flat hand, but by the thumb bending to the breast-bone; 40,000 by placing the hand on the navel; 50,000 by the same position, but the thumb being turned inwards to the navel; 60,000 by laying the flat of the hand on the thigh; 70,000 by laying the back of the hand on the same part; and so on. The corresponding motions of the right hand denoted ten times the quantity of those with the left.

It may appear surprising that with such rude methods the Anglo-Saxons could compute at all, whenever multiplication and division were concerned; yet that they did resolve several in position, or the rule of false, is evident from the examples given by the Venerable" to sharpen his pupils," ad acuendos juvenes. "A certain man walking on the way, met other men, and said to them, ' If you were as many again, half as many, and one quarter as many, your number would be 100;' how many were they?" That they were not unacquainted with the powers of numbers, with the square and the cube at least, is certain; and other quotations involve a knowledge of progression, both arithmetical and geometrical. But the process was so tedious, that we need not wonder at the saying of St. Aldhelm, that he had long found arithmetic not only the most difficult, but absolutely an insuperable study.*

The cosmogony of the Anglo-Saxons was founded on that of the ancient philosophers; but so far altered as to be accordant with the Mosaic economy. The philo sophical treatises of Bede have had the advantage of being commented by Bridferth of Ramsey, a monk as learned as Bede himself; and in a subsequent writer, the author of the four books, De Elementis, which are certainly not Bede's, though ascribed to him, we find notions still much more consistent with the present state of science. On this subject, however, we are imperfectly informed; we have hitherto had no opportunity

Bede, De Arithmeticis Numeris, p. 71. De Computo Dialogus, p. 87. De Arithmeticis Propositionibus, p. 100, &c., necnon De Indigitatione, cum Glossis Bridferti, p. 132, &c. (Opera, tom. i.).

of studying the ancient systems of the universe, from Pythagoras to Bridferth*, and we will not insult the reader by presuming to write on what we do not at present understand. Yet, as it is a most curious subject, we give its exposition in the words of one whom in the present and the preceding volume we have frequently quoted. We must, however, observe that even he has no scientific or very profound knowledge of it; but he writes much better on it than we could, unless we devoted much more time to its consideration than we can now spare.

"The origin of the visible universe had perplexed and confounded the philosophers of antiquity. At each step they sunk deeper into an abyss of darkness and absurdity; and the eternal chaos of the Stoic, the shapeless matter of Aristotle, and the self-existent atoms of Democritus, while they amused their imagination, could only fatigue and irritate their minds. But the Saxon student was guided by an unerring light; and in the inspired narrative of Moses, he beheld, without the danger of deception, the whole visible world start into existence at the command of the Almighty Creator. Of the scriptural cosmogony, his religion forbade him to doubt; but in explaining the component parts of sensible objects, he was at liberty to indulge in speculation. With the Ionic school Bede admitted the four elements: of fire, from which the heavenly bodies derive their light; of air, which is destined to the support of animal existence; of water, which surrounds, pervades, and binds together the earth on which we dwell; and of the earth itself, which is accurately suspended in the centre, and equally poised on all sides by the pressure of the revolving universe. To the different combinations of these elements,

We are ashamed to make such a confession, but candour requires it. If the poet should have run the whole circle of learning, surely such a race is more incumbent on the historian.

+ Lingard, Antiquities of the Anglo-Saxon Church. As for Mr. Turner, he has attempted no classification or analysis on the subject, but merely extracted a few unconnected opinions.

To explain and confirm, and often to amplify the text of Lingard, we give occasional extracts from the original: we do so that the learned reader to whom Bede is not accessible-and to few such can he be accessible-may judge.

Mundus est universitas omnis, quæ constat ex cœlo et terrâ, quatuor elementis in speciem orbis absolute globata; igne, quo sidera lucent; aere, quo cuncta viventia spirant; aquis, quæ terram irrigendo et penetrando communiunt. Atque ipsa terra, quæ mundi media atque sinu librata volnbili circa eam, universitate pendet immobilis.-Bede, De Natura Rerum, cap. 3.

*

with the additional aid of four primary qualities of heat and cold, moisture and dryness, he attributed the various properties of bodies, and the exhaustless fecundity of nature. Pythagoras had taught, though the conclusion was deduced, not from the observations of the phenomena, but from the principles of a fanciful and erroneous theory, that the centre of the world was occupied by the sun, round which the celestial spheres performed their revolutions. But the truth of his opinion was too repugnant to the daily illusions of the senses to obtain credit; and the majority of philosophers, for many centuries, adopted that arrangement of the heavenly bodies which forms the basis of the Ptolomean system. From them it was received by the Christians, and adjusted, with a few modifications, to their religious opinions. According to Bede, the terrestrial atmosphere is immediately surrounded by the orbits of the seven planets, and the firmament of the fixed stars; on the firmament repose the waters mentioned in the Mosaic cosmogony †, and these are again encircled by the highest and ætherial heaven, destined for the residence of the angelic spirits. From the diurnal motion of the stars, which describe concentric circles, of a smaller diameter as they approach towards the north, he infers that this immense system daily revolves with amazing rapidity round the earth, on an imaginary axis, of which the two extremities are called the northern and southern poles. In the present advanced state of astronomical knowledge, we are tempted to smile at the idea of the Grecian philosopher, who conceived the stars to be so many

* Elementa sibimet sicut natura, sic etiam situ differunt. Terra etiam, ut gravissima, et quæ ab alia natura sufferri non potest, imum in creaturis obtinet locum. Aqua vero, quanto levior terrâ, tanto est aere gravior. Ignis quoque materialiter accensus, continuo naturalem sui sedem super aera quærit. Quæ tamen quadam naturæ propinquitate sibimet ita commiscentur, ut terra quidem arida et frigida, frigidæ aquæ; aqua vero frigida et humida, humido aeri; porro aer humidus et calidus, calido igni; ignis quoque calidus et aridus, terræ societur aridæ.-De Natura Rerum, cap. 4.

"See Genesis, chap. i. 'How,' exclaims Bridferth of Ramsey, the commentator of Bede's philosophical works, can the waters rest on the firmament without falling to the earth ?—I know not,' he replies, but

authority of the Scriptures must silence the objections of reason.' (Glossæ in cap. 8.). The ancient author of the elements of philosophy published under the name of Bede, is justly dissatisfied with the answer, and explains the passage of the waters, which are separated by evaporation from the ocean, and suspended in the atmosphere."-De Elementis Philosophia, lib. ii.

+ Cœlum subtiles igneæque naturæ rotundumque et a centro terræ æquis spatiis undique collectum. Unde est et convexum mediumque quacunque cernatur, inerrabili celeritate quotidie circumagi sapientes mundi dixerunt, ita ut rueret si non planetarum occursu moderetur; argumento siderum nitentes, quæ fixo semper cursu circumvolant, septentrionalibus breviores gyros ordinem peragentibus, cujus vertices extremos circa quos sphæra cœli volvitur, polos nuncupant, glaciali rigore tabentes.-Bede, De Rerum

concave mirrors fixed in the firmament, to collect the igneous particles which are scattered through the heavens, and to reflect them to the earth. From the assertion of Bede, that they borrow their brilliancy from the sun, we might naturally infer that he had adopted the opinion of Epicurus; but his commentator, the monk of Ramsey, informs us, that he considered them as bodies of fire, which emitted a light too feeble to affect the organs of vision, except when it was strengthened by the denser rays of the sun. That they were not extinguishable in the morning, and rekindled each evening, as had been taught by Xenophanes, was proved by their appearance during the obscurity of a solar eclipse; and of their influence on the atmosphere no one could remain ignorant who had remarked the storms that annually attend the heliacal rising of Arcturus and Orion, and had felt the heat with which the dog-star scorches the earth.* The twofold and opposite motions which seem to animate the planets, could not escape the knowledge of an attentive observer; but satisfactorily to account for them, so long as the earth was supposed immovable, baffled all the efforts of human ingenuity. The Saxons justly considered the natural direction of their orbits to lie from west to east, but conceived that their progress was constantly opposed by the more powerful rotation of the fixed stars, which compelled them daily to revolve round the earth in a contrary direction. In their explanation of the other phenomena, they were equally unfortunate. The ingenious invention of epicycles was unknown, or rejected by them; and they ascribed most of the inequalities observed in the planetary motions to the more or less oblique action of the solar rays, by which they were sometimes accelerated, sometimes retarded, and sometimes entirely suspended. Yet they were acquainted with the important distinction between real and apparent motion. Though they conceived the planetary orbits to be circular, they had learned from Pliny that each possessed a different centre.; and thence inferred, that in the perigeum their velocity must be apparently increased, in the apogeum apparently diminished. Among

*Bede, De Rerum Natura, cap. 11.

+ Inter cœlum terrasque septem sidera pendent, certis discreta spatiis, quæ vocantur errantia, contrarium mundo agentia cursum, id est, lævum, illo semper in dextrâ præcipiti. Et quamvis assidua conversione immensæ celeritatis accoluntur ab ea, rapianturque in occasus, adverso tameni ire motu per imos quæque passus advertuntur; nunc inferius, nunc superius, propter obliquitatem signiferi vagantia.-De Natura Rerum, cap. 12. Sunt autem sui cuique planetarum circuli, quos Græci absidas in stellis vocant, alii que quam mundo, quoniam terra a verticibus duobus, quos appellaverunt polos, centrum cœli est, necnon et signiferi obliqui inter eos siti. Omnia autem hæc constant ratione circini semper indubitata. Ergo ab alio cuique centro absides suæ exurgunt: ideoque diversos habent orbes, motusque dissimiles.-Ibid. cap. 14.

the planets the first place was justly given to the sun, the great source of light and heat. They described this luminary as a globular mass of fiery particles, preserved in a state of ignition by perpetual rotation. Had it been fixed, says Bede, like the stars in the firmament, the equatorial portion of the earth would have been reduced to ashes by the intensity of its rays but the beneficence of the Creator wisely ordained that it should daily and annually travel round the earth; and thus produce the succession of the night and day, the vicissitudes of the seasons, and the divisions of time. Its daily revolution is completed between midnight and midnight; and is usually divided into twenty-four hours, each of which admits of four different subdivisions, into four points (five in lunar computations), ten minutes, fifteen parts or degrees, and forty moments. Its annual revolution through the twelve signs of the zodiac, which it divides into two equal parts, forms the solar year, and consists of 365 days.* As it recedes towards the brumal solstice, its rays in the morning and evening are intercepted by the convexity of the equator, and their absence prolongs the duration of darkness, and favours the cold of winter; but in proportion as it returns towards the tropic of Capricorn, the days gradually lengthen, and nature seems reanimated by the constant accumulation of heat. But here a rational doubt

will occur. If the rays, which daily warm and illuminate the earth, be emitted from the sun, is there no reason to fear that, after a certain period, the powers of this luminary may be totally exhausted? Bede readily answered, that its losses were quickly repaired by the numerous exhalations of the ocean situated under the torrid zone. To feed the sun with water is an idea which will probably appear ludicrous to the reader; but it originated from the tenets of Thales, the parent of the Grecian philosophy, and had been consecrated by the general adoption of his successors.‡ The regular increase and decrease of the moon have always called the attention of the learned towards the phenomena of that planet. Respecting its magnitude, the Saxons followed two opposite opinions. Some, on the authority of Pliny, maintained that it was larger, others, with greater truth, conceived that it was smaller, than the earth. Its phases they justly ascribed to the ever-varying position of the illuminated disk §; nor were they ignorant that its orbit was subject to several anomalies, which defied the precision of

Bedæ Opera, tom. ii. p. 26. 53. 206.

† Bede, De Rerum Natura, cap. 19. "Solis ignem dicunt aquâ nutriri." Aristotle, Metaph. lib. i. cap. 3. Cicero, De Natura Deorum, lib. i. cap. 10.

Bede, De Ratione Temporum, cum Commentariis Bridferthi,