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(and passed the highest mathematical attainments), the father at Westhoughton and the son at Bolton-le-Moors, Bilborough, Notts, and subsequently in London. Westhoughton, a long, straggling, colliery village like Royton, was singularly fortunate in having at the same time two such masters as Cunliffe and Winward. Both are respectfully and affectionately remembered by old scholars in the village as good teachers. Cunliffe, they say, though he had only one arm, knew well how to use it. Dobson, Peter, Preston. Dewhirst, John, Blackburn.

Ducket, George, Liverpool.

Ladies' Diary, 1808-9.
Ladies' Diary, 1813.

Ladies' Diary, 1813-14-15-16-17-2223; Gentleman's Diary, 1834-35-36-37-38-39-40-41; Mathematical Companion, 1813-24, twelve years consecutively. This gentleman is in London 1817, and Newcastle-on-Tyne 1822. Elliott, Richard, Liverpool. Ladies' Diary, 1796-7-8; Gentleman's Diary, 1794-7-8-1800; Mathematical Companion, 1806-7; Student, 1797. Emerson, Thomas, Liverpool.

Ladies' Diary, 1836-37-38-39-41

42-43; Gentleman's Diary, 1838-9-40.

Fildes, John, schoolmaster, Liverpool. Ladies' Diary, 1791, 1798; Student, 1797-8-9; Diary Supplement, 1788-1806. Mr. Fildes was better known as an accomplished poetical contributor to the Diaries, &c., than as a mathematician. He d. 1802.

Fletcher, John, Oldham. Ladies' Diary, 1781-2-4; Gentleman's Diary, 1779-83-6-7-90-2-3-4; Mathematical Companion, 1799 to 1818, every year inclusive; Student, 1798-1799-1800; Whiting's Geometrical, &c., Delights, 1793-8; Scientific Receptacle, 1791-2 and forward; British Diary, 1787-96. Mr. Fletcher was a journeyman hatter, mostly resident in Oldham, and afterwards Chester, London, and Liverpool. He was a pupil of Mr. Ralph Taylor, Hollinwood, who subsequently was "Teacher of Mathematics," Stretford, near Manchester. Fletcher was an intimate acquaintance of Wolfenden and Butterworth, and only second to them in originality and profundity of intellect.

Hacking,, Blackburn. Ladies' Diary, 1813.

Harrison, John, Manchester, Ladies' Diary, 1791.

D

Harrop, Joseph, Ashton, Ladies' Diary, 1837-8-9-40; Gentleman's Diary, 1838-9-40-41; Ladies' & Gentleman's Diaries, 1841-21850-1-2; York Courant, 1841-2-3. Mr. Harrop was a factory operative and entirely self-taught. Towards the end of his life he was a schoolmaster. He was clever, both as a geometer and algebraist. B. 1812, d. 1855.

Haslam, Jonathan, Westhoughton. Gentleman's Diary, 1820, B. 1800, d. 1820. A young man of great promise. Haydock, William, Blackburn. Ladies' Diary, 1800. Heap, John, schoolmaster, Royton. Gentleman's Diary, 1832-5; Scientific Mirror, 1829-30; York Courant, 1841-2-3; Ladies' Diary, 1835-6-7-8-9-40. B. 1803, d. 1869. When twenty years of age, Mr. Heap was a "factory lad," and could neither read nor write. He became a pupil to Butterworth, and soon became a clever mathematician. He was also a good botanist. Meteorology was his favourite study, and he long contributed his annual observations to the Manchester Infirmary.

Henry, David, Preston. Ladies' Diary, 1801-2-4. Hilton, William, Saddleworth. Gentleman's Diary, 1798-9-1800; Mathematical Companion, 1799, 1804-5; Student, 1797-8-91800. Mr. Hilton was a working man, for sometime one of Wolfenden's Sunday scholars, and afterwards a schoolmaster in Liverpool. He was editor of the Student in 1799 and 1800. A mathematician of considerable ability.

Hine, Joseph, Tyldesley. Gentleman's Diary, 1808-9 to 1817 inclusively. Mathematical Companion, 1810-11-12; The Enquirer, 1811-12-13; Leeds Correspondent, 1814-15-16. Author of a book entitled The Schoolmaster, and another, Hine's Selection of Wordsworth's Poems. Though not so fertile a correspondent to the mathematical periodicals of his time as some of his contemporaries, Mr. Hine was a remarkable man. His father, a native of Cumberland, came to Lancashire in the early years of his married life, and was employed as bookkeeper and cashier to a firm at Tyldesley. His children went into the mill when very young, and, in consequence of the long hours there, received no instruction except what he gave them at nights and on Sundays. As Joseph grew into a young man he became dissatisfied with

Ulti

the drudgery of the mill, and ran away from home. mately he "listed" in the 2nd Royal Lancashire Militia, which was sent to Hull and from there to Plymouth. From Hull he sent his first contribution to the Gentleman's Diary in 1808, and in 1809 he and Jesse Winward, a fifer in the same regiment, addressed their communications from Plymouth to the editor of the Diary (Dr. Gregory) who complimented them highly on the excellence of their work. Whilst in the regiment he and Winward gave private lessons to the officers' children. When the war was over, and they got their discharge, Hine married and started a school at Plymouth, in which he was very successful. Afterwards he bought a large house at Brixton and commenced a boardingschool there, by which he acquired (a very unusual thing in those days) a good fortune. On one occasion he had the misfortune to have his house burnt down, and, what perhaps he valued more, with it were burnt 2,000 volumes of books. In his declining years he retired to a quiet little nook in Derbyshire, where he married a third time, and died in 1865, in the eightieth year of his age. In 1809 he was one of three private soldiers whose names are attached to the solution of a question in the Diary. He and Jesse Winward got the prize in 1813 for answering the most difficult problem of that year, a problem in the rectification of a curve which I fear would have bothered Dr. Henry Clarke. Homer, it is said, sometimes nods, and as a remarkable instance of men who never err when engaged in a process of purely abstract mathematical reasoning can err, through the misapprehension of data, when they come to apply correct theory to actual phenomena, I may mention that in 1815 Mr. Hine proposed the following question in the Gentleman's Diary for 1815:"If a uniform bar of iron, six feet in length, be placed one end upon the horizon, and the other against a vertical wall, the angle of inclination is required when the pressure upon the horizontal plane is equal to twice the weight of the bar." In 1816 John Butterworth and W. G. Horner, two of the cleverest mathematicians of their time, gave geometrical solutions to the question as if it involved no error, whereas it is utterly absurd. It is like saying that if two men of unequal

height were carrying a plank on their shoulders, the shorter man would have to bear more weight than that of the plank itself! It is alike astonishing that the keen intellect of Wolfenden should make a similar mistake in his solution to question 67, Mathematical Companion, 1810, in respect to the angular position of greatest strength in a pair of canal lockgates.

Holt, John (Mancunienis), Manchester. Ladies' Diary, 1792-3; Gentleman's Diary, 1790-1-2-3; British Diary, 1787-96; · Burrow's Diary, 1776-88. Holt, Charles, schoolmaster, Blackburn. Ladies' Diary, 180916-18-19-22-3-5-6-9-37-40; Gentleman's Diary, 1821-2-3-4-6; Mathematical Companion, 1814 to 1827, every year inclusive; Scientific Mirror, 1829-30, of which periodical he was editor. His contributions to the Diaries and the Mathematical Companion, which were very numerous, prove him to have been a man of considerable ability.

Hopper, Thomas, exciseman, Manchester. Ladies' Diary, 18004-5-6-7; Mathematical Companion, 1800-3-4-5-6.

Huntington, John, Preston. Ladies' Diary, 1819-20-2-3-5-6-8-323-9-40; Gentleman's Diary, 1820-2-8..

Hindle, Thomas, Preston. Gentleman's Diary, 1830-7-9-41; Ladies' & Gentleman's Diaries, 1841-2-3.

Hodgkinson, Eaton, Manchester.

Mathematical Companion, 1821-2. I do not find this gentleman's name in any other mathematical periodical; but the few solutions he sent to the Companion in answer to questions by Mr. Butterworth show moderate ability. Of course he is best known for his original experiments on the strength of materials.

Jones, Griffith, Rochdale and Liverpool.

Gentleman's Diary,

1807 to 1835, every year inclusive except 1820 and 1827; Mathematical Companion, 1816.

Jones, Samuel, Liverpool. Ladies' Diary, 1816-45-6; Gentleman's Diary, 1807 to 1841, every year inclusive, except six, viz., 1811-12-13 and 16-17-18; Mathematical Companion, 1806-7→ 8-9-10-11-12-13-14-15-16-17. B. 1788, d. 1847.

It is impossible to over-rate the mathematical abilities of the two gentlemen last named. They were complete masters of both the ancient and modern systems of analysis, and

throughout their lives enjoyed the highest reputation as teachers and men of unblemished character.

Knowles, John, Liverpool. Gentleman's Diary, 1797-8-9; Student, 1797-8-9-1800. Was editor of the Student, 1797-8.

Kay, John, Royton. Gentleman's Diary, 1808-9-10-11-12-13-14-15; Enquirer, 1811-13; Mathematical Companion, during the same years. B. 1781, d. 1824. He was a pupil of Butterworth's, and his rival as a clever geometer.

Lytham, Joseph, Great Eccleston. Ladies' Diary, 1828-30-41-5; Gentleman's Diary, 1828; Mathematical Companion, 1823-7. Lightbown, Henry, Blackburn. Ladies' Diary, 1804-5-8-22; Mathematical Companion, 1805-6-7-9; Students' Companion, 1822-3, of which he was editor.

Lomax, Oliver, Bury.

Gentleman's Diary, 1764-66. Makinson, William, Manchester. Gentleman's Diary, 1811; Ladies' Diary, 1815-16.

Molineux, Thomas, Manchester. This gentleman was a pupil of Dr. H. Clarke, and as such sent a few contributions to Prescott's Journal and the Town and Country Magazine, 1771-1776. He was afterwards a teacher at Macclesfield, and was author of a treatise on arithmetic.-See Bailey's Memoirs of H. Clarke, pp. 38, 39, 41.

Nicholson, R., Liverpool. Ladies' Diary, 1798-9-1800-1-2-3-4-5-
6-7; Gentleman's Diary, 1784-5-6-96-7-8-1800; Mathematical
Companion, 1801-10-11; Student, 1797-8-9-1800.
Sidebottom, John, Hollinwood. Gentleman's Diary, 1784-5-6-
91-2-3-7-1801-4-5-6-7; Mathematical Companion, 1805-6-8;
Student, 1798-9-1800. A student and friend of Wolfenden's.
Simpson, William, Bolton. Gentleman's Diary, 1801-3-4-7 ;
Mathematical Companion, 1807-8-22-3-4; Student, 1799-1800.
Smith, William, Liverpool. Gentleman's Diary, 1802-3-4; Mathe-
matical Companion, 1804-5-7-8; Student, 1799-1800.
Terrey, Matthew, Lancaster. Ladies' Diary, 1788-9-90-1-6-1805.
Taylor, Ra., Stretford. Gentleman's Diary, 1782-3. This gentle-

man, though he wrote little, was a good mathematician, and
had a high reputation as a teacher. Wolfenden took lessons
from him.

Todd, Thomas, Manchester. Gentleman's Diary, 1837-9; Mathematical Companion, 1818-23-4-5-6.

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