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The literature embraced in this Dictionary covers a period of about one thousand years, and contains Hebrew and Aramaic elements in about equal proportions. The older Hebrew elements, which may conveniently be called the Mishnaic, and can in part be traced back to the first, if not to the second, century B. C. E., may be considered a continuation of the Biblical Hebrew—Biblical Hebrew tinged with Aramaisms. It is therefore apt to throw light, more directly than its successor, on many obscure words and passages in the Bible; nevertheless, the material for Biblical exegesis deposited in the later literature is an inexhaustible mine, which still awaits exploitation by sympathetic students. Besides the Mishnah and the Tosefta, the Mishnaic period embraces Sifra and Sifré, Mekhilta, and the older elements preserved in the Gemara, of which the prayers incidentally quoted are a very essential and interesting part.

The later Hebrew elements in the Gemara and in the Midrashim lead down to the fifth and the eighth century respectively, and to a larger degree than the earlier Hebrew sections are mixed with Aramaic elements, and with foreign words borrowed from the environment and reflecting foreign influences in language as well as in thought. The Aramaic portions of the literature under treatment comprise both the eastern and the western dialects. Owing to the close mental exchange between the Palestinian and the Babylonian Jews, these dialects are often found inextricably interwoven, and cannot be distinguished lexicographically.

The subjects of this literature are as unlimited as are the interests of the human mind. Religion and ethics, exegesis and homiletics, jurisprudence and ceremonial laws, ritual and liturgy, philosophy and science, medicine and magics, astronomy and astrology, history and geography, commerce and trade, politics and social problems, all are represented there, and reflect the mental condition of the Jewish world in its seclusion from the outer world, as well as in its contact with the same whether in agreement or in opposition.


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 Owing to the vast range and the unique character of this literature, both as to mode of thinking and method of presentation, it was frequently necessary to stretch the limits of lexicography and illustrate the definitions by means of larger citations than would be necessary in a more familiar domain of thought. Especially was this the case with legal and with ethical subjects.

Archaeological matters have often been elucidated by references to Greek and Roman customs and beliefs.

The condition of the texts, especially of the Talmud Yerushalmi and of some of the Midrashim, made textual criticism and emendations inevitable, but the dangers of arbitrariness and personal bias had to be guarded against. Happily there were, in most cases, parallels to be drawn upon for the establishment of a correct text, and where these auxiliaries failed, the author preferred erring on the conservative side to indulging in conjectural emendations. For the Babylonian Talmud Raphael Rabbinowicz's Variae Lectiones was an invaluable aid to the author.

The etymological method pursued in this Dictionary requires a somewhat fuller explanation than is ordinarily embodied in a preface.

The Jewish literature here spoken of is specifically indigenous, in which respect it is unlike the Syriac literature contemporary with it, which is mainly Christian, and as such was influenced, not only in thought but also in language, by the Greek and Latin tongues of the religious teachers of a people itself not free from foreign admixtures. Foreign influences came to Jewish literature merely through the ordinary channel of international intercourse. It is for this reason, if for no other, that the Jewish literature of post-Biblical days down to the ninth century may be called original. Hence it is natural to expect that, in extending the horizon of thought, it also extended its vocabulary on its own basis, employing the elements contained in its own treasury.

Starting from such premises, the investigator had to overhaul the laws regulating the derivation of words whose etymology or meaning is unknown from known Semitic roots; every word of strange appearance had to be examined on its merits both as to its meaning or meanings and as to its origin; the temptation offered by phonetic resemblances had to be resisted, and the laws of word-formation common to all other original languages as well as the environment in which a word appears had to be consulted before a conclusion could be reached. The foremost among these laws is that a word is imported into one language from another with the importation of the article it represents or of the idea it conveys. Unless these conditions of importation are apparent, the presumption should be in favor of the home market.

Take e. g. the word and its dialectic equivalent, which means

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 (a) a recess, an alley adjoining the market place to which the merchants retire for the transaction of business, also the trader's stand under the colonnade, and (b) an abscess, a carbuncle. The Latin semita, which since Musafia has been adopted as the origin of simṭa, offers hardly more than an assonance of consonants: a footpath cannot, except by a great stretch, be forced into the meaning of a market stand; and what becomes of simṭa as abscess? But take the word as Semitic, and, dialectically = , offers itself readily, and as for the process of thought by which 'recess', 'nook', goes over into 'abscess' in medical language, we have a parallel in the Latin 'abscessus.' How much Latin medical nomenclature may have influenced the same association of ideas among the Jews is a theme of speculation for students of comparative philology or of the physiology of language.

A superficial glance at the vocabulary of this Dictionary will convince the reader that the example here given represents an extremely numerous class. The cases may not always be so plain, and the author is prepared for objections against his derivations in single instances, but the number of indisputable derivations from known Semitic roots remains large enough to justify the method pursued.

The problem becomes more complicated when both the meaning and the origin of words are unknown. Such is the case e. g. with the word in the phrase (Num. R. s. 4$b$), he turned the isperes and leaped. Levy, guided by Musafia, resorts to, ankle; others suspect in it the name of a garment, , a rare form for. But the phrase itself and the context in which it appears indicate a native word, and this is found in the stem, of which is an 'Ispeel' noun, that is to say, a noun formed from the enlarged stem. As or  is the cloven foot, the latter being also applied to the human foot (Sifré Deuteronomy 2), so  is the front part of the foot, where the toes begin to separate. The phrase quoted is to be translated, 'he (David) inverted the front part of his foot', i. e. stood on tiptoe, 'and leaped' (danced).

We meet with the same stem in the Aramaic,. Referring to Lamentations III, 12, 'he has bent his bow and set me (literally: made me to stand) as a mark for the arrow', one Amora is recorded in the Midrash (Lamentations Rabbah a. 1.) as having explained kammaṭṭara laḥets by. Another is quoted as saying, 'like the pole of the archers (the Roman palus) at which all aim, but which remains standing.' What is ? and what is ? The medieval Jewish commentators frankly admit their ignorance. Musafia, however, reads, maintaining that he had found it in some editions, and refers to Latin parma, explaining isp'risa as sparus, and translating, 'as the shield to the spear.' Ingenious, indeed! But on closer inspection this explanation is beset with intrinsic difficulties. To begin with, parma as shield does not appear in the Talmudic literature again, from which we may infer that it was not generally known to the Jews in their


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 combats with the Romans. Furthermore, the sparus is a small hunting spear never used in battle to aim against the warrior's shield. As the entire passage in the Midrash quoted conveys the purpose of the interpreters to explain the Biblical text by means of a popular illustration, the Amora reported to have used this expression would have utterly missed his object, had he employed foreign and unfamiliar words, when he might have used plain words like, or their Aramaic equivalents. If, furthermore, it is taken into consideration that editio Buber of Lam. R., in agreement with the Arukh, reads for, thus distinctly referring to Babylonian authorities, the supposition of foreign origin for  and  falls to the ground. But, on the other hand, take as an 'Ispeel' noun of the stem, and it means 'that which is to be cloven', i. e. the log, corresponding to the Hebrew  What is , or , again on the assumption that it is a home word? The root. like means to divide, to split, and burma or rather bor'ma is 'the splitter', i. e. the wedge used to split the log. The Amora quoted in the Midrash therefore means to say that Israel, although the target of hostile attacks, is what the wedge is to the log: the wedge is struck, but the log is split. The other Amora quoted expresses the same idea by a different metaphor: 'as the pole of the arrows', and likewise a third, who lays stress on, 'he caused me to stand', in the sense of enduring. An analogous expression to, is (Pales of ), with which Targum renders the same Hebrew word  that forms the subject of comment in the Midrash just referred to (I Samuel XX, 20).

The following lines are intended to give some specimens of such extension of roots, both Hebrew and Aramaic, as have not been recognized heretofore, or, if recognized, have not been applied to their full extent.

Ithpaal or Ithpeel nouns in Aramaean and Aramaicized Hebrew, and Hithpael nouns in Hebrew are too well known to require more than mere mention. Formations like, , are recognized on their face. Except for the preconceived notions concerning the nature of the Talmudic vocabulary, it would seem no more than natural that the Mishnaic or  (Yoma VII, 1) should be an enlargement of, i. e. an Ithpaal noun of , and  merely a synonym of  in the same Mishnah, meaning 'covering', i. e. a suit of clothes, whereas the plainer form  is used for cloak or sheet. From among the vocables reclaimed for the Semitic store on the same principle, one more may be mentioned here: or  is a derivative of, and, as such, a phonetic and actual equivalent of the Biblical , and the meaning of the Hebrew word should be learned from its well-defined Aramaic representative: 'something which restrains the


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 flying locks' (Sabbath 57$b$), i. e. a hair-band worn, as we further learn from the discussion concerning isṭ'ma, under the hair net or cap. To uncover the (Isaiah XLVII, 2) therefore means to throw off the matron's head-cover and appear as a slave. The variant for  in these forms is a common phenomenon in Talmudic orthography.

In connection with this noun formation it may not be out of place to note that Ithpaal or Ithpeel nouns sometimes drop the initial Aleph, in which case they may resume the regular order of consonants, which is inverted in the verb. Thus (M'naḥoth 41$a$) is formed from, the Ithpaal of , 'to justify one's self (compare Genesis XLIV, 16), and means justification, excuse. Another is formed from the root, and means split, breaking through, damage (Baba Kamma 56$a$). (Giṭṭin 86$a$) is an Ithpeel noun of (=), and means a shining white spot, a suspicious symptom of leprosy; and, indeed, Alfasi reads. The Mandaic dialect offers analogies to these formations (see Noeldeke, Mand. Gramm. § 48, sq.).

The enlargement of stems by the prefix is well known in the Aramaic Shafel, but evidences of this same process are to be met with also in classical Hebrew. We have and,  and ,  and , and many more. More frequent is the use of the prefix for the formation of verbal nouns, as, , &c. Such verbal nouns may again become the basis for the formation of nominal verbs, as, 'to pray', which only by a stretch of the imagination can be explained as a plain Hithpael. So also, 'to shout' (Ps. LXV, 14; LX, 10; CVIII, 10), is to be taken as a derivative of. The Talmudic Hebrew offers these formations in abundance, as from,  from  (see Abraham Greiger, Die Sprache der Mischnah, § 7).

On this principle of enlarged stems many words in this Dictionary have been regained from foreign origin for Semitic citizenship, e. g., 'shield', and its derivatives in Hebrew and Aramaic, and  (see the Dictionary s. vv.).

The letter is an equivalent of  in the Shafel forms in the later Hebrew as in the Aramaic; hence words like, Piel  from ;  from ;  from ; , 'to be empty', from , and many more.

A further development of Safel stems consists in formations which for convenience' sake may be defined as 'Ispeel' nouns, of which the aforementioned and  may serve as examples.

The same letters,, , , and also , are used as intensive suffixes. The Biblical and  have been explained by some as enlargements of  ( = ) and  respectively. Be this as it may, the Talmudic Hebrew and the Aramaic possess such intensive suffixes. belongs to, 'to crush, grind, scrape', and the various significations of this enlarged stem and its derivatives can easily be traced back to the fundamental meaning (see Dict. s. v. I and II). Only to


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The Light of Other Days

 * "The Light of Other Days," a poem by Thomas Moore (1779-1852)
 * "The Light of Other Days", (1900) a short story by Gilbert Parker
 * Light of Other Days, (1890) a book by Thomas Willert Beale

title: The Light of Other Days


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User:Gabi Hernandez

When one door of happiness closes, another opens; but often we look so long at the closed door that we do not see the one which has opened for us." —Helen Keller

title: User:Gabi Hernandez


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Clayton he came to London and settled in Elizabeth Street, Eaton Square. In that year he sent to the Royal Academy a ‘Design for a Villa in the Isle of Wight.’ On 13 June 1842 he was elected an associate of the Royal Institute of British Architects, and was advanced to the dignity of fellow of the same body on 2 Nov. 1857. He exhibited architectural designs in the Royal Academy in 1844–7, 1853, and 1856, and in 1845 obtained the premium of the Royal Academy in architecture for the most finished drawing in detail of the church of St. Stephen, Walbrook. Clayton is best known for his architectural publications: ‘A Collection of the Ancient Timber Edifices of England,’ 1846, a most valuable record of those structures, most of which have now disappeared, and ‘The Dimensions, Plans, Elevations, and Sections of the Parochial Churches of Sir Christopher Wren, erected in the cities of London and Westminster,’ 1848. In addition to these he published the following sessional papers, contributed by him to the Royal Institute of British Architects: ‘Norman Refectory at Hereford,’ 1847; ‘Abbey Dore Church and Monastery near Hereford,’ 1851; ‘Towers and Spires of the City Churches, the works of Sir Christopher Wren,’ 1852; ‘Bridges and Viaducts of the Present Day,’ 1856. Clayton died in 1861, and at the opening meeting at the Royal Institute in November of that year allusion was made to the merits of his works and his architectural abilities.

[Redgrave's Dict. of English Artists; Graves's Dict. of Artists, 1760–1880; Royal Academy Catalogues; Catalogue of the Library, and Records of the Royal Institute of British Architects.]

 CLAYTON, NICHOLAS, D.D. (1733?–1797), presbyterian divine, son of Samuel Clayton of Old Park, Enfield, Middlesex, was born about 1733. He was educated partly by private teachers at St. Albans and Chelmsford, and partly at a dissenting academy at Northampton and at the university of Glasgow. He was minister from 1759 to 1763 of the presbyterian chapel at Boston in Lincolnshire, and was invited thence in 1763 to the newly built Octagon Chapel at Liverpool, the promoters of which had the design of introducing a liturgy which dissenters and members of the established church might join in using. The scheme was carried on for thirteen years, but as it was not supported by the members of the church who had professed to be dissatisfied with the Book of Common Prayer, the chapel was then sold to a clergyman of the church of England, and Clayton went to the chapel in Benn's Garden, Liverpool, as the colleague of the Rev. Robert Lewin. The sermon with which he concluded the services at the Octagon on 25 Feb. 1776 was published under the title of ‘The Importance of Sincerity in Public Worship to Truth, Morals, and Christianity.’ Besides this sermon, he printed one in the same year entitled ‘The Minister of the Gospel represented in a sermon on 1 Cor. x. 33’ (, Bibl. Brit.), and another in 1776 on prayer. In the spring of 1781 he was appointed divinity tutor at the Warrington Academy, in succession to Dr. John Aikin, but that establishment was then in a declining state, and in 1783 he returned to Liverpool broken in health. While at Warrington, in 1782 he received the degree of D.D. from the university of Edinburgh. From 1785 to 1795 he ministered at Nottingham as the colleague of the Rev. George Walker. In the latter year he returned once more to Liverpool, and died there on 20 May 1797, aged 66. He married in 1765 Dorothy, daughter of James Nicholson of Liverpool. Clayton was a highly accomplished man, and outside his own calling was a good mathematician and skilled in natural philosophy. His sermons were accounted excellent compositions.

[Monthly Repository, 1813, viii. 625–9; Thom's Liverpool Churches and Chapels, 1854, p. 71; Mem. of Gilbert Wakefield, 1804, i. 226, 321, 555; Thompson's Hist. of Boston, p. 263; Brooke's Liverpool, 1853, p. 58; Kendrick's Warrington Profiles (portrait); Gent. Mag. 1776, xlvi. 369, 450 (notice of the Octagon sermon); Cat. of Edinb. Graduates, 1858, p. 246. The liturgy used at the Octagon Chapel was published in 1763.]  CLAYTON, RICHARD, D.D. (d. 1612), dean of Peterborough, son of John Clayton, gentleman, of Crook in Lancashire, was admitted a pensioner of St. John's College, Cambridge, in 1572, but removed to Oxford, where he proceeded B.A., and was incorporated in that degree at Cambridge in 1576. In the following year he was admitted a fellow of St. John's, on the Lady Margaret's foundation. He commenced M.A. at Cambridge in 1579, and was incorporated in that degree at Oxford on 12 July 1580 (, Fasti, ed. Bliss, i. 217). He proceeded B.D. at Cambridge in 1587, was elected a college preacher at St. John's the same year, was created D.D. in 1592, became master of Magdalene College, Cambridge, in 1593, was installed archdeacon of Lincoln on 30 Aug. 1595, collated to the prebend of Thorngate in the church of Lincoln on 11 Dec. 1595, and admitted master of St. John's College, Cambridge, on the 22nd of the same month. The second court of the college was the great


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 Clayton work of this master; but during his mastership the college declined in learning, its inmates 'being so overbusied with architecture that their other studies were intermitted, and the noise of axes and hammers disturbed them in their proper business' (, Hist. of St. John's, i. 190, 191, 196). Under his government puritanism was in great measure rooted out of the college. He was collated to a canonry of Peterborough on 21 June 1596; was vice-chancellor of the university of Cambridge in 1604; and was installed dean of Peterborough on 28 July 1607 (, Fasti, ed. Hardy, ii. 539). He died on 2 May 1612, and was buried in St. John's College chapel with great solemnity.

[Cambridge Antiquarian Communications, i. 349; Addit. MS. 5866, f. 8; Hacket's Life of Abp. Williams, pp. 17, 18, 22.]   CLAYTON, RICHARD (d. 1828), translator, was the son of John Clayton of Northall, Lancashire, by Elizabeth, daughter of the Rev. Dr. Goodwin, rector of Tankersley, near Barnsley, Yorkshire, and nephew of Richard Clayton, serjeant-at-law and lord chief justice of the common pleas in Ireland, who by his will, dated 16 March 1770, left him his manors of Adlington and Worthington. He was created a baronet on 3 May 1774, was recorder of Wigan (1815-28), constable of Lancaster Castle, and British consul at Nantes, where he died on 29 April 1828. He was a fellow of the Society of Antiquaries, and a member of the Inner Temple, where he was admitted in 1762, called in 1771, and reader in 1811. He married in 1780 Ann, daughter of Dr. Charles White, an eminent surgeon of Manchester, and left an only daughter, who married Lieutenant-general Robert Browne. Lady Clayton died at Cheltenham on 23 Nov. 1837.

Clayton published the following translations and other works: 1. 'On the Cretins of the Vallais,' a paper in the 'Memoirs' of the Manchester Literary and Philosophical Society, 1790. 2. 'Connubia Florum Latino carmine demonstrata auctore D. De la Croix, notas et observationes adjecit,' Bath, 1791, 8vo. 3. 'A Critical Inquiry into the Life of Alexander the Great by the Ancient Historians, translated from the French of the Baron de St. Croix,' Bath, 1793, 4to, which he rendered by his additions more valuable than the original. 4. 'Memoirs of the House of Medici, from the French of M. Tenhove, with notes and observations,' Bath, 1797, 4to, 2 vols. 5. 'The Science of Legislation, from the Italian of Filangieri,' 1806, 8vo. 6. 'A Treatise on Greyhounds,' in the 'Pamphleteer,' vol. ix. 1817.

[Baines's Lancashire, 1870, ii. 165; Literary Memoirs of Living Authors (by Rivers), 1798, i.101; Biog. Dict. of Living Authors, 1816, p. 66; Burke's Extinct and Dormant Baronetcies, 1844, Addenda, p. 600; De Quincey's Autob. Sketches, 1854, ii. 67, where he writes of Sir R. Clayton having honourably distinguished himself in literature by translating and improving the work of Tenhove.]   CLAYTON, ROBERT (1629–1707), merchant and politician, was born at Bulwick, Northamptonshire, on 29 Sept. 1629, being one of several children of a small farmer called Clayton or Cleeton (described by Le Neve as 'carpenter or joyner, a poor man of no family'), who resided in that parish. At an early age he was apprenticed to his uncle, a London scrivener, of the name of Robert Abbot, who left him a large sum of money. Among the manuscripts of W.M. More Molyneux of Losely Park, near Guildford, is a document witnessed by Abbot and his nephew, who there signed his name as Robert Cleton, in 1648 (Hist. MSS. Comm. 7th Rep. 678). Alderman John Morris was a fellow-apprentice and partner in business, and on the death of Morris in February 1682 without issue, his estates came to his old friend, Clayton, who by his own exertions, aided by these accessories of wealth, amassed a fortune sufficient to give him a commanding influence in the councils of the corporation of London.

He was a member of the Scriveners' and Drapers' Companies, alderman of Cordwainer ward from 1670 to 1676, and of the ward of Cheap from that year to 1688. In 1671 he was elected sheriff (being knighted at the Guildhall on 30 Oct.), and elected as lord mayor in 1679-80, when the pageants performed at his cost on the day (29 Oct. 1679) of 'initiation and instalment' were described by Thomas Jordan in a tract entitled 'London in Luster.' All his influence in commerce was exerted on the side of the protestant or whig interest, and he became one of its chief partisans. He was returned to parliament for the city of London in 1678-9, in 1679, and in 1680-1. To the last of these parliaments, which was summoned to meet at Oxford, heand his three whig colleagues in the representation of the city came in great state, with troops of supporters wearing on their hats ribbons with the words 'No popery, no slavery,' and at the request of his constituents he moved for leave to bring in a bill for excluding any papists from succeeding to the English throne. Clayton was accused, with Slingsby Bethel [q. v.], Cornish, and other champions of whiggism, of having endeavoured to induce Fitz-Harris to make false confessions on the popish plot, but the charge was merely


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 HIS FACE

tell you Lincoln was ungainly, plain?

To some he seemed so: true.

Yet in his look was charm to gain

E'en such as I, who knew

With how confirmed a will he tried

To overthrow a cause for which I would have died.

The sun may shine with naught to shroud

Its beam, yet show less bright

Than when from out eclipsing cloud

It pours its radiant light;

And Lincoln, seen amid the shows of war

Clothed in his sober black, was somehow felt the more

To be a centre and a soul of power,—

An influence benign

To kindle in a faithless hour

New trust in the divine.

Grave was his visage, but no cloud could dull

The radiance from within that made it beautiful.

A prisoner, when I saw him first—

Wounded and sick for home— 11


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Aleph, the first letter of the alphabet, interchanging with other gutturals, e.g., , , ; , &c.

often used to form second roots of verbs, e. g. ,.

frequ. prosthetic, e. g., , v..

sometimes inserted to replace a radical, as =, esp. in verbs, as fr. ,  fr. &c.

frequ. (in Talm. Y.) dropped in the beginning of words, e. g. = ; =.

affixed to the end of Chald. nouns, corresponding to prefixed in Hebrew (status emphaticus), e. g. =.

as numeral letter, one, as = one letter. Sabb. 104$a$; a.fr. [Editions and Mss. vary, according to space, between the full numeral and the numeral letter, for, ;  for , ,  &c.]

&c. a prefix, 1) for the formation of nouns in Kal, Peel, Afel (Hifil) &c., e. g., , , &c; 2) demonstrative, e. g. =h. ;, &c.—3) euphonic (prosthetic) =; =h.  &c, esp. before foreign words beginning with two consonants, e. g. , = &c.

a prefix (followed by Dagesh Forté)= upon, over, e. g. =; even before gutturals, e. g..

plur. of q. v.

a fictitious word made up of each third letter in. (Dan. V, 25). Snh. 22$a$; Cant. R. to. III, the inscription on the wall was so arranged as to form words composed of its every first, every second and every third letter respectively.

v..

a prefix of words of Greek origin answering to, au-, e. g. =; or to , e. g. =.

(Assyr. A-bu, Schr. K. A. T., p. 247) Aḅ, the fifth month of the Jewish calendar (of thirty days) beginning between the eighth of July and the seventh of August, and ending between the sixth of August and the fifth of September. R. Hash. I, 3, for announcing the beginning of Ab messengers are sent out, for the sake of the fast. Ib. 18$b$ the ninth of Ab, anniversary of Temple destruction. Taan. IV, 6 with the beginning of Ab. Ib. 29$b$ let him try to be relieved of (the law-suit) in Ab. Meg.5$b$; a.e.

m. (b. h.;, cmp. ), const. , [embracer], father, ancestor, progenitor; teacher; chief, leader; author, originator. Ex. R. s. 46 end the educator is the real father. Lev. R. s. 1, the father of all wisdom,. . the father of prophets. Y. Ned. V, 39$b$; a. fr.— (abbr. ) president of the Court (Great Sanhedrin), next in dignity to the Nassi. Taan. II, 1; a. fr.—Metaph. origin, cause. Num. R. s. 10 (play on, Prov. XXIII, 29) the cause of woe (sin).— (for which also ) one of the chief labors forbidden on the Sabbath, opp. a labor the prohibition of which is based on the ground of its being a species of the former, or derived from the former. Sabb. VII, 1 sq.; a. fr.—[Y. Sabb. II, 5$a$,, sub. .]— one of the original or direct causes of levitical uncleanness, opp. (child) secondary cause. Toh. I, 5 ; a. fr.— v. Pl.— creation of a class, i. e. a conclusion, by analogy, from a case explicitly stated in the bibl. law on all similar cases not specified in detail. Sifra introd.—Ib. K'doshim, end, ch. 11 (ref. to Lev. XX, 27) this forms the rule for all cases in which the Bible uses the word d'mēhem bam (that the penalty is stoning to death); a. fr.; v. also —Pl. , const. , 1) fathers, ancestors, patriarchs &c. Ber. 26$b$ prayers have been instituted by the Patriarchs; a. fr.—, v. supra. Ḥag. II,  a woman of noble descent. Num. R. s. 1; a. e.—Metaph. principal, chief, v. supra.  Kel. I, 1; v. supra.— (sing. ) the chief actionable injuries or damages, from which the subordinate are deduced . B. Kam. I, 1; a. e.—2) Aboth, the first section of the Prayer of Benedictions (v. ), so called because it alludes to the Patriarchs.


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 12 His presence soothed my yearning's thirst

While yet his lips were dumb;

For such compassion as his countenance wore

I had not seen nor felt in human face before.

And when, low-bending o'er his foe,

He took in his firm hand

My wasted one, I seemed to know

We two were of one Land;

And as my cheek flushed warm with young surprise,

God's pity looked on me from Lincoln's sorrowing eyes.

His prisoner I was from then—

Love makes surrender sure—

And though I saw him not again,

Some memories endure,

And I am glad my untaught worship knew

His the divinest face I ever looked into!


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Cause, Effect, Efficiency & Soft Systems Models

ABSTRACT
The logical connectives in the conceptual models of Soft Systems Methodology are limited to relations of "necessity". This is not enough to achieve a correspondence with states of affairs in the physical world. In order to attain this correspondence connectives representing "sufficiency" must be included. When this is done a logical account of efficiency is possible. This defines efficiency as the arbiter between two or more sufficient but unnecessary conditions of a desired effect.

Key Words: Information systems, Soft Systems Methodology, Modelling, Logic, Efficiency, Systems.

INTRODUCTION
During the last decade Soft Systems Methodology (SSM) has had considerable success as a general purpose problem solving methodology. The ability of SSM to address unstructured (soft) problems can be contrasted with traditional O.R. which aims at solving structured (hard) problems. Although there is a contrast this does not amount to an incompatibility. During the process of SSM analysis a soft problem will often turn into a hard problem which can be solved by structured methods.

A key device in SSM is the development of a conceptual model. This type of model is not intended to represent what exists but to represent a view of what could exist. The difficulty here is that having constructed a desirable conceptual model there is no guarantee that it will correspond to anything that actually can exist. In most uses of the methodology this does not matter as the primary aim is a change of perspective on the part of those concerned rather than a change in a state of affairs in the physical world. However, the models are sometimes used as the starting point for the design of information systems intended to support physical processes. In these cases a correspondence between the models and the physical world is required.

The relationships between concepts and the physical world form a substantial part of the subject matter of modern analytical philosophy. In the following, some of the tools used in the theory of knowledge, the theory of meaning and the philosophy of logic will be used to address the problem of how the models in SSM can relate to physical states of affairs.

In the first section an analysis of the logical status of SSM conceptual models is undertaken. It is suggested that a correspondence between the models and the physical world will hold if two conditions are met. Firstly, the terms or elements of the model must refer, directly or indirectly, to objects or events in the physical world. Secondly, the relations between the terms or elements in the models must have the same logical form as the relations that hold between the objects and events in the physical world. In respect of this last condition, SSM models are inadequate in their logical form. The elements in the models are connected only by relations of necessity. Relations of sufficiency are also required in order to match the causal sequences in the physical world.

The second section shows that sufficiency can be introduced into the models without difficulty. With this additional relation a logico-linguist model is produced which is exhaustive and capable of representing any conceivable state of affairs.

Section three considers applications resulting from the fact that a logico-linguistic model functions as a conceptual cause and effect diagram. The ability to represent all logical possibilities in a cause and effect sequence gives the model greater scope than the empirical models that tend to be used in quality control.

The fourth section discusses applications concerning efficiency. In SSM, a criterion for efficiency is one of three measures of performance that accompany every system, but it is not clear what this criterion is meant to operate on. It is suggested that efficiency can operate as the arbiter between two or more conditions that are sufficient for a desired effect. This gives efficiency a systemic and logical role that can be complimentary to quantitative accounts of efficiency in terms inputs and outputs.

The final section considers, briefly, how logico-linguistic models relate to information system design.

The outcome of using SSM
General descriptions of Soft Systems Methodology (SSM) are highly diverse. SSM has been characterized as a learning system [Checkland 1], part of a new paradigm for O.R. [Rosenhead 2] and as a front-end for information system design [Curtis 3, p 524]. However, such diversity is to be expected considering that its aim is to address any kind of unstructured "soft" problem in any organizational or social context.

SSM functions as a learning system because it facilitates a greater understanding of the problem situation on the part of those concerned. By bringing out the world views (Weltanschauung) of the people involved in the problem situation, SSM can produce various types of result. The problem might simply disappear as the result of a consensus. A fairly unstructured solution might result, such as agreement to adopt a new role for the organization. A third possibility is that the problem becomes structured, in this case a soft problem resolves into an identifiable "hard" problem. It is this third type of result that will be the subject of this paper.

The seven stage process
The classic SSM method is a seven stage process comprising: (1) entering the problem situation, (2) expressing the problem situation, (3) formulating root definitions of relevant systems, (4) building conceptual models of Human Activity Systems, (5) comparing the models with the real world, (6) defining changes that are desirable and feasible, and (7) taking action to improve the real world situation. [Checkland 4, Checkland & Scholes 5, Wilson 6].

The dynamics of the method come from the fact that stages (2) through (4) are always an iterative process. The stake-holders (defined as Client, Actors and Owner) engage in a debate guided by the analyst/facilitator. During this debate various root definitions (succinct statements of appropriate systems) and conceptual models are put forward, modified and developed until a desirable model is achieved by consensus. This model then forms the basis for real world changes.

Models and concepts
The conceptual models, therefore, have a vital role and it essential to understand that they are "notional"; they are not intended to represent an existing state of affairs.

"It cannot be emphasized too strongly that what the analyst is doing, in developing a HAS [Human Activity System conceptual] model, is not trying to describe what exists but is modeling a view of what exists." [Wilson 6]

The name "conceptual model" is ambiguous. It could mean a model of concept or it could mean a model that is conceptual. Wilson would seem to be saying that the SSM models are intended to be models of concepts. However, it is worth reflecting on the difference here.

We can distinguish between what models are and what models are models of. With the exception of iconic models, such as a scale model of Winchester Cathedral, most models are concepts. But they are, mostly, intended to be models of real world states of affairs. The value of a model is usually directly proportional to how well it corresponds to a past, present, future, actual or potential state of affairs. A model of a concept is quite different because in order to be a good model it need not have this real world correspondence.

Modelling concepts is by no means new. Plato's Republic begins by asking the question “What is justice?”. The book is essentially a model of this concept which when fully explored is seen to involve a model of an ideal society. Plato's method is to undertake an analysis of of the concept of justice in terms of its meaning and its logical relations to other concepts.

One of the features of modeling concepts is the ability to represent notions that have no easily defined physical equivalent. Rules, laws, values, and judgements can easily be represented. This, plus the ability to represent, compare and integrate various Weltanschauungen, gives models of concepts tremendous scope. This scope must always be greater than the scope of a model of a physical state of affairs for the simple reason that models of concepts are limited only by what is conceivable. As no model of a physical states of affairs can be inconceivable, every model of a physical state of affairs must be capable of being paired with a model of a concept. This unlimited modelling scope allows Checkland to achieve solutions that could not have been identified using models of actual states of affairs. This is particularly true where the problem has been non-physical i.e. a problem about goals, gaining a consensus, values etc.

Models of concepts and the physical world
In SSM it is not clear what sort of relationship can exist between a conceptual model (in the sense of a model of a concept) and the physical world.

When a physical solution is required to resolve a problem situation, Checkland does not, in practice, take the models far beyond a general description. This is clear in the results of case studies. In Checkland and Scholes Soft Systems Methodology in Action [5] the outcome of the case studies are described as changes in thinking or perspective, changes of role for the organization as a whole, problem identification, or what has been learned about the organization. While these changes in thinking have lead on to real world changes such as detailed organizational restructuring and new information channels, the real world changes were not specified by the methodology.

By contrast, the case studies in Wilson's Systems: Concepts, Methodologies and Applications [6] come up with specifications for new information processing procedures intended to support physical processes. This implies that there must be some relationship between the conceptual model and the information system; just as there must be some relationship between the information system and the physical process.

There is a prima facie dilemma here. What has been said so far is that a conceptual model need not be based on anything in the physical world. If this is so, then it would seem to follow that there can be no guarantee that a desirable conceptual model will ever correspond to anything in the physical world. The literature of SSM is not enlightening on this point. It is not clear how the transition from a model of a concept to a change in the physical world is effected. At stage (4) in the methodology we have a model of a view of what exists, but a view of what exists might bear no relation at all to what actually exists. In this case, the model can be no help in taking action to improve the real world situation as is required in stage (7). The most simple solution to the dilemma is to take the conceptual models to be a number of inductive hypotheses connected together. Given this, the models would be empirical and could be tested against events in the real world. However, this would mean that they are not models of concepts but models of putative physical states of affairs. As such they would not be significantly different from most other types of model.

A second solution to the dilemma is more difficult. This is to take the conceptual models as being logico-linguistic models. On this interpretation model building is a type of Wittgensteinian language game in which the stake-holders create an agreed language for describing the problem situation. The iterative process enables the sense (connotation, intension) of the various terms in the models to become fixed, thereby establishing a syntactical structure. In this way the models are analogous to formal systems such as arithmetic.

There are two requirements for a formal system to correspond to the physical world. The first is that its terms should have direct or indirect reference (denotation, extension) to objects, events or states or affairs in the physical world. The second is that the functional connectives should be capable of reflecting the behaviour of objects, the sequence of events or changes of states of affairs in the physical world. In arithmetic the terms are numbers, the functional connectives are addition, subtraction etc. In SSM models the terms are contained in the bubbles and the functional connectives are the arrows between the bubbles.

Exactly how reference is established, and what reference is, has been the subject of ongoing debate among some of the world's most eminent philosophers and logicians for nearly a century; from Meinong [7] to Kripke [8]. It is well beyond the scope of the present paper. However, although reference is difficult in theory it tends to be unproblematic in practice. If people can agree about the sense of a word there is usually no problem about establishing whether it has reference or not. In the present case, sense is unproblematic because it is established by building the model.

This leaves the second requirement. The most general principles governing the behaviour of objects, the sequence of events and changes of states of affairs in the physical world are the laws of cause and effect. The remainder of this paper will show firstly, that the connectives in SSM models do not reflect the laws of cause and effect, secondly, that this shortcoming can be easily avoided by a modification of the models, thirdly, that such modification could have interesting applications.

The logic of Soft Systems models
According to Checkland and Wilson the SSM modeling language consists of English verbs. These are formulated into elements which express commands. This has the advantage of being easily understood by the stake-holders in the client organization and this is essential as their participation is a fundamental requirement in the development of the model.

The connectivity between the elements is defined as "logical dependence" [Wilson 6, p26]. Thus, in Figure 1, r is dependent on u and v. This supports the view that the SSM conceptual models are intended to be models of concepts, rather than models of physical objects or events, because logical relations cannot exist between physical objects or events.

There is a problem here because the elements of the SSM models are commands and generally accepted logics only operate on truth bearers. Statements, or more strictly propositions, can be true or false and are, therefore, truth bearers. Commands can be neither true nor false and have no place in generally accepted logics. A logic of commands, an imperative logic, has been discussed by some authors [9] but Probert [10] finds that an imperative logic is not enough to fulfil the role required of it in an SSM model.

This problem can be easily overcome by replacing the imperative phrases in the models with declarative phrases. Instead of putting "wash rice" we could put "the activity wash rice has occurred" and now the truth of this proposition could be said to be dependent on the truth of the proposition "the activity obtain rice has occurred". Or, more concisely, we could say "rice is washed" instead of "wash rice" and "rice is obtained" instead of "obtain rice". Figure 2 shows how the commands of Figure 1 can be replaced by propositions.

The problem of insufficiency
Accounts of the logic of causation are in terms of necessary conditions, sufficient conditions and necessary and sufficient conditions [11-14]. Logical dependency, which is the only relation used in SSM models, is parallel to a necessary condition. If the truth of the statement "rice has been washed" is logically dependent on the truth of the statement "water has been obtained", then obtaining water will be a necessary condition of washing rice. However, the relation of logical dependency does not amount to sufficiency; obtaining water is not sufficient for washing rice.

In Figures 1 and 2 if we say r is logically dependent on u and v we are saying the same thing as saying u and v are necessary for r, but this does not mean that u and v are sufficient for r. The logical way of expressing this is to say that r implies u and v. In symbols:

$$r \to (u \And v)$$

Here the truth of r allows us to infer the truth of u and v. However, the truth of u and v does not allow us to infer anything about r. In causal terms the fact that r happens means that u and v must have happened but the fact that u and v happen does not mean that r will happen. If we think of the arrows as representing implication, as they do in symbolic logic, then the arrows point the wrong way in SSM models. The upshot of this, in simple English, is that the fact that rice and water are obtained does not mean that the rice gets washed. This entails that a physical system that is based on a model that contains only necessary conditions can never be guaranteed to work. It may work because the necessary conditions may in fact be sufficient but it is also possible that they might not be.

This deficiency can easily be remedied by adding another condition that, in conjunction with the existing conditions, forms a set which is sufficient. The way this can be done is shown in Figure 2. Here the set comprising w and u and v is sufficient for r. As each of these conditions (w, u and v) is also necessary for r, the set is a necessary and sufficient condition (N&S condition) of r.

In Figure 2 the new elements are agents which could correspond to people, machines or, in the case of an information system, a computer program. Traditional SSM models are models of human activity systems and it is reasonable to think that implicitly the presence of a human agent has been assumed.

Introducing SUN conditions
As well as necessary conditions and N&S conditions, conditions that are sufficient but unnecessary (SUN conditions) are required for a comprehensive account of causation. These are indicated by broken lines in the top part of Figure 2.

It is self evident that if it is true that polished rice is obtained then it will be true that rice is obtained. We can, therefore, say that obtaining polished rice is a sufficient condition of obtaining rice, and that "polished rice is obtained" implies "rice is obtained". While the truth of "polished rice is obtained" is a sufficient condition of the truth of "rice is obtained" it is not a necessary condition because rice can be obtained without obtaining polished rice, in the case in point rice can be obtained by obtaining unpolished rice.

The SUN conditions for any event, or for the truth of any proposition, form a set. The occurrence of the event or the truth of the proposition does not entail that any individual member of the set obtains or is true; however, it does require that at least one member of the set obtains or is true. This means that if we know that u is true then one of c, d, e and f must be true, if this is not the case then the set of SUN conditions for u (the set comprising c, d, e and f) will not be exhaustive. If the model is not exhaustive then it cannot be universal and cannot account for every case. The way to make sure that a model is exhaustive is to make sure that each set of SUN conditions cover all possibilities.

In Figure 2, c and d cover all the possibilities for b. That is, if polished rice is obtained then the rice that is obtained must be domestic or imported. There is no other possibility, therefore, c and d form an exhaustive set of SUN conditions for b.

The break down of q, in Figure 2, has deliberately been left so that it is not exhaustive. It is reasonable to think that if rice can be cooked with borrowed equipment it can be cooked with stolen equipment. Therefore, "equipment is stolen" is a SUN condition of q. The easiest way to correct this is to include "equipment is stolen" as an additional element. However, in many cases the stake-holders would not want to consider the possibility of stealing being part of their system. Fortunately other solutions are possible. We can omit stealing from the model but still make it exhaustive by altering p from "rice is cooked" to "rice is cooked by legal means". In this way the models begins to become linguistically as well as logically dynamic.

A third possibility is to take it that "legal means" is part of the Universe of Discourse for the system. That is, we can take it that the model is not intended to cover all possibilities but only to legal possibilities. This limitation could be recorded by amending the root definition to include legality.

Other SUN conditions for q readily spring to mind. For example, there might be the possibility of inheriting equipment. This will depend upon the “Owner” of the system and this will be specified in the root definition. If the owner of the system is a commercial company, inheritance is not a possibility, but there is the possibility of acquiring equipment by bequest. Thus the root definition will, in part, determine what can form an exhaustive set of SUN conditions.

This going back to modify the root definition following an inadequacy in the model would be undertaken as part of the iterative process. The interrogation of the stake-holders' concepts is a large part of what the model building is about.

With the inclusion of necessary, N&S conditions and SUN conditions conceptual models are capable of representing any conceivable cause and effect sequence. These types of model will have far greater scope that models which are based directly on past experience.

Ishikawa's diagrams
Cause and effect diagrams are closely identified with the name of Ishikawa [15]. His book on quality control devotes considerable space to the subject. Ishikawa's account of causation is inadequate in two ways. Firstly, he does not distinguish between necessary conditions and sufficient conditions. Secondly, he does not take logical possibilities into account.

There is some dispute about what is meant by “a cause”. Papineau [13] takes a cause to be a sufficient condition. Taylor [14] takes it to be an N&S condition. Mackie [12] argues that what is ordinarily meant by a “cause” is an insufficient but non-redundant part of an unnecessary but sufficient condition. Nevertheless, the distinction between necessary conditions and sufficient conditions is the starting point of the analysis of causation, and this is for the simple reason that in ordinary language the word “cause” is sometimes used in the sense of necessary condition and sometimes in the sense of sufficient condition [Copi 11, p 322].

Ishikawa fails to event mention this distinction. For Ishikawa "a cause" is broken down into other causes and these in turn can be further broken down into other causes. At any given point, therefore, it is difficult to understand what Ishikawa means when he uses the word "cause". He could be meaning a necessary condition, a sufficient condition, or a necessary and sufficient condition.

The Fishbone Diagram shown left gives only the general outline of an Ishikawa diagram. A fully detailed diagram is to be found on page 153 (figure 13.6) of the Ishikawa's Guide to Quality Control [15]. In the detailed diagram the effect, delicious rice, is represented at the end of the main arrow. Leading into this are four arrows labelled "Pretreatment (washing)", "Raw Materials (rice)", "Equipment (cooker)", and "Second treatment (steaming)". It appears that these are meant to represent necessary conditions but it is not clear if they are meant to represent a set that is sufficient.

At the lowest level the diagram seems to list SUN conditions. The the upper right part of the diagram would seem to be saying that obtaining rice from Thailand or obtaining rice from China are SUN conditions of obtaining rice from foreign countries. However, it seems unlikely that these could be intended as an exhaustive set of SUN conditions. If it was so intended it would mean that it would be impossible to make delicious rice from, say, American rice or Indian rice. A more probable explanation is that Thai and Chinese rice were the only types of foreign rice that Ishikawa had come across when he constructed his cause and effect diagram.

The rice diagram is one of the most comprehensive of the Ishikawa diagrams. In practice, cause and effect analysis in the Ishikawa tradition sometimes gives little more than an ordered sequence of events that have been involved in a production or distribution system (for example, see Jones & Clark [16]). Ishikawa's research method is confined to the study of the past performance of a system. Like all such work its scope is very limited. It tells us very little about what could happen nor, in a rapidly changing environment, is it likely to tell us what will happen.

Conceptual Cause and effect models
Distinguishing between necessary conditions and sufficient conditions has fairly obvious applications in operations. If we want to bring about a given effect all we have to do is bring about an event that is sufficient for that effect. If we want to stop an effect all we have to do is eliminate a factor that is a necessary condition of that effect.

The distinction between various types of causal conditions is made in the physical sciences and these are empirically based. It is not, therefore, necessary to build a logico-linguistic conceptual model in order to make the distinction. However, building one of these models will force the distinction to be made and will force it to be made in a structured context. This could help to eliminate errors of a logical kind.

The greatest advantage of logico-linguistic models over the Ishikawa type is the fact that they can cover all logical possibilities. This brings us back to the point that a conceptual model need never have a smaller scope than an empirically based model. This is because anything that is known empirically is conceivable and can, therefore, be included in a conceptual model. By contrast some things that are conceivable can never be known empirically.

Efficacy, Efficiency and Effectiveness
Checkland & Scholes indicate that most systems should be accompanied by three measures of performance: efficacy (E1), efficiency (E2) and effectiveness (E3).

The criterion for efficacy will tell us whether the desired effect has occurred or not. In the case of Figure 2 this will amount to whether p is true or not. If p is false we know that t or r or q or s must be false, and if r is false we know that w or u or v must be false. From this an algorithm can be formulated that will find the faults in a system and take remedial action (Gregory 17). E1, therefore, has a useful role.

Effectiveness is the measure of whether the system meets a longer term aim. In the case of our example this might be to enjoy a good meal. The criterion for E1 would be is rice cooked? If the criterion for E1 is met it remains an open question whether the criterion for E2 is met. The fact that rice has been cooked does not entail that we enjoy a good meal. Better systems might be to fry potatoes, go to a restaurant or to hire a caterer. E2, therefore, also has a useful role.

Problems arise when we come to consider efficiency. Checkland & Scholes define efficiency as "amount of output divided by amount of resources used" [5]. There is a difficulty here because SSM models consist entirely of necessary conditions. If a system is to work, no necessary condition can be left out. This means that any system that consists entirely of necessary conditions can operate in only one way. Which leaves the question: what is the criterion for efficiency meant to measure?

For example, if fermenting mashed apples is a necessary condition of making cider, then it is pointless to ask if fermenting mashed apples is an efficient way of making cider. This question would only make sense if there was another way of making cider by, say, fermenting mashed pears. The question of efficiency only arises when there is more than one possible way in which the transformation can be achieved.

It has been suggested that this problem can be solved by taking the model to a higher resolution level. This is the traditional way of putting more detail into a conceptual model and is similar to the way a data flow diagram is decomposed. However, this is no solution because the decomposition would still be in terms of necessary conditions.

For example, in Figure 1 activity r “wash rice” could be expanded to g “immerse rice in water”, h “agitate rice in water”, i “drain rice after agitation”. These would be connected in the normal fashion such that g is a necessary condition of h and h is a necessary condition of i. The set g and h and i is the logical equivalent of r. In other words to say “wash rice” is the same thing as to say “immerse rice in water, then agitate it and then drain it”.

The decomposition theory would only solve the difficulty with efficiency if there were a number of different ways in which each element could be decomposed. If this were the case each decomposition would have to be a SUN condition of the base level element. The SUN conditions into the models can provide the role for the criterion of efficiency. We can say that the system is efficient if the only SUN conditions that are true are those that meet the criterion of efficiency. Suppose that the criterion for efficiency is low cost and it is true that polished rice is obtained. In this case our system can only be called efficient if the cost of polished rice is lower than, or the same as, the cost of unpolished rice.

This lends itself to quantitive interpretation. In the context of c, d, e and i from Figure 2 we can talk about the degree of efficiency. If unpolished rice is cheaper than polished rice and domestic rice is cheaper than imported rice, then the system will be most efficient if domestic unpolished rice is obtained; it will be least efficient if imported polished rice is obtained, and will be of intermediate efficiency if either imported unpolished or polished domestic rice is obtained.

In a real world situation the criterion for efficiency is likely to be more complex than low cost. It is likely to be a ratio of time and costs and involve certain thresholds. While this might involve considerable mathematics and complicate the data collection to support the system, it does not effect the basic logic of the system. It is worth pointing out that there is nothing in the logic of SSM that requires that the criterion for efficiency be qualitative. In the example the criterion for efficiency could be palatability. In this case the system would be efficient only if it is the case that all the SUN conditions that are true are those that result in tasty cooked rice.

We can take this account of efficiency in terms of SUN conditions to be a logical concept of efficiency. As such it can be contrasted with the mathematical concept.

Mathematical concepts of efficiency
The mathematical idea of efficiency takes a system to consist of inputs, a black box and outputs. A system A will be taken to be more efficient than system B if the ratio of outputs to inputs is higher in A than in B. Data Envelopment Analysis is more sophisticated but the black box remains and, for the purposes of this discussion, it can be treated as the same as the simple input/output account.

While the mathematical concept will help to identify efficiency it does not identify the cause of efficiency. Given two systems, A and B, with comparable inputs and outputs but in which A is determined to be more efficient, there are there are possibilities as to the cause:

1 The cause of efficiency is external to the systems.

2 The cause of efficiency is internal to the systems.

3 The cause of efficiency is both internal and external to the systems.

If the cause is a factor that is external to the system then it would seem that the cause is really an input, but perhaps one that has been overlooked. Let us suppose that A and B are farms in which the inputs are seed, fertilizer, manpower and equipment, and the output is grain. Let us suppose A does better then B because A is situated in a place where the weather is better than it is at the location of B. We do not want to say that the weather is internal to the systems as far as efficiency is concerned. This is because our concept of efficiency, unlike the concept of productivity, requires that we can make changes that can improve it. So, as we cannot change the weather we add it to the list of inputs. If the weather was the only cause of the low productivity of B, then B should now have the same efficiency rating as A.

Given this we must conclude that any true cause of efficiency is internal to the system. But if the cause of efficiency is internal an analysis of inputs and outputs cannot locate it. To identify the cause of efficiency or inefficiency of two systems would require a comparison of their internal configuration. Logico-linguistic conceptual models are one of the ways in which a system's internal configuration can be described.

A logical concept of efficiency
Figure 4 gives a model of a system to make chair legs. The input for the system is square lengths of wood and the output is round lengths with holes provided for cross piece joints.

The model serves to illustrate how time can be introduced into the models as well as showing how causes of efficiency can be identified. If the final event, p, takes place at T, then q, s, r and w must take place at T minus 1. If q, s, r and w take place at T minus 1, then u, b, a, c and v must take place at T minus 2.

There are two ways in which this system can operate. One is by drilling the holes in the square lengths and then making the lengths round on the lathe; this way invokes the w SUN condition. The other is to make the lengths round and then drill the holes; this way invokes the s SUN condition.

Given a criterion for efficiency as the number of lengths produced per day, it is quite likely that one method will conform to the criterion better than the other. It might be that difficulties in positioning a round piece of wood prior to drilling make the s route less productive. Alternatively a hole in the length might interfere with the smooth operation of the lathe, making the w route less efficient.

To determine which of the possibilities is, in fact, the most efficient, would require experiment or monitoring the system in real world application. However, the important thing here is that this question of efficiency was recognized without comparison with other systems as would be required for an input/output account of efficiency. The other important thing is that the parameters of efficiency here have been recognized without acquaintance with any real world chair leg making system. This suggests applications in a green field situation.

APPLICATIONS OF THE MODELS – INFORMATION SYSTEMS
Ideas on the subject of SSM and information system design can be divided into three positions. The first position sees conceptual modelling as a front end to other systems analysis methodologies such as SSADM or Information Engineering (Curtis, 6). On this view conceptual models have a minor role which is limited to helping analysts to understand the social context in which they are working. Implicit in this view is the belief that the conceptual models have no logical, epistemological or methodological connection to information system design as such. If this is correct SSM and conceptual modelling techniques will be unable to solve the fundamental problems that are now becoming apparent in traditional systems analysis.

The second position takes conceptual models not to be models of concepts but models of states of affairs. This is the way in which conceptual models are used by Avison and Wood-Harper in the “Multiview” (18) information systems development methodology. They say that the arrows in conceptual models are used to “join the activities that are logically connected to each other by information, energy, material or other dependency”. As has been stated above logical connectives are quite different from physical ones. It is clear that Avison and Wood-Harper are confusing relations between ideas with ideas of relations. Their models are not models of concepts but data flow diagrams based on general knowledge; as such their method is not significantly different from traditional methods.

The third position is Wilson's Information Requirements Analysis which suffers from the absence of N&S and SUN conditions.

The logico-linguistic interpretation of conceptual modeling, which has been developed in this paper, avoids the difficulties in the second and third positions. It does not solve all the logical, epistemological and methodological problems needed to resolve the first position. This is because a procedure for establishing the reference of the terms in the models still needs to be established. Nevertheless, it does lead in the direction of a derivation of an information system design from a conceptual model.

CONCLUSIONS
The main objectives of this paper have been twofold. Firstly, to show that SSM conceptual models of human activity systems can be interpreted as models of concepts. Secondly, to show that, under this interpretation, the logic of the models can be developed to a point where it is capable of reflecting cause and effect relations in the physical world. The resulting logico-linguistic models, to a large extent, bridge a gulf between soft systems and hard O.R. This theoretical thesis has three areas of application.

The logico-linguistic models are capable of an exhaustive description of cause and effect. It has been shown that with cause and effect diagrams of the Ishikawa school this is not possible due to limited scope. These diagrams are in any case inadequate due to the fact that they fail to distinguish between sufficient conditions and necessary conditions.

With regard to efficiency it has been shown that the input/output account of efficiency is not in itself capable of identifying the cause of inefficiency and that such identification is dependent upon a logical concept of efficiency. The logic-linguistic models are capable of expressing this concept and, therefore, could, in conjunction with quantitative analysis, be used to identify the true cause of inefficiency.

The applications in information system design have only been briefly discussed. It has been shown how some of the constrains on taking SSM through to information system design can be avoided but it is clear that more research is needed in this area.

ACKNOWLEDGEMENTS
The findings in this paper were the result of research funded by the Science and Engineering Research Council (SERC).


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Talk:Cause, Effect, Efficiency & Soft Systems Models

This paper is in process of being uploaded and edited by the author--Logicalgregory (talk) 05:45, 29 November 2010 (UTC) Upload is now complete, but some sections required re-typing and proof reading is needed.--Logicalgregory (talk) 11:25, 2 December 2010 (UTC)

In the Introduction section, O.R. is mentioned. Does this refer to Operations research?

Peter Riches (talk) 01:02, 18 February 2011 (UTC)

 * More or less, Operations Research is the term used in the USA while Operational Research is the term used in the UK. Some however, would argue that Operational Research has a wider scope. Soft Systems is part of Soft OR, and Soft OR is not well known in the USA. Thanks for your interest.--Logicalgregory (talk) 07:25, 18 February 2011 (UTC)


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Page:The Unconquered Air, Coates, 1912.djvu/30

 DEATHLESS DEATH

who have seen the seed fall without sound

Into the lifeless ground,

Through wintry days are tempted to forget

How Spring will come with the first violet

In her dark hair,

Fresh and more fair

Than we remembered her, a glad surprise

In the veiled azure of her shadowy eyes.

Fear doth the heart deceive,

And still we grieve

Where we should lift the voice

In triumph, and rejoice

Amid our sorrow,

Because of what the past

Has given that is beauteous and shall last—

A heritage of blessing for the morrow.

Lo, in what perfect trust

Nature confides her darlings to the dust!

The rose, the crocus, the narcissus sweet,

She lays to rest, undoubting, at her feet 14


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 'Who wins, or the Widow's Choice' (Covent Garden, 25 Feb.). and in 1810 wrote music for F. Reynolds's 'Bridal Ring' (Covent Garden, 16 Oct.) In the same year 'Transformation,' ascribed to Allingham, with music by Condell, was produced by the Drury Lane company at the Lyceum (30 Nov.) In 1811 he gained a prize at the Catch Club for his glee 'Loud blowe the wyndes.' Condell also wrote overtures to 'The House to be sold,' probably Kelly's opera, which was played at Drury Lane in 1802, and to 'Love laughs at Locksmiths,' besides some incidental music in 'Aladdin,' performed at Covent Garden, a set of six songs dedicated to Lady Lake, and a few harpsichord duets. He died at Cave House, Battersea, after a severe and lingering illness, on 24 June 1824.


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 Rh Who from the meadows bright

Was snatched away to rule in the sad light

Of Hades, and to learn

Its lessons stern.

For Nature's faith is deep

That, waking from the dark and dreamless sleep,

Her flowers toward the sun shall wistful yearn,

And in the fragrant breast of Proserpine return.

Ah, lover true of men,

Forgive, forgive us, then,

If choked by tears we falter in our praise,

Remembering that we no more again

Shall hold glad converse with thy spirit brave,

Nor from thy lips hear words that lift and save,

Through all the lengthening number of our days!

By the great Silence thou art set apart

From all the restless travail of the heart

That beats in us

So passionate and strong—

Art passed beyond the evening angelus

And Memnon's morning song.

Man's life on earth—how brief!

Yet we with Nature hold the high belief,

E'en when our hearts are breaking,

That death is but the vital way,


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 16 Darkness the shadow of the day,

And sleep the door to waking!

And shall we still with tears

Pay tribute sad to one whose soul endears

Even the dark, dark river it hath crossed?

Shall we in grief forget

The sweetness and the glory of our debt,

And that no good, once given, can be lost?

Distant thy dwelling seems,

Poet and patriot!—but, ah, thy dreams

Are living as the flame of sacrifice!

Therefore love's roses now

We lay amidst the laurel for thy brow,

Grateful that souls like thine our earth emparadise.


text: Dictionary of National Biography, 1885-1900/Colwall, Daniel


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COFFIN, ROBERT ASTON, D.D. (1819–1885), catholic prelate, was born at Brighton on 19 July 1819. and educated at Harrow School and at Christ Church, Oxford (B.A. 1841, M.A. 1843). In 1843 he became vicar of St. Mary Magdalene, Oxford, but he resigned this preferment two years later,and was received into the Roman catholic church on 3 Dec. 1845. For a year after this he resided with Mr. Ambrose Lisle Phillips at Grace Dieu manor, and then be proceeded with Dr. (now Cardinal) Newman to Rome, where he was ordained priest in 1847. He joined the oratory of St. Philip Neri, and in 1848-9 he was superior of St. Wilfrid's, Cotton Hall, Staffordshire. Feeling strongly drawn to the congregation of the Most Holy Redeemer, he entered the novitiate of the Redemptorist Fathers at Trond in Belgium, and made his profession on 2 Feb. 1852. In 1855 he was chosen rector of St. Mary's, Clapham, and in 1865 appointed to the office of provincial, in which he was successively confirmed every three years until his elevation to the episcopate. From 1852 to 1872 he was almost constantly employed in preaching missions and giving clergy retreats throughout England, Ireland, and Scotland. In April 1882 Pope Leo XIII nominated him to the see of Southwark, in succession to Dr. James Danell. He was consecrated by Cardinal Howard in the church of St, Alfonso, on the Esquiline, at Rome, 11 June 1882, and enthroned at St. George's Cathedral, Southwark, on the 27th of the following month. He died at the house of the Redemptorists at Teignmouth on 6 April 1885.

He published excellent English translations of many of the works of St. Alphonso de' Liguori; and of Blosius's 'Oratory of the Faithful Soul.'

COGAN, ELIEZER (1762–1855), scholar and divine, born at Rothwell, Northamptonshire, in 1762, was the son of John Cogan, a surgeon, then sixty-four years old. The father, who survived until 1784, and was the author of ‘An Essay on the Epistle to the Romans’ and of other anonymous pieces, married twice; by his first wife he had a son, called [q. v.], the physician, and by the second he was the father of Eliezer. The boy had a wonderful memory, and mastered the Latin grammar before he was six years old. For six months he was placed at Market Harborough in the school of the Rev. [q. v.], but his early life was mainly passed under his father's roof, and he was self-taught in the rudiments of Greek. To complete his education he was sent to the dissenting academy at Daventry, where for the space of six years, three as pupil and three as assistant tutor, he had the advantage of the society of [q. v.] There were at this time about fifty pupils in that institution, and nearly the whole of them became distinguished in after life as unitarians. When the Rev. John Kenrick moved from Daventry to Exeter in 1784, his place was taken by Cogan, who thus became Belsham's colleague in the work of instruction. In the autumn of 1787 Cogan was elected as minister of the ancient presbyterian congregation at Cirencester, and continued in that position until 1789. During this period of his life he printed for his friends, though he did not publish, a ‘Fragment on Philosophical Necessity.’ On 21 Sept. 1790 he married Mary, the daughter of David Atchison of Weedon, and in the following July he settled for a short time at Ware in Hertfordshire, but after a few months he removed first to Enfield and then to Cheshunt. Cogan was elected minister of the chapel in Crossbrook Street, Cheshunt, in 1800, and in January of the subsequent year he was appointed to a like position over the dissenting congregation at Walthamstow. During that year he preached alternately there and at Cheshunt, but at its close he transferred his school from Cheshunt to Higham Hill, Walthamstow, and confined his ministerial services to the congregation of the latter village. The school over which he presided soon reached to great fame, the secret of his success as a teacher lying in his zeal for his labours and his skill in laying the foundations of instruction. Among his pupils were Samuel Sharpe, the Egyptologist and translator of the Bible, Benjamin Disraeli, afterwards earl of Beaconsfield (of whom he used to say, ‘I don't like Disraeli; I never could get him to understand the subjunctive’), Mr. Milner Gibson, Mr. Russell Gurney, and Lord


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 . He preached his farewell sermon at Walthamstow on the last Sunday of 1816, and in 1828, after thirty-six years of scholastic life, during which he had never been absent from his duties in pursuit of pleasure, he withdrew from the task of teaching into private life. His portrait in life-size was painted at the cost of his pupils by Thomas Phillips, R.A., and engraved by Samuel Cousins, and the picture was presented to him at a dinner at the Albion tavern on 20 Dec. 1828. Cogan lived many years after his retirement, his days being passed in incessant reading. Whether he walked in the streets of London or in the country lanes of Hertfordshire, a book was his companion, and at the time of his death he is supposed to have read more Greek than any of the students whom he left behind him. He died at Higham Hill on 21 Jan. 1855, and was buried on 27 Jan. in a vault in the burial-ground at the Gravel Pit Chapel, Hackney, which contained his wife's remains. She died on 1 Dec. 1850, aged 81.

Cogan had a high reputation as a Greek scholar. In the section of 'Porsoniana' appended to Dyce's 'Table-talk of Samuel Rogers,' p. 302, occurs the anecdote that when Cogan was introduced to Porson with the remark that he was intensely devoted to Greek, the reply of Porson was, 'If Mr. Cogan is passionately fond of Greek, he must be content to dine on bread and cheese for the remainder of his life.' Dr. Parr highly praised Cogan's 'intellectual powers, his literary attainments, and candour,' and in 1821 stated that he had given directions that on his death a ring should be presented to Cogan. His works were numerous. To the 'Fragment on Philosophical Necessity,' already mentioned, must be added: 'An Address to the Dissenters on Classical Literature,' 1789, in which he strongly urged the study of the classics. 'Moschi Idyllia tria, Græce,' 1795, which he edited with notes for the use of his scholars, but afterwards suppressed. 'Reflections on the Evidences of Christianity,' 1796. 'Purity and Perfection of Christian Morality,' 1800. 'Christianity and Atheism compared,' 1800. To this an answer was issued by a Mr. Robinson, whereupon Cogan published: 'An Examination of Mr. Robinson's reply to Mr. Cogan on the Practical Influence of a belief in a Future State,' 1800. 'Sermons chiefly on Practical Subjects,' 1817, 2 vols. 'Contributions to the Monthly Magazine, Dr. Aikin's Athenæum, the Monthly Repository, and the Christian Reformer, by the late Rev. Eliezer Cogan, 2 parts, I. Classical; II. Theological, Metaphysical, and Biblical. Extracted and compiled by his son, Richard Cogan,' 1856. He was the author of several sermons on the deaths of members of his congregation at Cheshunt and Walthamstow, and he read in manuscript and suggested some alterations in Dr. Alexander Crombie's 'Natural Theology' (1829). Dr. Priestley was his guide in theology and metaphysics. A long memoir of Cogan appeared in the 'Christian Reformer,' xi. 237–59 (1855), and was printed at Hackney as a pamphlet the same year. His daughter, Mrs. Gibson of Tunbridge Wells, printed recently for private circulation twenty-five copies of a little work entitled 'Recollections of my Youth,' giving some pleasing particulars of school-life under Cogan.

 COGAN, THOMAS (1545?–1607), physician, was born about 1545 at Chard, Somersetshire. He was educated at Oxford, graduated B.A. 1662-3, M.A. 1666, and M.B. 1574. He became fellow of Oriel in 1663. In 1574 he resigned his fellowship, and then (or in 1575) was appointed master of the Manchester grammar school. He practised as a physician at Manchester. Before 1686 he married Ellen, daughter of Sir Edmund Trafford, and widow of Thomas Willott, who had property in Manchester. In 1591-3 he was the family physician of Sir Richard Shuttleworth. In 1595 he presented Galen's works and other medical books to the library of Oriel, where they are still preserved. He resigned the schoolmastership before 1602, died in June 1607, and was buried on the 10th of that month in the church at Manchester. His will mentions property both in Somersetshire and Manchester, and bequeaths books to all the fellows and other officers of the college, and 4d. to each boy in the school. His widow died in December 1611.

His works are:

 * 1) 'The Well of Wisedome, containing Chiefe and Chosen Sayinges … gathered out of the Five Bootes of the Olde Testament …,' 1577.
 * 2) 'The Haven of Health, made for the comfort of Students …,' 1584 (several later editions). With this was published 'A Preservative from the Pestilence, with a short censure of the late sickness at Oxford,'
 * 3) 'Epistolarum familiarium M. T. Ciceronis epitome …' (with an 'Epistle to all Schoolmasters,' the book being intended as an introduction to Latin). Wood also mentions:
 * 4) 'Epistolæ item aliæ familiares Ciceronis,'
 * 5) 'Orationes aliquot faciliores Ciceronis.


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COGAN, THOMAS (1736–1818), physician and philosopher, born at Rothwell in Northamptonshire on 8 Feb. 1736, was the half-brother of [q. v.] For two or three years he was placed in the well-known dissenting school at Kibworth Beauchamp, but was removed from this establishment at the age of fourteen, and spent the next two years with his father. He was then sent to the Mile End academy, where Dr. John Conder was the divinity tutor, but being dissatisfied with its management was transferred at his own request to a similar institution at Homerton. Doubts as to the truth of the doctrines of Calvinism prevented him from joining the dissenting ministry. While he was undecided an accident induced him to cross in 1759 from Harwich to Holland, where he found that the Rev. Benjamin Sowden, the English minister of the presbyterian church, maintained at Rotterdam, by the joint authority of the English and Dutch governments, with two pastors, required a substitute to enable him to revisit his native shores. Cogan promptly applied for and obtained the place. He still, however, continued to seek for a pastorate over a dissenting congregation in England, and about 1762 he was selected as the minister of a chapel at Southampton, where he soon publicly renounced Calvinism and adopted the doctrines of unitarianism. A quarrel with his congregation naturally followed, and Cogan thereupon returned to Holland, becoming the junior minister of the English church at the Hague. He was introduced to Mr. Graen or Groen, originally a silversmith at Amsterdam, and afterwards a banker, and was wooed and won, as the story goes, by the banker's only daughter, a beauty and an heiress, with a fortune of eight or ten thousand pounds. It was a condition of the marriage that Cogan should enter the more settled profession of medicine, and he accordingly matriculated at Leyden on 16 Oct. 1765, and took his degree of M.D. in 1767. Restlessness was his characteristic in early life, and he is said to have practised during the few years which he passed in Holland ‘successively at Amsterdam, Leyden, and Rotterdam.’ From the latter city he returned to London and settled in Paternoster Row, where he soon obtained a lucrative practice, especially in midwifery. This could not well have been later than 1772, and by 1780 he was once more in Holland. According to one account his labours had told on his health, according to another the fortune which he had inherited and the fees he had pocketed during his short term of professional life satisfied his desire for wealth. In 1780 at any rate he resigned his connection to Dr. John Sims, for many years the leading accoucheur in London, and retired to Holland to prosecute his studies in moral philosophy. To gratify his wife they rented the noble mansion of Zulestein, the ancestral home of the family ennobled in this country by the title of Rochford, and in this magnificent retreat they dwelt until the invasion of Holland by the French republicans in 1795 drove them once more back to Harwich. After resting for a time at Colchester, so as to be in a convenient position to return to Holland on its liberation from the invader, Cogan and his wife fixed their home at Bath. Although authorship was always his chief pleasure, a subordinate attraction was now found in farming. He rented a farm at South Wraxall, near Bradford-on-Avon, studied agriculture, practically and scientifically, competed for and won some of the prizes awarded at the meetings of the Bath and West of England Society, and if he did not by his exertions materially add to his resources, at least he found pleasure in his work and preserved the natural vigour of his mind. Farming remained a joy to him throughout his life; when he quitted Bath he took farms at Clapton and at Woodford, and at the time of his death he was the tenant of a farm near Southampton. Mrs. Cogan died at Bath in 1810 and was buried at Widcombe; her niece, Miss Gurnault, died soon after. Cogan gave up housekeeping at Bath and removed to London. The last years of his life were mainly passed in his lodgings in London or at his brother's house at Higham Hill. On the closing day of 1817 he caught a cold by walking in a thick fog from his rooms in Covent Garden to visit a friend. A few weeks later he went to his brother's with a presentiment that he could not recover, and died there on 2 Feb. 1818. On 9 Feb. he was buried at Hackney. His vivacity and good temper remained with him until the last.

Cogan's thesis for his medical degree at Leyden was delivered there on 20 Feb. 1767, and printed in the same year. It was entitled ‘Specimen Medicum inaugurale de animi pathematum vi et modo agendi in inducendis et curandis morbis,’ and could have been amplified by him had not a want of leisure at first and the subsequent labours of others rendered such a proceeding unnecessary. A society for the preservation of life from accidents in water was instituted at Amsterdam


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 in 1767, and its operations became known to Cogan. On his return to England a few years later he found that Dr. William Hawes had expended much time and money on a similar project, and the two doctors thereupon united their energies in the undertaking. Each of them brought fifteen friends to a meeting at the Chapter Coffeehouse in St. Paul's Churchyard in the summer of 1774, when the Royal Humane Society was duly formed. Cogan translated from the original Dutch in 1773 the ‘Memoirs of the Society instituted at Amsterdam in favour of Drowned Persons,’ 1767–71, and prepared the first six annual reports of the English society. His interest in this charitable work lasted unimpaired throughout his life. He started a branch at Bath in 1805, and left the mother-foundation in his will the sum of 100l. One of the five gold medals minted for the society is inscribed to the memory of Cogan, and in its annual report for 1814 is a portrait of him, with a handsome eulogy of his talents as an author and of his zeal as the co-founder of the Royal Humane Society. His next publication was an anonymous account of ‘John Buncle, junior, gentleman,’ 1776, which purported to be a memoir of the youngest son of Thomas Amory's whimsical creation of John Buncle, by his seventh wife, Miss Dunk. In 1793 he published, without his name, two volumes entitled ‘The Rhine; or, a Journey from Utrech [sic] to Francfort [sic], described in a series of letters in 1791 and 1792.’ The success of this labour justified its republication in 1794 with his name on the title-page, and the printing at Haarlem of a Dutch translation in 1800. This translation of Cogan's work into Dutch was balanced by his translating into English from that language in 1794 the work of Professor Peter Camper, ‘On the Connexion between the Science of Anatomy and the Arts of Drawing, Painting, Statuary.’ All these books were, however, eclipsed by his elaborate treatises on the passions. The first of them bore the name of ‘A Philosophical Treatise on the Passions,’ 1800, 2nd edit. 1802. Then succeeded an ‘Ethical Treatise on the Passions,’ in two parts, the first of which appeared in 1807 and the second in 1810. Two volumes of ‘Theological Disquisitions on Religion as affecting the Passions and on the Characteristic Excellencies of Christianity’ followed in 1812 and 1813 respectively, and the whole five treatises were published in a set in 1813. Last of all came in 1817 a bundle of ‘Ethical Questions, or Speculations on the principal subjects of Controversy in Moral Philosophy.’ His design was ‘to trace the moral history of man in his pursuits, power, and motives of action,’ and the excellence of his definitions and illustrations has been highly extolled. He analysed the subject with as much tenderness as he had been taught to dissect the human body. A long analysis of Cogan's writings will be found in Jared Sparks's ‘Collection of Essays and Tracts in Theology’ (1824), iii. 196–233, which also contains (pp. 237–362) a reprint of his ‘Letters to William Wilberforce on the doctrine of Hereditary Depravity, by a Layman’ (pseud. i.e. T. Cogan), in which he warmly denounced the view supported by Wilberforce in his ‘Practical View of the prevailing Religious Systems of Professed Christians,’ and strongly argued, as he always did, for the happiness of all mankind. These letters originally appeared in 1799, and were printed in more than one cheap edition for the use of the unitarian book societies. A fragment of his ‘Disquisition on the Characteristic Excellencies of Christianity’ was appended in 1822 to a discourse by Lant Carpenter [q. v.] A miniature portrait of Cogan is preserved in the museum at Bristol.

[Gent. Mag. lxxxviii. pt. i. pp. 177–8, 648 (1818); Nichols's Lit. Anecd. ix. 181, 239, 732; Jay's Autobiography, pp. 465–70; Monthly Repository, xiv. 1–5, 74–6, 105 (1819), with portrait; Annual Biography, iii. 73–99 (1819); Hunter's Old Age in Bath, Sherwen and Cogan (1873), pp. 29–56; Notes and Queries, 5th ser. ix. 116 (1878).]   COGAN, WILLIAM (d. 1774), philanthropist, son of John Cogan by Elizabeth, daughter of John Battie, was a citizen of Kingston-upon-Hull of which town he was chamberlain in 1712, sheriff in 1714, and mayor in 1717 and 1736. In 1753 he founded a charity school for twenty girls In Salthouse Lane, Kingston-upon-Hull, endowing it with stock to the amount of 2.000l., which he subsequently increased by 500l. He lived on terms of intimacy with the Wilberforces and other benevolent families. By his will he bequeathed 2,000l. in trust for apprenticing poor lads to certain trades. He died in 1774.  COGGESHALL, HENRY (1623–1690), mathematician, was the third son of John Coggeshall of Orford in Suffolk, where he was baptised 23 Dec. 1623, and buried 19 Feb. 1690. He married, and left one son, William Coggeshall of Diss, Norfolk. He invented the sliding-rule known by his name, first described by him in 1677 in a pamphlet entitled. 'Timber-Measure by a Line of more Ease, Dispatch, and Exactness than any other