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He was entirely, self-taught,
After leaving the

Winward, Jesse, Westhoughton. Ladies' Diary, 1812-20-8-39-42; Gentleman's Diary, 1809-11-12-13-14-15-16-18-20-21-2-33; Mathematical Companion, 1809-10-11-17-22-5; Quarterly Visitor, 1813-14-15; Enquirer, 1811-12-13; Scientific Receptacle, 1825; Students' Companion, 1822-3; York Courant, 1841-2-3-4. B. 1786, d. 1861. Like Hine, Winward was a private soldier for many years. and a mathematician of great capacity. army in 1816, he established a school in his native village of Westhoughton, and subsequently became Master of the Grammar School at West Derby, in both of which places he is still remembered as a good teacher and an upright man. Wolfenden, James, Hollinwood. Gentleman's Diary, 1783-4-9099; Mathematical Companion, 1800-1-7-8; Student, 1797-8-91800; Burrow's Diary, 1781. B. 1754, d. 1841.

Wild, J., Ashton. Ladies' Diary, 1841-2; York Courant, 18412-3. This gentleman, who was brought up in a mill and self-taught, died very young in 1843. The Courant for January 11th, 1844, speaks highly of his abilities, and as being of great promise.

Wright, J., Westhoughton. Ladies' Diary, 1795-6-7; Mathematical Companion, 1810-27 (inclusive); Student, 1798-9, 1800. Wilkinson, T. T., Burnley. This gentleman, who will be remembered as a member of the Manchester Literary Club, and who only recently died (February 6th, 1875), though a mathematician of only average ability, was the most active and prolific writer of what he was pleased to call the Lancashire school. He left a detailed account of his life and writings, which has been embodied in a paper entitled "Memorials of the late T. T. Wilkinson, F.R.A.S.," and read before the Lancashire and Cheshire Historic Society, November 11th, 1875, by Mr. W. A. Abram of the Blackburn Times. His mathematical contributions to the Ladies' Diary commenced in 1839, and continued with slight intermissions till it ceased in 1871. He was an occasional correspondent of the mathematical departments of the York Courant, the Northumbrian Mirror, and the Educational Times. He wrote brief memoirs of Wolfenden, Kay, and Butterworth; but the most useful and valuable of his papers are those

printed in Vols. 48, 49, 50, 51, 52, 53, and 54, in which he gives an account of twenty-nine mathematical periodicals published at various times from 1704 to 1835. At pages 158, 182, and 200, Vol. 60, there is a painful correspondence between him and Mr. Septimus Tebay, of Rivington, in which Mr. Tebay (truthfully to my own knowledge) accuses him of exchanging solutions of mathematical problems with other correspondents in order to increase the number of each, a kind of plagiarism much too common amongst the last generation of mathematicians. In one of his letters Mr. Tebay well observes, "The system of exchange I believe to be practised to a considerable extent among the present degenerate race of Lancashire mathematicians, of the glory of which so much has been said. Such is the general wreck, that with one or two solitary exceptions there does not remain a single spark of that sterling genius which characterises the labours of Butterworth, Smith, and Wolfenden." There is an article on porisms in one of the numbers of the Educational Times by Mr. Wilkinson, almost entirely the work of another man, who in turn borrowed most of his work from the papers of Mr. Butterworth. Of the value of Mr. Wilkinson's writings on Antiquities, Folk-lore, and other similar subjects I cannot speak, never having read them.

LIST OF MATHEMATICAL PERIODICALS PUBLISHED DURING THE LAST AND PRESENT CENTURIES.

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II. Scientific Repository

12. British Diary

13. Diary Supplement

14. Scientific Receptacle

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15. Stockton Bee................................. 1793 Atkinson

16. Mathematical and Geometri

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22. New Quarterly Visitor......... 1813. Passman

23. Leeds Correspondent

24. Students' Companion

25. Liverpool Apollonius

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30. Northumbrian Mirror

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32. The Mathematician

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[The two last-named journals are still in existence, both of them devoted to the cultivation of the highest branches of what is called Modern Analysis.]

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TENNYSON'S "PALACE OF ART."

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BY THE REV. W. ANDERSON O'CONOR, B.A.

[Read October 22, 1877.]

T is commonly said that there is no waste in creation, and that the displacement of an atom would unsettle the balance of the universe. This is true only in a metaphysical relation. In the external world, so far as our power of observation can reach, waste is the rule, use the exception. Our earth during unnumbered ages was a wilderness. Even now its inhabited and cultivated portions are only islands and oases. The interplanetary spaces teem with fragments of worlds which are apparently as useless as the dust of our globe would be if it were blown about for ever by the winds. Every life of plant and animal is rescued from the midst of countless failures. Every creature that moves in densest shoal or flock is also the centre of a ruined region of unreached existence. All organisation is only a germ in a gigantic involution of unproductive expenditure, a minute kernel in a 'colossal integument of sterility.

Is this apparent waste real? Does this superfluity exist in vain? Nature is what it is-in its immensity, its variety, its redundancy-for the sake of man. The soul of man is the reflection of the outside world; and that it may be multifarious, vast, infinite' in inexhaustible resources, affluent in unconceived possibilities, nature is so. God does his work with boundless margin, that man's soul may expand and soar as in unlimited space. There is no waste in the lavish prodigality of matter, time, and space, because it only provides a field wide enough for the imagination to traverse. Man does not live on bread alone. The desert places are more fertile than the blossoming garden or the

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yellow field of corn. That which is limited and practical in man is the shadow of earth's symmetry and organisation; all that is sublime in him is the gloom of her barrenness and deformity. If the elements put forth just so much force and material as was needed for the designed effect, if there was an accurate proportion always between the effort and the product, every exertion of the human will would be narrowed to a calculation in arithmetic, Man would repress his power to visible and definite ends, and nothing would be left for aspiration. Exact law is ever lost in some undefined principle whose orbit is beyond our vision, and even our measured actions have a meaning whose echoes are heard in the pathways of the stars.

The indefiniteness of the universe is reproduced in us. Our thoughts swell beyond the compass of possible achievement. Our desires outstrip our knowledge. Our distinct conceptions are fertile spots amid wildernesses of vagueness and obscurity. The waste of light in morning dawn and evening sunset, the waste of genial warmth as summer is slowly killed by cruel winter, the waste of consciousness as we pass dimly into the darkness of sleep, all leave their impress upon us. Wonder, awe, mystery are the perfumes of the flowers that never bloom, the echoes of the voices that never become articulate, the impalpable sway of the uncreated creation. Our faculties melt into the immeasurable. Language imitates the extravagance of nature, and spreads into hyperbole and rhetoric. Belief is surrounded by an infinitude of mental space, which we call doubt; but which, in truth, is the field of progress and of action, the atmosphere of light and life, the breathing place of mental health. God risks our loyalty to Him to make us ceaseless in our pursuit of truth. Indetermina- . tion of aim answering to nature's vastness, her eternity, her infinity, her stores of wealth too great for any known end, gives birth to poetry. We can see the spendthrift outlay of creation bearing fruit in local and national life. The industry of a district is arrested to save a fellow-being from death. The nation puts forth thirty million hands to rescue one or two captives from a savage. Such is the connection between man's soul and the outer world. Art in its æsthetic sense undertakes to embody, to arrange into rule, and to mirror back on the soul, its own grandeur, its own ever-widening universality, imprinted upon it by the universality

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