Chapter XXI (4)

The only other work that Napier published in his lifetime was his short treatise on the method of computing by figured rods, known by the name of Napier’s bones, 1617: it contained the most important of his minor inventions touching various numerical properties. The following is a part of his own description of it, from the dedication to the Earl of Dunfermline:――“Of which logarithms, indeed, I have found out another species much superior to the former; and intend, if God shall grant me longer life and the possession of health, to make known the method of construction, as well as the manner of using them. But the actual computation of this new canon I have left, on account of the infirmity of my bodily health, to those conversant in such studies; and especially to that truly and most learned man, Henry Briggs, public professor of geometry in London, my most beloved friend. In the meantime, however, for the sake of those who prefer to work with the natural numbers as they stand, I have excogitated three other compendious modes of calculation, of which the first is by means of numerating rods, and these I have called ‘Rabdologia.’ Another, by far the most expeditious of all for multiplication, and which on that account I have not inaptly called the promptuary of multiplication, is by means of little plates of metal disposed in a box. And lastly, a third method, namely, local arithmetic performed upon a chess-board.”¹

¹ M. Napier’s _Memoirs of John Napier_, pages 413‒415. The
original edition of this little work is now extremely scarce.

In 1619 Napier’s son published the work which his father had left incomplete――“Logarithmorum Canonis Constructio,” that is, the method of their construction. The purpose of the work is to show the way that he conquered the second difficulty in his path to the logarithms; namely, how to calculate the numbers to be intercalculated between the terms of his progressions, in order to reap the fruits of his original conception. Though the author did not live to give it the final touches, the book is teeming with profound thought, and exhibits a grasp of the subject and a clearness of exposition which is rare even among the efforts of the highest genius. Professor Playfair has well said, “Napier’s view of the subject is as simple and profound as any which after two hundred years has yet presented itself to mathematicians. The mode of deducing the results has been simplified; but it can hardly be said that the principle has been more clearly developed.” Sir John ♦Lesly has said, “his sublime invention of Logarithms about this epoch eclipsed every minor improvement, and as far transcended the denary notation, as this had surpassed the numerical system of the Greeks.” Robert Napier in the preface to his father’s posthumous work said――“Some years ago, my father, of ever venerable memory, published the use of the wonderful Canon of Logarithms; but the construction and method of generating it, he, for certain reasons, was unwilling to commit to types, as he mentions upon the seventh and the last pages of the Logarithms; until he knew how it was judged of and criticised by those who were versed in this department of letters. But since his death, I have been assured from undoubted authority, that this new invention is much thought of by the most able mathematicians; and that nothing would delight them more than if the construction of his wonderful Canon, or so much at least as might suffice to illustrate it, were published for the benefit of the world.... I doubt, not, however, that this posthumous work would have seen the light in a far more perfect and finished state, if the author himself, who according to the opinion of the best judges, possessed among other illustrious gifts this one in particular, that he could explicate the most difficult matter by some sure and easy method, and in the fewest words――if God had granted a longer use of life. You have the doctrine of the construction of Logarithms――which here, he calls artificial numbers, for he had this treatise composed for several years before he invented the word Logarithms, most copiously unfolded, their nature, accidences, and various adaptations to their natural numbers, perspicuously demonstrated. I have thought good to subjoin to the construction a certain appendix, concerning the method of forming another and more excellent species of Logarithms, to which the inventor himself alludes in his epistle prefixed to the Rabdologia, and in which the Logarithm of unity is 0.... I have also published some lucubrations upon the new species of Logarithms, by that most excellent mathematician, Henry Briggs, public professor in London, who undertook most willingly the very severe labour of calculating this Canon, in consequence of the singular affection that existed between him and my father, the method of construction and explanation of its use being left to the inventor himself.”¹

♦ “Leslie” replaced with “Lesly” for consistency

¹ M. Napier’s _Memoirs of John Napier_, pages 417‒418, 445,
_et seq._ This book contains a vast amount of information,
but its author is rather too laudatory of the inventor of
Logarithms.

Henry Briggs was the greatest mathematician of his day in
England; he was a man of remarkable powers of mind, and
of great industry. He is the author of several valuable
treatises on Logarithms, his greatest work appeared in 1624,
entitled “Arithmetica Logarithmica.” He died in 1630.

It was observed in the preceding volume, that there was little or no medical science among the Scots at the end of the fifteenth century.¹ According to the statement of the elder Scaliger, who visited Scotland about the middle of the sixteenth century, the kingdom did not contain more than one regular practitioner. It is known, however, that this learned man was rather fastidious in his taste and in his mode of life.² It is possible that he might have exaggerated a little, or that his information may have been incomplete. At least, this science had made some progress in the country before the end of the century; though as yet there was no medical school in the kingdom, as now understood; and Scotsmen intending to follow this profession were trained abroad.

¹ MackMackintosh’s _History of Civilisation in Scotland_,
Volume I., pages 414‒415.

² “At ♦Agen the elder Scaliger was now exercising the
profession of a physician. That city, when he there
fixed his residence, could not furnish him with a single
individual capable of supporting literary conversation,
and he was therefore led to cultivate an intimacy with some
of the more enlightened inhabitants of Bordeaux. Buchanan,
Tevius, and other accomplished scholars, who then belonged
to the College of Guienne, were accustomed to pay him an
annual visit during the vacation. They were hospitably
entertained at his house; and he declared that he forgot
the torture of his gout whenever he had an opportunity
of discussing topics of learning with his guests. For
the society of this singular man, who possessed some bad
and many good qualities, Buchanan has expressed a natural
relish” (in Latin verses).――Dr. Irving’s _Memoirs of
Buchanan_, pages 45‒46.

♦ “Ageu” replaced with “Agen”

The people suffered greatly from the frequent recurrence of pestilence; and in 1568 Gilbert Skene, doctor in medicine, published at Edinburgh, “A Brief Description of the Pest,” which was the first medical treatise printed in Scotland. This treatise consists of forty-six small pages, and may be supposed to give the views of the learned of those days touching the pest. He described it as “a feverable infection, most cruel, and in sundry ways striking down many in haste. It proceeded from a corruption of the air, which has strength and wickedness above all natural putrefaction, and springs from the wrath of the just God at the sins of mankind.” He recognised, however, other causes, “as stagnant waters, corrupting animal matters and filth, the eating of unwholesome meat and decaying fruits, and the drinking of corrupt water. Great humidity of the atmosphere, dearth of victual, whereby men are forced to eat bad meat.” He adverts to the suspicious intermeddling of the comets and the shooting stars. He observed that the poor were more subject to this fearful disorder than the rich; indeed, his description of the state of the former was deplorable――“Every one is become so detestable to another, which is to be lamented, and especially the poor in the sight of the rich, as if they were not equal with them touching their creation, but rather without soul or spirit, as beasts degenerated from mankind.” This worthy doctor’s regimen for the pest, regarding both its prevention and its cure, consisted of a vast variety of curious recipes and rules of treatment, written partly in Latin and partly in English.

Dr. Peter Lowe had practised in various parts of the Continent, and returned to his native country toward the end of this century. He published a system of surgery in 1597, giving a popular view of the healing art, along with some description of cases which had occurred in his own practice. The title of Dr. Lowe’s work will give the best idea of its character:――“The Whole Course of Surgery; wherein is briefly set down the Causes, Signs, Prognostications, and Curations of all sorts of Tumours, Wounds, Ulcers, Fractures, Dislocations, and all other Diseases, usually practised by Surgeons, according to the opinion of all our ancient Doctors in Surgery: Compiled by Peter Lowe, Scotsman, Arellian Doctor in the Faculty of Surgery in Paris, and Surgeon Ordinary to the King of France and Navarre. Whereunto is annexed the Book of Presages of Hippocrates, divided into three parts; also the Protestation which Hippocrates caused his Scholars to make. The whole collected and translated. London, 1596.” Reprinted in 1597, 1612, 1634, 1654. It was regarded as a work of merit in its day, and was translated into several languages. Dr. Lowe also wrote a book entitled, “An Easy, Certain, and Perfect Method to Cure and to Prevent the Spanish Sickness. Published at London in 1596.”

About this time he was appointed by the Government to examine the persons that proposed to practise the art of surgery in the West of Scotland. He resided in Glasgow, and was the founder of the faculty of physicians and surgeons of that city.

Dr. Duncan Liddel was born in Aberdeen, 1561, and attained an eminent position as a professor of mathematics and as a physician. In the later part of the sixteenth, and the early part of the seventeenth centuries, he was a professor of mathematics and of medicine in the University of Helmstadt; he also acted as first physician to the court of Brunswick, and had a large practice among the families in the neighbourhood. He was elected to fill several posts of honour in connection with the University of Helmstadt, and achieved much celebrity. About 1608 he returned to Scotland, and directed his attention to the diffusion of science among his countrymen. He died in December, 1613. Dr. Liddel was the author of several works composed in Latin, which were well received on the Continent. His work entitled, “Disputationes Medicinales,” in four volumes, was published in 1605; and it was reprinted as late as 1720; it contained the theses maintained by himself and his pupils at Helmstadt from 1592 to 1605. In 1607 his well known work, “Ars Medica, succincte et perspicue explicata,” was published at Hamburg; a second edition was published at Lyons, 1624, and a third at Hamburg in 1628. This work was pretty highly esteemed during the seventeenth century. Like other works of the period in this department it treated largely on metaphysics as well as on medicine.¹

¹ A sketch of the life of Dr. Duncan Liddel, Aberdeen, 1730.
There is also an interesting article relating to Dr. Liddel
in the eleventh volume of the proceedings of the Society of
Antiquaries of Scotland, by the late Mr. A. Gibb, F.S.A.,
Scotland, pages 450, _et seq._

Having concluded the examination of the literature of the nation in the sixteenth century; we may pause a little, and reflect on the characteristics of the works, the opinions, the sentiments, and the feelings, manifested in them. Looking backwards we find that there had been some advance in physical knowledge amongst the Scots during the century, but by no means a marked progress in this department. Although Napier announced an important invention in the department of mathematical science early in the seventeenth century, no one can fail to see that the intellectual and scientific advancement of the Scots was comparatively meagre as contrasted with the radical changes of their religious belief, their sentiments and feelings. The great intellectual revival in Europe, however, was beginning to be felt in the sixteenth century. The Copernican system of the universe was first printed in 1543, but it met with much opposition, even among the learned its acceptance was extremely slow, probably not ten men in Europe had adopted it in the sixteenth century; and there is not the slightest reason to believe that any of the chief Reformers recognised or comprehended it. Even Buchanan, though not ignorant of the Copernican system, yet in his own philosophical poem, “The Sphere,” he rejected it, and followed the Ptolemaic system. Long after their day, the far famed Lord Bacon rejected the Copernican system to the last; he also treated the valuable discoveries of Gilbert about the magnet with the most arrogant contempt. When this great philosopher assumed such an attitude to the greatest conception of his age, we can hardly suppose that the mind of the Scots had as yet been in the least affected by these scientific ideas; though it is possible that some individual Scotsmen toward the end of the century might have been aware of them; but the religious revolution was accomplished before this; and the conclusion pointed to is that the Reformation depended more upon moral causes than intellectual and scientific ones. Throughout the literature of the period it will be found that there is more evidence of change in the feelings and sentiments of the people, than of any display of increasing intellectual power.

The writers in the Scottish dialect of the latter part of the century are inferior to those of the first quarter of the century in point of intellectual power. After the Reformation there is no Scottish poet equal to Dunbar or even to Gavin Douglas, the versifiers of the close of the century stand lower than those of its opening years; the balance in conception, range of imagery, of ideas, and in appropriate construction, is on the side of the earlier poets. If, however, we look to the feelings and the sentiments which were expressed in the compositions of both, the later writers appear in a more favourable light; as the extremely coarse expressions which Dunbar and Sir David Lyndsay frequently used, were gradually cast aside, and a better moral tone observed. The improvement of the moral sentiments and the broadening of the national sympathy were indicated in various directions, as in the emphatic complaints touching the oppression of the poor and the earnest efforts to relieve them.

Thus, the revolutionary waves of the sixteenth century were mainly religious and moral, and considering the state of society, not merely in Scotland, but throughout Europe, it was not surprising that the Reformers were only partly successful. The reactionary spirit of Roman Catholicism was great, and it long presented an undaunted opposition to every form of liberal policy and moral freedom; and Rome still claims a supremacy in all matters of morality and religion. The Pope is the supreme and only visible head of this planet, appointed by God to rule over the human mind, and if necessary, to spurn the accumulated wisdom and knowledge of the race. Centuries roll on, revolutions in governments, in knowledge, and in education, may be brought to pass among the nations; but the Pope remains unchanged, the same circumscribed views characterise the Popes of the sixteenth and the nineteenth centuries.