again. Thus, upon the probability that bodies will continue to fall to the ground; that violent motion will be followed by heat; that similar inducements or motives will be followed by similar acts in men; we found the doctrine of cause and effect, and establish our knowledge of physical and moral history, so as to give credit to the past, and confidence in many respects to the future. It is evident that analogical propositions have much less certainty than those of in tuition or demonstration. Though in our investigations of truth we must necessarily have recourse to observations of individual objects and events, as the ground-work of all; yet in our inductions, reasonings, proofs, and processes of instruc tion, we proceed from generals to individuals. And, as in strict demonstration the subject and predicate of a proposition are connected by a train of axioms,-so in every other argumentation it will be the endea vour of a wise man to follow the same course as nearly as may be possible. But, from the confusion arising from the relations of the complicated objects of social intercourse, and from the rapidity of language with its abridgements and transpositions, so many things are left to be understood that it is not often an easy task to show, whether the reasoner does really pursue the course of pure argumentation, or whether he deceives himself or others. Logicians have therefore adopted a formal arrangement for each of the steps of comparison which they call a syllogism; not calculated indeed for the discovery of remote truths from the use and application of the more immediate or intuitive, but well calculated to give regularity to the mind by scientific discipline, and to shorten controversy by a clear detection of the component parts of false reasoning. And here, by the way, it may be remarked that the inexplicable disorder of the logical reasonings of the middle ages is less to be attributed to the nature of their science of reasoning, loaded as it was with needless distinctions, than to their theological and psychological dogmas, and the delusions into which they wandered with regard to the objects called transcendental; delusions which a sound and bold application of their own science, if it could have been dared, would not have confirmed, but overthrown. But to return; the syllogism consists of three propositions. In the first, called the major proposition, something is predicated of a general subject: in the second, called the minor, the subject of the major becomes Major. All men are fallible. The major and minor terms are often called the premises, and the minor is sometimes called the argument. The premises are supposed to be intuitive, or at least incontestable, and the conclusion is established upon the axiom, that whatever can be predicated or affirmed of a genus, may also jects, and the predicate, terms of the syllo- Here it is not pretended, that all men should upon every occasion reason according to the rules of logic, any more than that a writer should upon all occasions insert each individual member of a sentence, and leave nothing to be supplied or understood. But as the man who is a sound grammarian can analyse and parse every member of a sentence, and will write with order, precision, and correctness; so will the logician, who is able to arrange the parts of an argument in mood and figure, be quick in discerning the imperfect, defective, or inadmissible assertions, and will so dispose his own notions and principles, that his proofs shall be conclusive and clear. The works evt of mathematical writers would, in many instances, be benefited by this severity of conduct; and there are few indeed which might not be rendered more perfect by strict logical examination and correction. Mood and figure are words applied by logical writers to denote the arrangement of the terms of a syllogism. It is done by the use of the letters A, E, I, O, of which A denotes universal affirmative; E, universal negative; I, particular affirmative; and O, particular negative. But as it would be difficult to retain in the memory the various in which the types, instead of answering only to a single letter, are made to correspond to whole words. The properties of the logographic art are, 1. That the compositor shall have less charged upon his memory, than in the common way. 2. It is much less liable to error. 3. The type of each word is as easily laid hold of as that of a single letter. 4. The decomposition is much more readily performed. 5. No extraordinary expense, nor greater number of types, is required in the logographic, than in the common method of printing. LOLIUM, in botany, ray grass, a genus of the Triandria Digynia class and order. Natural order of Gramineæ, or grasses. Essential character: calyx one-leafed, fixed, many-flowered. There are five species. LOMENTACEÆ, in botany, the name of the thirty-third order in Linnæus's Fragments of a Natural Method, consisting of plants, many of which furnish beautiful dyes, and the pericarpium of which, uni changes in the order of these letters, if prefixed to the three parts of a syllogism, fourteen artificial words have been formed, of three syllables each, containing the vowels so to be prefixed in the order of the mood to be denoted by each word. The fourteen moods are classed under these different figures, by which terms logicians mean to denote the particular situation of the middle term, with respect to the major and minor. The first figure is distinguished by the middle term being the subject of the major, and predicate of the minor proposition, and its four moods are denoted by the words Barbara, Celarent, Darii, Ferio. The second figure admits of negative conclusions only, the major being always universal, and one of the premises negative. Its moods are Cesare, Camestres, Festino, Baroco. And in the third figure the middle term is the subject of both premises, the minor af firmative, and the conclusion, particular. Its moods are Darapti, Felapton, Disamis, Datisi, Bocardo, Ferison. We shall not ex-versally a leguminous pod, contains seeds that tend our article to exemplify these moods, nor shall we proceed to give instances of the form and complexities of syllogisms, which systematic writers have been more solicitous to enumerate and name, than to analyze and develope. In like manner we shall pass over the consideration of the various sophisms treated of by them, because these objects would lead us too far, and their detection follows immediately upon a statement of the premises and conclusions, according to rule. And upon the whole, we shall conclude by observing, that though the old logic was burthensome, from the manner in which it had been suffered to enlarge itself; yet since much of our present modes of reasoning, and of the expressions made use of at the bar, in the senate, and among our best writers, are derived from its rules; and, since the moderns, when they decried and rejected it, have not been solicitous to establish any determinate or correct system, we deem it entitled to more attention than has usually been paid to it. LOGISTIC curve, the same with that otherwise called logarithmic. See LOGA RITHMIC. are farinaceous or meally like those of the bean. The cassia, wild senna; hæmatoxylon, logwood; mimosa, sensitive plant, &c. are of this order. LOMONITE, in mineralogy, is of a snow white colour, with a slight tendency to reddish white. It occurs massive; the fracture is foliated, and the surface of the folia are streaked, which gives a peculiar glimmering aspect to the surface of the fossil; it is easily frangible, and not heavy: when preserved from the air it has a slight degree of coherence; but if it is exposed to the action of that fluid, the folia spontaneously separate from each other, and it is soon reduced to a heap of unconnected parts. It forms a kind of jelly with acids, and is found in the lead mines of Huelgoet in Lower Brittany. It received its name from Gillet Laumont, who discovered it about twenty years ago. LONCHITES, in botany, a genus of the Cryptogamia Filices class and order. Natural order of Filices, or ferns. Generic character: capsule disposed in lunulated lines lying under the sinuses of the frond. There are five species, all natives of very LOGISTIC spiral. See LOGARITHMIC and hot climates. SPIRAL. LONCHIURUS, in natural history, a LOGISTICA numeralis, the same with genus of fishes of the order Thoracici. algorithm. See ALGORITHM. LOGISTICAL arithmetic, the doctrine of sexagesimal fractions. See SEXAGESI Generic character: the head scaly ; ventral fins separate; the tail lanceolated. The bearded lonchiurus, the only species belonging to this genus, is a native of SuriLOGOGRAPHY, a method of printing, nam, about twelve inches in length, has a MALS. slightly lengthened nose, two beards at the lower jaw, and the first ray of the ventral fins elongated into a bristle. Its colour is a ferruginous brown. LONG (ROGER), D. D. Master of Pembroke-hall in Cambridge, Lowndes's professor of astronomy in that university, &c. was author of a well known and much approved treatise of astronomy, and the inventor of a remarkably curious astronomical machine. This was a hollow sphere of 18 feet diameter, in which more than 30 persons might sit conveniently. Withinside the surface, which represented the hea vens, was painted the stars and constellations, with the zodiac, meridians, and axis parallel to the axis of the world, upon which it was easily turned round by a winch. He died December 16, 1770, at 91 years of age. A few years before his death, Mr. Jones gave some anecdotes of Dr. Long, as follows: "He is now in the 88th year of his age, and for his years vegete and active. He was lately put in nomination for the office of vice-chancellor he executed that trust once before, I think in the year 1737. He is a very ingenious person, and sometimes very facetious. At the public commencement, in the year 1713, Dr. Greene (master of Bennet College, and afterwards Bishop of Ely) being then vice-chancellor, Mr. Long was pitched upon for the tripos performance: it was witty and humorous, and has passed through divers editions. Some that remembered the delivery of it, told me, that in addressing the vice-chancellor, (whom the university wags usually styled Miss Greene) the tripos orator, being a native of Norfolk, and assuming the Norfolk dialect, instead of saying, 'Domine vice-cancellarie,' archly pronounced the words thus, Domina vice-cancellaria;' which occasioned a general smile in that great auditory. His friend, the late Mr. Boufoy, of Ripton, told me this little incident That he and Dr. Long, walking together in Cambridge, in a dusky evening, and coming to a short post fixed in the pavement, which Mr. Boufoy, in the midst of chat and inattention, took to be a boy standing in his way, he said in a hurry, 'Get out of my way, boy.' That boy, sir,' said the Doctor, very calmly and slyly, is a post-boy, who turns out of his way for nobody.' I could recollect several other ingenious repartees, if there were occasion. One thing is remarkable, he never was a hale and hearty man, always : of a tender and delicate constitution, yet took great care of it; his common drink water; he always dines with the fellows in the hall. Of late years he has left off eating flesh-meats; in the room thereof puddings, &c. sometimes a glass or two of wine." LONGEVITY, the continuance of life beyond its ordinary period of duration. The term of human life does not in general much exceed 80 years, but it is well known that instances occasionally occur of persons living to the age of 100 years and upwards. Such instances however have not excited that general attention, which from the nature of the subject might be expected, and it is only of late years that any extensive collection of them has been formed, or attempts made to ascertain the circumstances and situations in which the different individuals preserved their lives to an age so much beyond the usual lot of man. The most extensive catalogue of this kind, is that published by J. Easton, which, though very defective, contains the names and some particulars of 1712 persons who had attained to a century and upwards, having died at the following ages: from 100 to 110 years...... 1310 120 to 130.... 277 84 The circumstances which chiefly tend to promote longevity may be reduced to the following heads: 1. Climute. A large majority of the recorded instances of great age were inhabi. tants of Great Britain or Ireland, of France, Germany, or the north of Europe, from which it appears that moderate or even cold climates are the most favourable to long life. Heat relaxes and enfeebles, while cold consolidates and strengthens the human frame. The diet also of hot countries is less nourishing than that of cold ones; and there is generally a greater disposition, and greater opportunities to indulge in various excesses in the former, than in the latter. There are however a few instances of natives of very hot climates having attained to great age, but they have been chiefly negroes in the West Indies and America, whose ages were probably not very correctly ascertained. 2. Parentage. Being born of healthy parents, and exempted from hereditary disease, are circumstances evidently favourable to the duration of life; and numerous instances warrant the opinion, that longevity prevails in some families more than in others, or that descent from longlived ancestors is one of the circumstances which give the greatest probability of attaining to extreme old age. 3. Form and size of the individual. It is generally admitted, that persons of a compact shape, and of a moderate stature, are the most likely to live long. Tall persons frequently acquire a habit of stooping, which contracts the chest, and is a great impediment to free respiration; whereas the short sized find little difficulty in keeping themselves erect, and are naturally much more active, by which the animal functions are retained in a state of greater perfec. tion; the only disadvantage attending a short stature is, that it is frequently accompanied with corpulence, which is rather unfavourable to long life. 4. Disposition of Mind. Nothing is more conducive to longevity than to preserve equanimity and good spirits, and not to sink under the disappointments of life, to which all, but particularly the old, are necessarily subjected. This is a point which cannot be too much inculcated, as experience continually shows that many perish from despon dency, who, if they had preserved their spirits and vigour of mind, might have survived many years longer. Neither the irritable, who are agitated by trifles, nor the melancholy, who magnify the evils of life, can expect to live long. Even those who suffer their strength and spirits to be exhausted by severe study, or other mental exertions, seldom reach great age. In the list before referred to, of 1712 persons who lived about a century, Fontenelle (who did not quite reach 100 years) is the only author of any note; and his great age is ascribed to the tranquil ease of his temper, and that liveliness of spirits for which he was much distinguished. Among those who have devoted themselves to the study or practice of music, a profession which encourages cheer fulness of mind, instances of great age have been very frequent. 5. Occupation. No person that leads an idle life will ever attain to great age; but health and long life must depend much on the manner in which the individual is employed. Those occupations are certainly the most conducive to the duration of life, which are carried on in the open air, and require activity or labour; thus farmers, gardeners, and labourers in the country, are in general the longest lived. Foot soldiers also, who have survived the dangers of war, are remarkable for long life: they are generally stout and vigorous men, and the regularity to which surviving soldiers must have accustomed themselves, whilst their careless and disorderly companions have dropped off, the erect posture to which they have been trained, and being of course men well formed by nature, and habituated to walk well (by which they enjoy the most natural exercise in perfection) all combine in their favour. Sailors also would furnish many instances of longevity if comfortably provided for in their old age of this a striking proof is given in the accounts drawn up by Dr. Robertson of the pensioners in Greenwich Hospital. In the year 1801, the complement of in-pensioners was 2410, of whom there were 96 of the age of 80 years and upwards; of this number 13 were above 90 years of age, and one man 102 years old. The number of out-pensioners was about 2500, of whom it appeared there were only 23 from 80 years of age and upwards. Of the former therefore about 4 in 100 survived 80 years of age, but of the latter not 1 in 100 attained that age, a sufficient evidence of the benefits of regularity and ease in the advanced period of life, and of the attention paid to the health of the in-pensioners at that excellent institution. 6. Mode of Living. If persons were to live with the simplicity of ancient times, it is probable that they would attain long life, without experiencing any material illness, merely by a proper attention to air, exercise, clothing, and diet. But in the present state of society, the great bulk of the community follow, not a natural, but an artificial mode of life, and thence are perpetually exposed to various temptations, which they find it difficult always to resist, and to dangers which they cannot always avoid. Most persons however have it in their power in some degree to regulate their manner of living by their own choice; and by a little attention to their food, clothing, employment, rest, and temper of mind, might not only contribute materially to the prolongation of their lives, but preserve themselves from many diseases, and greatly increase their relish for all the enjoyments of life. The importance of wholesome food, for the preservation of health and promoting long life, and the avoiding of excess, whether in eating or drinking, is sufficiently obvious. Some instances, indeed, are recorded of persons who have continued to commit excesses, and have lived long; but these are to be considered in no other light than as exceptions to a general rule; and it may reasonably be contended, that if such persons lived to a great age, notwithstanding their intemperance, they would have lived much longer had they followed a different course. Experience will point out those articles of food which are best adapted to the constitution of each individual, and there cannot be a better rule than to adhere to them as far as circumstances will permit. It may be observed, however, that people in general, especially those who do not labour, eat much more than nature requires; that a little abstinence or selfdenial may often be of use, either to prevent or to cure disease; and at any rate, that none but hard working people, the young who are growing fast, or persons who are travelling about, 'should eat more than one full meal each day. As to clothing, much must depend on si tuation and climate; but it is generally found a useful practice to wear woollens next the skin. It is remarked in many parts of Scotland, that since the use of flannel shirts has been given up by the lower orders, the rheumatism and other diseases formerly unknown, have become very frequent, and are daily increasing. In the West India islands, if care be taken to make the troops wear flannel shirts, they are generally exempt from various disorders, which otherwise would probably have attacked them. Even the negroes themselves are said to prefer flannel to cotton or linen, and find it a much more comfortable and useful dress. Exercise cannot be too much recommended; and as the inhabitants of large towns, and persons engaged in sedentary occupations, cannot take all the exercise abroad that may be necessary for their health, they ought as much as possible to accustom themselves to be walking about even in their own house, for though this practice does not make up for the want of exercise abroad, it is certainly the best substitute for it. Exercise is attended with the advantage of creating an inclination to retire early to rest, and of inducing sound sleep. Every one should take all the repose that nature requires, but should never continue long in bed without sleeping. Early rising, even if carried to an extreme, is far more conducive to health and long life, than late hours at night and slumbering in bed in the morning. There is nothing that can tend more to long life than for a person to obtain a complete command of his passions, and in particular to preserve his mind from being ruffled by the occurrences of life. Perhaps there is no maxim more likely to promote good health, and consequently the duration of life, than that of paying a proper attention to temper, temperance, and sleep. By good temper the mind is preserved from disease; and by temperance, the body; and both the mind and the body, when exhausted, are again recruited and restored to their former strength, by a sufficient quantity of repose. LONGIMETRY, the art of measuring lengths, both accessible, as roads, &c. and inaccessible, as arms of the sea, &c. See SURVEYING. LONGITUDE of a star, in astronomy, an arch of the ecliptic, intercepted between the beginning of Aries and the point of the ecliptic cut by the star's circle of longitude. See CIRCLE, &c. LONGITUDE of a place, in geography, is an arch of the equator intercepted between the first meridian, and the meridian passing through the proposed place; which is always equal to the angle at the pole, formed by the first meridian and the meridian of the place. The first meridian may be placed at pleasure, passing through any place, as London, Paris, Teneriffe, &c. but among us it is generally fixed at London, or rather Greenwich, and the longitudes counted from it will be either east or west, according as they lie on the east or west side of that meridian. The difference of longitude between two places upon the earth is an arch of the equator comprehended between the two meridians of these places; and the greatest possible is 180 degrees, when the two places lie on opposite meridians. Since the parallels of latitude always decrease, the nearer they approach the pole ; it is plain, a degree upon any of them must be less than a degree upon the equator, in the ratio of the co-sine of the latitude to the radius. Hence, as the radius is to the co-sine of any latitude; so is the minutes of difference of longitude between two meridians, or their difference in miles upon the equator, to the distance of these two meri. |