this everything is ruled by the properties of numbers.[119] Heat and moisture are the only real qualities in Nature, the first being the formal, and the second the material, cause of all things; these conceptions he gleaned probably from some criticisms of Aristotle on the archaic doctrines of Herac.l.i.tus and Thales as to the origin of the universe.

It is no marvel that a writer, gifted with so bizarre and imaginative a temper, so restless and greedy of knowledge, sitting down to work with such a projection before him, should have produced the richest, and at the same time the most chaotic, collection of the facts of Natural Philosophy that had yet issued from the press. The erudition and the industry displayed in the gathering together of these vast ma.s.ses of information, and in their verification by experiment, are indeed amazing; and, in turning over his pages, it is impossible to stifle regret that Cardan's confused method and incoherent system should have rendered his work comparatively useless for the spread of true knowledge, and qualified it only for a place among the _labores ineptiarum_.

Cardan begins with a definition of Subtilty. "By subtilty I mean a certain faculty of the mind by which certain phenomena, discernible by the senses and comprehensible by the intellect, may be understood, albeit with difficulty." Subtilty, as he understood it, possesses a threefold character: substance, accident, and manifestation. With regard to the senses he admits but four to the first rank: touch, sight, smell, and hearing; the claims of taste, he affirms, are open to contention. He then pa.s.ses on to discuss the properties of matter: fire, moisture, cold, dryness, and vacuum. The last-named furnishes him with a text for a discourse on a wonderful lamp which he invented by thinking out the principle of the vacuum. This digression on the very threshold of the work is a sample of what the reader may expect to encounter all through the twenty-one books of the _De Subtilitate_ and the seventeen of the _De Varietate_. Regardless of the claims of continuity, he jumps from principle to practice without the slightest warning. Intermingled with dissertations on abstract causes and the hidden forces of Nature are to be found descriptions of taps and pumps and syphons, and of the water-screw of Archimedes, the re-invention of which caused poor Galeazzo Rosso, Fazio's blacksmith friend, to go mad for joy. There are diagrams of furnaces, of machinery for raising sunken ships, and of the common steelyard. Cardan finds no problem of the universe too recondite to essay, and in like manner he sets down information as to the most trivial details of every-day economy: how to kill mice, why dogs bay the moon, how to make vinegar, why a donkey is stupid, why flint and steel produce fire, how to make the hands white, how to tell good mushrooms from bad, and how to mark household linen. He treats of the elements, Earth, Air, and Water, excluding Fire, because it produces nothing material; of the heavens and light: metals, stones, plants, and animals. Marvellous stories abound, and the most whimsical theories are advanced to account for the working of Nature. He tells how he once saw a man from Porto Maurizio, pallid, with little hair on his face, and fat in person, who had in his b.r.e.a.s.t.s milk enough to suckle a child. He was a soldier, and this strange property caused him no slight inconvenience. Sages, he affirms, on account of their studious lives, are little p.r.o.ne to s.e.xual pa.s.sion. With them the vital power is carried from the heart to a region remote from the genitals, _i.e._ to the brain, and for this reason such men as a rule beget children weak and unlike themselves. Diet has a valid effect on character, as the Germans, who subsist chiefly on the milk of wild cows, are fierce and bold and brutal. Again, the Corsicans, who eat young dogs, wild as well as domestic, are notably fierce, cruel, treacherous, fearless, nimble, and strong, following thus the nature of dogs. He argues at length to show that man is neither an animal nor a plant, but something between the two.

A man is no more an animal than an animal is a plant. The animal has the _anima sensitiva_ which the plant lacks, and man transcends the animal through the gift of the _anima intellectiva_, which, as Aristotle testifies, differs from the _sensitiva_. Some maintain that man and the animals must be alike in nature and spirit, because it is possible for man to catch certain diseases from animals. But animals take certain properties from plants, and no one thinks of calling an animal a plant.

Man's nature is threefold: the Divine, which neither deceives nor is deceived; the Human, which deceives, but is not deceived; the Brutish, which does not deceive, but is deceived. Dissertations on the various sciences, the senses, the soul and intellect, things marvellous, demons and angels, occupy the rest of the chapters of the _De Subtilitate_.

At the end of the last book of _De Varietate_, Cardan gives a table showing the books of the two works arranged in parallel columns so as to exhibit the relation they bear to each other. A comparison of the treatment accorded to any particular branch of Natural Philosophy in the _De Subtilitate_ with that given in the _De Varietate_, will show that in the last-named work Cardan used his most discursive and anecdotic method.

Mechanics are chiefly dealt with in the _De Subtilitate_, and all through this treatise he set himself to observe in a certain degree the laws of proportion, and kept more or less to the point with which he was dealing, a system of treatment which left him with a vast heap of materials on his hands, even after he had built up the heavy tome of the _De Subtilitate_.

Perhaps when he began his work upon the fresh volume he found this _ingens acervus_ too intractable and heterogeneous to be susceptible of symmetrical arrangement, and was forced to let it remain in confusion. Few men would sit down with a light heart to frame a well-ordered treatise out of the _debris_ of a heap of note-books, and it would be unjust to censure Cardan's literary performance because he failed in this task.

Probably no other man living in his day would have achieved a better result. It is certain that he expended a vast amount of labour in attempting to reduce his collected ma.s.s of facts even to the imperfect form it wears in the _De Varietate Rerum_.[120]

Considering that this book covers to a great extent the same ground as its predecessor, Cardan must be credited with considerable ingenuity of treatment in presenting his supplementary work without an undue amount of repet.i.tion. In the _De Varietate_ he always contrives to bring forward some fresh fact or fancy to ill.u.s.trate whatever section of the universe he may have under treatment, even though this section may have been already dealt with in the _De Subtilitate_. The characteristic most strongly marked in the later book is the increased eagerness with which he plunges into the investigation of certain forces, which he professes to appreciate as lying beyond Nature, and incapable of scientific verification in the modern sense, and the fabled manifestations of the same. He loses no opportunity of trying to peer behind the curtain, and of seeking--honestly enough--to formulate those various pseudo-sciences, politely called occult, which have now fallen into ridicule and disrepute with all except the charlatan and the dupe, who are always with us. Where he occupies in the _De Subtilitate_ one page in considering those things which lie outside Nature--demons, ghosts, incantations, succubi, incubi, divinations, and such like--he spends ten in the _De Varietate_ over kindred subjects. There is a wonderful story[121] told by his father of a ghost or demon which he saw in his youth while he was a scholar in the house of Giovanni Resta at Pavia. He searches the pages of Hector Boethius, Nicolaus Donis, Rugerus, Petrus Toletus, Leo Africa.n.u.s, and other chroniclers of the marvellous, for tales of witchcraft, prodigies, and monstrous men and beasts, and devotes a whole chapter to chiromancy,[122] a subject with which he had occupied his plenteous leisure when he was waiting for patients at Sacco. The diagram of the human hand given by him does not differ greatly from that of the contemporary hand-books of the "Art," and the leading lines are just the same. The heavenly bodies are as potent here as in Horoscopy. The thumb is given to Mars, the index finger to Jupiter, the middle finger to Saturn, the ring finger to the Sun, and the little finger to Venus. Each finger-joint has its name, the lowest being called the procondyle, the middle the condyle, and the upper the metacondyle. He pa.s.ses briefly over as lines of little import, the _via combusta_ and the _Cingulus Orionis_, but lays some stress on the character of the nails and the knitting together of the hand, declaring that hands which can be bent easily backward denote effeminacy or a rapacious spirit. He teaches that lines are most abundant in the hands of children, on account of the tenderness of the skin, and of old men on account of the dryness, a statement which might suggest the theory that lines come into existence through the opening and closing of the hand. But the adoption of this view would have proved more disastrous to chiromancy than ridicule or serious criticism; so he straightway finds an explanation for this fact in the postulate that lines in young people's hands speak as to the future, and in old men's as to the past. Later he goes on to affirm that lines in the hand cannot be treated as mere wrinkles arising from the folding of the skin, unless we are prepared to admit that wrinkled people are more humorous than others, alluding no doubt to the lines in the face caused by laughter, a proposition which does not seem altogether convincing or consequential, unless we also postulate that all humorous men laugh at every joke. There is a line in the hand which he calls the _linea jecoraria_, and the triangle formed by this and the _linea vitae_ and the _linea cerebri_, rules the disposition of the subject, due consideration being given to the acuteness or obtuseness of the angles of this triangle. Cardan seems to have based his treatise on one written by a certain Ruffus Ephesius, and it is without doubt one of the dullest portions of his work.[123]

It is almost certain that Cardan purposed to let the _De Varietate_ come forth from the press immediately after the _De Subtilitate_, but before the MS. was ready, it came to pa.s.s that he was called to make that memorable journey to Scotland in order to find a remedy for the ailment which was troubling the Archbishop of St. Andrews, a journey which has given to Britons a special interest in his life and work. In dealing with the Cosmos in the _De Subtilitate_ he had indeed made brief mention of Britain; but, writing then, he had no personal relations with either England or Scotland, or the people thereof; and, but for his subsequent visit, he would not have been able to set down in the pages of his second book so many interesting and suggestive notes of what he had seen and heard, and his ideas of the politics of the time. Again, if he had not been urged by the desire all men feel to read what others may have to say about places they have visited, it is not likely that he would have searched the volumes of Hector Boethius and other early writers for legends and stories of our island. Writing of Britain[124] in the _De Subtilitate_ he had praised its delicate wool and its freedom from poisonous beasts: a land where the wolf had been exterminated, and where the sheep might roam unvexed by any beast more formidable than the fox.

The inordinate breeding of rooks seems even in those days[125] to have led to a war of extermination against them, carried on upon a system akin to that which was waged against the sparrow in the memory of men yet living.

But besides this one, he records, in the _De Subtilitate_, few facts concerning Britain. He quotes the instances of Duns Scotus and Suisset in support of the view that the barbarians are equal to the Italians in intellect,[126] and he likewise notices the use of a fertilizing earth--presumably marl--in agriculture,[127] and the longevity of the people, some of whom have reached their hundred and twentieth year.[128]

The first notice of us in the _De Varietate_ is in praise of our forestry, forasmuch as he remarked that the plane tree, which is almost unknown in Italy through neglect, thrives well in Scotland, he himself having seen specimens over thirty feet high growing in the garden of the Augustinian convent near Edinburgh. The lack of fruit in England he attributes rather to the violence of the wind than to the cold; but, in spite of our cruel skies, he was able to eat ripe plums in September, in a district close to the Scottish border. He bewails the absence of olives and nuts, and recommends the erection of garden-walls in order to help on the cultivation of the more delicate fruits.

In a conversation with the Archbishop of St. Andrews he was told that the King of Scots ruled over one hundred and sixty-one islands, that the people of the Shetland Islands lived for the most part on fish prepared by freezing or sun-drying or fire, and had no other wealth than the skins of beasts. Cardan pictures the Shetlanders of that time as leading an ideal life, unvexed by discord, war, or ambition, labouring in the summer for the needs of winter, worshipping Christ, visited only once a year by a priest from Orkney, who came over to baptize the children born within the last twelve months, and was remunerated by a tenth of the catch of fish.

He speaks of the men of Orkney as a very lively, robust, and open-hearted crew, furnished with heads strong enough to defy drunkenness, even after swallowing draughts of the most potent wine. The land swarms with birds, and the sheep bring forth two or even three lambs at a time. The horses are a mean breed, and resemble a.s.ses both as to their size and their patience. Some one told him of a fish, often seen round about the islands, as big or even bigger than a horse, with a hide of marvellous toughness, and useful for the abundance of oil yielded by its carcase. He attributes the bodily strength of these northerners to the absence of four deleterious influences--drunkenness, care, heat, and dry air. Cardan seems to have been astonished at the wealth of precious stones he found in Scotland--dark blue stones, diamonds, and carbuncles[129]--"maxime juxta academiam Glaguensis oppidi in Gludisdalia regione," and he casts about to explain how it is that England produces nothing of the kind, but only silver and lead. He solves the question by laying down an axiom that the harder the environment, the harder the stone produced. The mountains of Scotland are both higher and presumably harder than those of England, hence the carbuncles.

He was evidently fascinated with the wealth of local legend and story which haunted the misty regions he visited. In dealing with demons and familiar spirits he cites the authority of Merlin, "whose fame is still great in England," and tells a story of a young woman living in the country of Mar.[130] This damsel was of n.o.ble family and very fair in person, but she displayed a great unwillingness to enter the marriage state. One day it was discovered that she was pregnant, and when the parents went to make inquisition for the seducer, the girl confessed that, both by day and night, a young man of surpa.s.sing beauty used to come and lie with her. Who he was and whence he came she knew not. They, though they gave little credit to her words, were informed by her handmaid, some three days afterwards, that the young man was once more with her; wherefore, having broken open the door, they entered, bearing lights and torches, and beheld, lying in their daughter's arms, a monster, fearsome and dreadful beyond human belief. All the neighbours ran quickly to behold the grisly sight, and amongst them a good priest, well acquainted with pagan rites. When he had come anear, and had said some verses of the Gospel of Saint John, the fiend vanished with a terrible noise, bearing away the roof of the chamber, and leaving the bed in flames. In three days' time the girl gave birth to a monstrous child, more hideous than anything heretofore seen in Scotland, wherefore the nurses, to keep off disgrace from the family, caused it to be burnt on a pile of wood. There is another story of a youth living about fourteen miles from Aberdeen, who was visited every night by a demon lady of wonderful loveliness, though he bolted and locked his chamber-door; but by fasting and praying and keeping his thoughts fixed on holy things he rid himself at last of the unclean spirit.[131] He quotes from Boethius the whole story of Macbeth,[132] and tells how "Duffus rex" languished and wasted under the malefic arts of certain witches who made an image of the king in wax and, by using various incantations, let the same melt slowly away before the fire. The unhappy king came near to die, but, as soon as these nefarious practices were discovered, the image was destroyed, whereupon the king was restored to health.[133]