had been himself condemned to do some penalty. Descartes thereupon dispatched his revolutionary treatise to a distant part of the country so that the temptation to publish it might be put out of his way. Only a fragment of it appeared after his death. The vicious doctrine of the treatise, that the earth was in motion, was later included in his Principles of Philosophy in a mitigated form. Motion, says M. Descartes in this later statement, consists in a change of the relations of a body to its immediate surroundings. Thus the earth, carried round the sun in a stream of subtle matter which immediately envelops it, is no more in motion than a man asleep in a ship that is passing from Calais to Dover.

Toward the end of his life, Descartes formed a friendship with the Princess Elizabeth, the eldest daughter of the exiled elector palatine, who was then living with her mother, the Queen of Bohemia, at the Hague. The princess is the first of "les femmes savantes”, later satirized by Molière. She is a true savant, enamoured of mathematics and physics, and worthy of the honor Descartes did her in dedicating to her his Principles of Philosophy.

His second royal pupil, Queen Christina of Sweden, the daughter of Gustavus Adolphus, was less of a scholar. Through the French ambassador at the Swedish court, the young queen, not yet twenty, conducted a learned correspondence with the celebrated philosopher, beginning with a philosophical analysis of love and ending with a complete essay from Descartes on The Passions of the Soul, the most important of his later works. The queen begged Descartes to come to Stockholm. After much hesitation and against the advice of his friends, he set out in September, 1649, on the long journey. He reached Stockholm toward the end of October, but almost at the moment of his arrival, despite the gracious

reception of the queen, he wished that he might depart. Anxious that he should have a part in the celebration of the peace of Westphalia in December, the queen set him to composing a ballet; but, "worse still, our philosopher, who had always been accustomed to remain in bed till a late hour, was obliged, at the pleasure of the queen, to arise before sun-up; it was at five o'clock in the morning that this exacting woman chose to make appointments with him, in her study, to learn from him 'how to live happily in the sight of God and man.'

"He suffered cruelly with the cold: the thoughts of the people of this country, he said, chilled him as did the water. He was unable to resist this fashion of living. He took cold as he was going from the embassy to the court and fell seriously ill. Christina sent a German doctor to attend him, whom he believed to be his enemy and received unwillingly. When the doctor desired to bleed him, he said, 'You shall not shed a drop of French blood'; and he would accept nothing but a homely remedy, which consisted of a weak infusion of tobacco in a warm drink. The fever became more intense; the lungs were affected; on the 11th of February, 1650, at four in the morning, after having dictated a letter to his brothers commending his old nurse to their care, and after having received the religious offices with fervour, he exclaimed, 'Now, my soul, it is time to depart.' He then breathed his last, 'passionately moved that he was about to discover and possess a truth that he had sought all his life.' He was not yet fifty-four years of age."

The queen offered the principal church of Stockholm for the funeral services, but the French ambassador declined; "a gentleman who was Catholic and French could not lie in ground that was foreign and Lutheran." J. Chevalier, "Descartes," Paris, 1921.

Descartes' remains were deposited in the cemetery for children who had died before baptism; a few years later, in 1667, his body was brought to Paris and placed in the church of Sainte-Geneviève, and in 1819 it was transported to the church of Saint-Germain des Près, where it now reposes. Even at that time, in 1667, a royal order was issued to prevent the Chancellor of the University of Paris from pronouncing the eulogy he had prepared for the occasion of Descartes' burial in French soil. The storm of opposition to Cartesianism was beginning to burst, but it was too late.

III

The

The Cartesian philosophy is usually described as dualistic, which means that it divides the universe into two mutually exclusive realms, spirit and matter. physical world with its motions, its geometry, its measurable relationships, constitutes one realm, and the soul with its free will, its thoughts, its sensations, constitutes the other. But this is not all. There is a third realm, or entity, which is not on the same level as the others and yet is essential to Descartes' universe. This is the Divine Being, who creates and sustains the realms of spirit and matter. Cartesianism is really "trialistic." Its basic realities, substances, Descartes calls them, are three-mind, matter, and God. The first two are the created substances; the third, the uncreated substance. Matter and mind need only the concurrence of God to exist, they do not depend on one another; while God requires nothing but Himself. The examination of these three realms of being and of their relations to one another constitutes the system.

Cartesianism thus harbors under a single roof the elements of at least three widely different philosophies,

pantheism, materialism, and idealism. Make mind and matter coördinate aspects of God, who becomes the indwelling substance of all things, and you have the pantheism of Spinoza. Abolish the realm of thinking substance and explain thought as a function of the bodily machine, and you have the materialism of Hobbes or La Mettrie. Absorb matter into spirit, as a thought in the Divine Mind, and you have the idealism of Malebranche and Berkeley. Descartes stoutly resisted all these ways of thinking, which were later to grow out of his premises. Mind and matter are not for him mere aspects of God: they are God's creatures, brought into being by a free act of His will, and hence they are distinct from Him. Matter is much more than a thought in the Divine Mind or in the human mind: it is a substantial reality, issuing from God as its source. And, though the bodily machine can do many remarkable things, Descartes would never grant, with the materialists, that it could think.

Descartes' doctrines of the Divine Being are his link with the Middle Ages; his doctrines of mechanics and mathematics, his link with the modern world; while his theory of the soul, as a thing not to be embraced within mechanical categories, gives scope to physical science to develop, unembarrassed by questions of psychology, morality, and religion. But his views on the soul and the Divine Being would not have sufficed to write his name large at the beginning of modern philosophy; in these matters he is a conservative. His radicalism expresses itself in his theory of the physical world. From the point of view of the twentieth century, the realm of matter completely overshadows the other realms of the Cartesian universe.

The great French philosopher is always, first, a mathematician. The germ of his thought appears in his

brilliant, and permanent, mathematical invention, the method of analytical geometry, which is a way of correlating algebraic equations with geometrical figures. No idea is ever without its roots, and Descartes had his predecessors as well as his successors in this field. The idea of the application of algebra to geometry is found in Appolonius, (Greek geometer of the third century B. C.), in Vieta, (French mathematician of the sixteenth century) and even among the Arabs; while Fermat, Descartes' contemporary, advanced notions similar to his own on this subject, and Leibniz (the great German philosopher of the seventeenth century) somewhat later introduced the term "coördinates," if not the idea. But Descartes was the first to formulate, in a generalized and effective way, the principles of analytical geometry. To him goes the credit for this important step forward in mathematics, as well as for numerous minor additions to the same science. He introduced numerical exponents to indicate the powers of numbers; he made use, for the first time, of the letters at the end of the alphabet for unknown quantities and those at the beginning for known quantities; he stated the rule of signs for determining the number of negative and positive roots of an equation.

These inventions were of slight importance, however, beside his geometrical method. The analytical power of that method fired his mind to generalization; hence, the Cartesian system. It is easy to understand how the philosopher, in the light of this discovery, might say, as he does in the Principles: "I do not accept or desire any other principle in Physics than in Geometry of abstract Mathematics, because all the phenomena of nature may be explained by their means, and a sure demonstration can be given of them."

Analytical geometry is a method by which a numeri