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suggested by the movements now in progress among the working classes. Production and enjoyment of wealth by men as the condition of the attainment of those nobler ends of life in society, is in fact the motto implied in the organisation and exertions of trades' unions, and in so far as they offer the prospect of its realisation they hold out the hope of consolidated power, peace, and happiness for England and her people. The Legislature of Great Britain, cautiously following in the wake of events, enacts by "The Trade Union Act, 1871" (the 34 & 35 Vict. c. 31), that the purposes of a trade union shall not, merely because they are in restraint of trade, be deemed to be unlawful, so as to render any member liable to a criminal prosecution for conspiracy or otherwise, or to render void or voidable any agreement or trust.

The following agreements, however, are not to be enforceable at law or in equity (at the same time that they are not, therefore, to be deemed unlawful), viz. :—

1. Any agreement between members of a trade union as such, concerning the conditions on which any members for the time being of such trade union shall or shall not sell their goods, transact business, employ, or be employed.

2. Any agreement for the payment by any person of any subscription or penalty to a trade union.

3. Any agreement for the application of the funds of a trade

union

(a) To provide benefits to members; or (b) To furnish contributions to any employer or workman not a member of such trade union, in consideration of such employer or workman acting in conformity with the rules or resolutions of such trade union; or,

(c) To discharge any fine imposed upon any person by sentence of a court of justice; or,

4. Any agreement made between one trade union and another; or,

5. Any bond to secure the performance of any of the abovementioned agreements.

A register of trade unions is established under the Act, and any seven or more members subscribing their names to the rules of a union and otherwise complying with the registry provisions of the Act are entitled to have such union registered; but if any one of the purposes of the union be unlawful the registration is void.

Registered trade unions are enabled to purchase or hold upon lease in the names of trustees a limited extent of real property for the purposes of the union, and to vest their property generally in trustees with a right of succession in such trustees and a right to sue or be sued at law or in equity. The Act provides for the responsibility of such trustees and of the other officers of the union who may have committed to their hands property, money, books, or documents belonging to the union.

It is required that a general statement of the receipts, funds, effects, and expenditure of every trade union registered under the Act shall be transmitted annually to the registrar before the first day of June, and that the same shall show fully the assets and liabilities at the date, and the receipts and expenditure, and separately the expenditure in respect of the several objects of the union, during the year preceding the date to which it is made out. This act was immediately followed up by the legislature with a statute (34 & 35 Vict. c. 32) whereby the criminal legislation of the country was applied in the case of threats, molestations, and obstruction by fellow-workmen, and in the case of oppressive acts by the employer of labour, with the view to coercion thereby of working men.

TRAIN RESISTANCE. In a locomotive with cylinders d inches in diameter, and 7 inches stroke, with a mean effective steam pressure of p lbs. per sq. in., and having driving wheels D inches diameter, the tractive force in lbs. which the engine is capable of exerting is given by the formula

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That tractive force is transformed into useful work by the longitudinal displacement of the machine. But, in order that that displacement may take place, the bite or adhesion between the wheels and the rails must be at least equal to the tractive force. If we designate by P, the load on the driving wheels of the engine, that is, the weight of that part of the engine which is supported on the driving wheels, in tons, and by f the coefficient of friction of the wheels on the rails, then the force of adhesion in virtue of which the engine moves forward is 2240 f P2 lbs.. (2)

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The value of the coefficient of adhesion ƒ depends on the state of the surfaces of the rails as to smoothness and dryness.

If the tractive power developed by the engine is greater than the adhesion of the driving wheels, then the wheels slip on the rails and revolve without moving the train. On heavy gradients, and with heavy trains on moderate gradients, the tractive power of the engine is practically limited by its adhesion, and for such cases engineers have been driven to augment the adhesion weight of their engines, not only by increasing their gross weight-and with that the proportion of weight carried by the driving wheels-but also by coupling the wheels, so as to convert all the wheels into driving wheels, and the whole weight of the engine into adhesion weight. In order to surmount extreme gradients other devices have to be adopted [STEAM ENGINE, Locomotives, E. C. S. col. 1974]. In the best circumstances of rails and weather an adhesion of th, or perhaps even 1th, is sometimes obtained; but with damp and greasy rails the adhesion may be reduced to th. In ordinary circumstances the adhesion is probably seldom less than 3th, and that proportion is often assumed, in calculating the limit to the tractive force of engines. Perhaps, however, th is the greatest proportion which can be depended on in varying circumstances of weather. According to M. Dieudonné, that proportion is seldom exceeded in tunnels. The heaviest load which should be placed on a single pair of driving wheels is 14 tons. Assuming that load, and taking the coefficient of adhesion at th, an express engine with one pair of driving wheels would have an adhesion of 3400 lbs. engine with four-coupled wheels might have an adhesion of 6800 lbs., and a luggage engine with six-coupled wheels, an adhesion of 10,200 lbs.

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The tractive power of a locomotive being thus limited, first by the mean steam pressure and second by the adhesion, is in the third place limited by the evaporative power of the boiler. On ordinary lines, an express engine of the largest size may be taken to be capable of evaporating so much water as is sufficient to generate an effective power of 400 horses, and a luggage engine 300 horses. At high speeds, however, the power may be somewhat greater, and at low speeds somewhat less than this.

In maintaining a train in motion, work is expended in overcoming the friction of the wheel tyres and rails, the shocks and concussions of the carriages against each other, the friction of the wheel axles, and the displacement of the air by the progress of the train. Theory does not enable us to estimate the amount of these resistances, but numerous experiments have been made, and the results have been expressed in empirical formulæ, by means of which the resistance to traction of any given train can be very approximately determined.

On a level and straight line, and at low speeds, the principal resistance is that due to the friction of the axles. This resistance varies, according to the accuracy of adjustment and state of lubrication of the axles, from 4 to 9 lbs. per ton of the weight of the train. It may be taken as amounting on the average to 6 lbs. per ton for the carriages of the train, or to 8 lbs. per ton for carriages and engine together, the latter estimate including the friction of the working parts of the engine. Above 10 miles an hour, the resistance of the air sensibly increases the train resistance; and the air resistance increases nearly as the square of the velocity; so that, at high speeds, the air resistance is more important than any other. These rules are expressed conveniently in the following formula of Mr. Clarke. Putting V for the speed of the train in miles per hour, the resistance in lbs. per ton, on a level and straight line, is nearlyfor engine, tender, and train,

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In addition to the above resistance there is the friction of the working parts of the locomotive due to the steam pressure transmitted through them. It has been found, by calculating a special case, that about 15 per cent. of the engine power was expended on the transport and friction of the engine itself, and that the tractive force at the draw bar was only 0.85 of the tractive force calculated from the mean steam pressure.

If, instead of being level, the line has a gradient, then the resistance due to the component of the weight of the train acting down the slope is added to the other resistances of the train in ascending, and diminishes them if descending. If the gradient is 1 in, so that i is the sine of the inclination, and r is the resistance on the level, then the resistance on the gradient is r+ 2240 i in ascending; and

↑ 2240 i

in descending, in lbs. per ton.

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ing and sweating were the two processes by which training was accomplished; but such notions are now quite exploded. The great thing to be borne in mind is that the old body has to be gradually unbuilt and then built up again, the ordinary lungs and heart have to be reconstructed, bit by bit, in a manner suitable for the branch of exercise to be indulged in. The four primary points to attain this end are diet, sleep, clothing and exercise.

How the above course should be prescribed requires great care, the temperament and condition of the trainee's health having to be minutely studied. Public-school boys are generally in a more or less high state of training all the year round, as they keep regular hours, have good and wholesome food, and take a great deal of exercise. The gentleman who has been accustomed to good living has probably some superfluous flesh to be reduced; but then he has a good constitution-if unimpaired by excesses-and can better stand hard exercise. The student, counting-house clerk, and poor man-who has probably been a public-house loafer for some time past — require solid beef and mutton and port wine, with very moderate exercise at first, in order to strengthen their constitutions for the ordeal. If the trainee be stout and inclined to make flesh quickly, he will require some two months to get thoroughly fit; but if a lean spare man half that time will suffice. Our eastern coast sea-side resorts are the best places in the world for training, since they combine bracing air with sea-bathing, and the climate is not relaxing as on our southern and western shores. The next best spot is any country place which lies high, has bracing air, and is generally healthy. The selection of a trainer is an all-important point, since, in addition to being a thorough master of the art, and being able to regulate the diet and exercise, he must be of a cheerful and witty temperament in order to keep his pupils in good spirits. If the stomach requires setting in order at the commencement mild rhubarb pills are the best physic, since Epsom salts, blue pills, and castor oil often exhaust the system. Unless the trainee be accustomed to it, early rising is a mistake. Few can stand hard exercise before breakfast, and the only result is drowsiness later in the day. From 6 to 7:30 A.M., according to the time of year, is plenty soon enough, and the first thing to be attended to is the weir, or into a running stream; but it must only just be an "in and out." To swim more than a few strokes at such an early hour, and moreover before breakfast, knocks a man up for the rest of the day. In winter time of course the sponge bath is the sole resource; but however the tub be taken the man must be rubbed thoroughly dry all over with rough towels.

Curves increase the resistance also to an extent not very certainly ascertained. Professor Rankine found the additional resistance due to curves, for light passenger carriages with truly cylindrical wheels, to amount to 14 radius of curve in miles. But he points out that, if the wheels are coned, the resistance on the level is increased, and that on the curve diminished, so that the difference between the resistance on straight and curved parts of the line is less felt. Experiments in America by Mr. Latrobe give for the resistance on curves 0.578 radius in miles. MM. Guebhard and Dieudonné found no sensible increase of resistance with passenger car-bath. A plunge into the sea is the best, next to that under a riages, at low speeds, on curves of more than 75 chains radius. At 35 miles per hour, on a curve of 75 chains, the resistance of a train of passenger carriages was increased five per cent., which gives for the resistance due to the curve 08 radius in miles. For goods trains at 16 miles per hour on curves of 50 and 40 chains, the additional resistance was 15 radius in miles.

TRAINING may be described as the process by which the human being, the horse, the dog, or other animal, is prepared to encounter a fellow human being or animal in a trial of skill, strength, speed, or endurance as the case may be. Man can stand the process of training better than any animal, and is more improved by the process. We shall accordingly confine our attention to the training of man alone, premising that the training of the horse, dog, &c., comes rather under the heads of racing and coursing.

Nothing requires more care and attention than the training of man. Whatever kind of contest he be training for; whether walking, running, rowing, swimming, &c., the courses of medicine, diet, and exercise will be nearly similar, the only difference being in the kind of exercise taken, e.g. walking and running for pedestrians, swimming for swimmers, and the like. A thoroughly trained man will go through violent exercise without much inconvenience and no injury to himself; whilst in the untrained man, although pluck will to a certain extent compensate for want of condition, great inconvenience and often serious injuries result. In the case of weakly constitutions training is undoubtedly injurious, and where the soundness of the lungs and heart is doubtful, no one should think of going into training without previous medical advice. On the other hand, training has of late years been made the bugbear of many individual cases of illness in after-life, which were properly attributable to totally different causes. Violent excesses on going out of training constitute these causes, especially after the body has been living in strict "temperance, soberness, and chastity" for a couple of months or so.

The Greek and Roman ideas of training were, to say the least, peculiar, as their chief diet seems to have been pork and similar adipose food, yet, somehow or another, their system proved successful. At the beginning of the present century, in the days of the celebrated Captain Barclay, everlasting physic

The diet must be a judicious mixture of herbivorous and carnivorous food, or of vegetables and meat. Sugar is about the worst thing that can be touched in training; and, in addition to refraining from the said article of diet, butter, cream, milk, bread, potatoes, all kinds of roots-e.g. carrots, turnips, parsnips, beetroot, and the like-and beer must be consumed in less quantities by the man inclined to obesity. Breakfast from 7:30 to 8:30 A.M. should consist of two cups of tea, always without sugar, not too hot, dry toast or stale bread, any cold meat except pork-although it must be remembered that veal and lamb contain less nutriment than beef and mutton-or a mutton chop or rump steak. Coffee is too heating, and is moreover seldom palatable without sugar. Nothing is better than a little watercress, as it purifies the blood; whilst boiled or poached eggs, chicken, fowls, and any fish except salmon, eels, mullet, and flounders, are admissible for a change. Dinner comes from 12:30 to 2 P.M., when a joint of roast, never boiled, of beef or mutton should be set on the table, or venison once or twice a week when in season. As at breakfast fish and fowl may be used as a variety, and any vegetable in seasonexcept the roots above mentioned-are admissible. Spinach, asparagus, and French beans are the healthiest in the order named. Pepper and mustard cause thirst, so no condiment except salt is allowable. Fruit pies or puddings may be indulged in two or three times a week; but the crust must be carefully eschewed. Of drinkables at dinner nothing is preferable to a pint of the best dry champagne, unless the trainee is weak and requires to make blood, when a pint of old ale and a glass or two of port wine must be had recourse to. All alcoholic drinks are heating, and consume the vital powers of the stomach; whereas champagne gives life and energy without causing the same deleterious effects or fulness of blood like port wine. Good sound claret is also a wholesome liquor if it does not produce diarrhoea. The evening meal, whether termed

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tea or supper, must be a light one, as it is bad to sleep on a full stomach. If the stomach can stand gruel nothing is better than a basin of it, otherwise much the same food as at breakfast may be allowed-though less in quantity—with half a pint of tea or old ale. In hot weather it is not necessary to strictly limit the amount of liquid provided it is taken at meals. Want of drink makes a man equally as feverish and restless as too much of it, especially when he perspires freely from exercise. Rinsing the mouth out with cold water, or bathing the hands and feet in cold water, will often alleviate thirst between meal times. Nothing should be eaten or drunk immediately before or after taking hard exercise. Smoking unquestionably does harm; but when a man has been accustomed to a free use of tobacco, it must be knocked off gradually, not all at once.

Eight hours a night will generally be found enough for sleeping purposes, and the retiring hour should be not later than 11 P.M. The bed-room should always be kept more or less open, according to the season of the year, to let out the foul air generated by sleep. Too much clothing must not be placed over the chest, and a feather bed should never be allowed in the trainee's sleeping apartment.

As regards clothing the only restriction is that flannel should always be worn next the skin all the year round. The special description of dress necessary when at exercise is regulated according to the description of sport the trainee is preparing himself for.

In the matter of exercise a certain amount of walking is invariably gone through in the day, whatever be the special exercise the pupil is preparing himself for. Always being on the move keeps the muscles pliant and the spirits up. The ordinary or habitual muscles are in daily use, whereas certain extraordinary or special sets of muscles are only brought into use according to the kind of exercise the pupil takes. The best way is to get rid of any superfluous flesh as soon as possible without weakening the system. This is done either by sheer sweating or working the flesh into muscle by long and steady exercise. Except the Turkish bath all artificial modes of sweating are hurtful, and nothing equals putting on a close-knit rough woollen jersey next the skin, with one or two more over it, and sweating by means of any kind of exercise, though alternately running and walking are perhaps the easiest. After a man is once in tolerably good condition the special kind of exercise need not be indulged in more than once a day; in summer-time after 6 P.M., when the heat is gone down, and in winter between 10 A.M. and noon. Directions on this head will be found under the various headings of ROWING, RUNNING, WALKING, and the like, according to the sport a man is training for. Rest must be taken for a day or two before the actual contest, to allow the muscles to gain their full elasticity. After the special exercise has been taken a cold bath may be indulged in, and the body well rubbed down with rough towels.

Such slight accidents in training, as blisters and corns, are easily treated at home; but in the case of rupture, strained muscles, rheumatism, varicose veins, or piles, medical aid should

be at once summoned.

To sum up we cannot do better than quote the maxim of a once-celebrated aquatic trainer-viz., "the great thing in training is to find out as soon as possible what mode of living the subject has been accustomed to; and, as it must be to a great extent the most suitable in his peculiar case, to adopt it without hesitation."

TRAMWAYS, iron rails laid along the carriage ways of streets and roads, to lessen friction. They resemble railways in having a definite width or gauge between the rails, and on that account being suited to such vehicles only as have their wheels similarly adjusted. Vehicles experience much friction in travelling over a carriage-way paved with dressed stones or macadamised granite, or only loosely covered with gravel, earth, or brick rubbish; hence the adoption of narrow, smooth surfaces for the wheels to run upon. Mr. Outram, a civil engineer, was one of the first to lay out colliery roads in this way; they were hence called Outram roads, a name afterwards contracted to tramroads and tramways. Wood was first used as the smooth material; but iron is more usually adopted. The wheels require to be flanged, in order to prevent them from diverging from the rails.

Tramways appropriated exclusively to omnibus traffic have been in use for several years in the broad streets of some of the larger towns of the Continent and the United States of America. An attempt was made to introduce them into London a few years ago, under the management of Mr. G. F. Train; but the rails

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being badly laid down, and the opposition of vested interests strong, the attempt proved a failure. In 1869 the system was recommenced under better arrangements, and is now (1873) becoming important. In order to remodel the carriage-ways along which the tram-rails are to be made, parliamentary powers are necessary; and these powers were obtained by three companies, one for a tramway in Whitechapel, a second in the Westminster Road, and a third in the Kent Road. In 1870 new lines were sanctioned in Camden and Kentish Towns, St. Pancras, City Road, Holloway, Mile End, Brixton, Clapham, Pimlico, and Vauxhall. Subsequent years have added to the number of Tramway Acts. In February, 1873, the length of tramways open in the metropolis was forty-two miles; but a much greater length was planned and in progress. Many of the large towns in England and Scotland have obtained legislative powers for a similar purpose.

The surface of the carriage-way requires careful reconstruction in laying out a tram. Dressed granite stones between the iron rails form a firm road on which the horses travel; the upper surface of the rails is on a level with this road, and a groove at the side of the rail admits the flange of the wheel. So smooth is the motion, that two horses can draw much heavier loads than along an ordinary road. The tram cars, longer, wider, and loftier than London omnibuses-better seated, better lighted, and better ventilated-have come much into favour; the ingress and egress, ascent and descent, are easier. It is not yet certain that the system could be advantageously adopted in the more crowded streets of the metropolis; and on this account permission has hitherto been refused to the construction of tramways in the busy thoroughfares of the city. Hodgson's Wire Tramway is noticed under RAILWAYS, É. C. S. col. 1780.

TRAMWAYS (LAW OF). By the 33 & 34 Vict. c. 78, provision is made to facilitate the construction and to regulate the working of tramways in England and Scotland. Provisional orders for the construction of tramways may be obtained from the Board of Trade by Local Authorities in the respective districts where the intended tramways are to be made, or by any company, with the consent of the local authority of the district. In constructing the tramways the promoters are placed under strict conditions with regard to breaking up and reinstating the roads, and the repair from time to time of such parts of the road as are occupied for the tramway; and they are enabled, so far as it may be expedient, in order to prevent frequent interference with their line of rails, to divert gas and water pipes, and even sewers, provided proper notice is given to the authorities and care be taken that such alteration be made without permanent obstruction or injury.

The use of the tramways may be by means of flange-wheeled carriages, and may be extended to licensees, if the Board of Trade should think such extension necessary to the public interests of the district. If the tramway be disused for three months by the promoters, except for cause beyond their control, the Board of Trade may determine their powers, unless the same are purchased by the district; and the lines of rail may be removed by the road authorities at the cost of the promoters.

Provisions are inserted in the Act enabling and compelling the promoters after twenty-one years from the making of the line to sell the same to the local authority of the district, if such local authority should so require.

TRANSCENDENTS, ALGEBRAICAL.

We discuss the periods of the hyperelliptic functions in the article entitled WEIERSTRASS' METHOD, E. C. S. But the periods of algebraical integrals have been'ascertained generally by M. Hermite, 'Comptes Rendus,' vol. xviii., for 1844. His method is founded on Abel's great memoir, published in the Mémoires par divers Savants,' tome vii., French Academy.' M. Hermite thus writes :— Let, following Abel's notation,

x (y) = Po + P1Y + P2 Y2 + ... + Pn-1 y”-1 + y", an irreducible algebraical equation whose coefficients are rational and entire functions of the same variable (x). Let us call its roots y, ya Ys Yn, and denote by

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in f (x, y); this function will be susceptible of a number (2) of different forms, which we shall represent by fi (x, y), ƒ2 (X, Y), • . ƒ, (X, Y). Then in denoting by 1, 2 Xu, (u) variables, when (u) is any number greater than (7), and by Y(1) Y(2) ・・・ y(u) irrational functions chosen arbitrarily among the (n) roots, y1, Y2,... Yn, we shall have, by means of Abel's theorem, under an algebraical form, the complete integrals of the system of equations:

f2 (X1, YN
x' (y))

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Puiseux has derived these formulæ, by a geometrical method, 0, which has been developed in the Theorie der Abelschen Functionen' of Clebsch and Gordau.

The method of Riemann, which differs in some important = 0. respects from that of Puiseux, although geometrical, will be found in the fifty-fourth volume of Crelle's 'Journal.' This has been lucidly explained in a work of Neumann's, entitled Vorlesungen über Riemann's Theorie der Abelschen Integrale.' A long series of memoirs on this subject have appeared in Crelle's Journal.' We give the titles of some of them.

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X1 = λ1 (U2 U2 • Ug), Xq = λg (U1 Ug • • Uz) • • • Xy = λy (Uz u... u). It follows, that the integrals of the system of differential equations considered above, integrals immediately given by Abel's theorem, afford without difficulty, by a suitable change of constants, the fundamental theorem, which informs us that they functions A (+219 U2+Vq · · · Uz +) are the roots of an equation of the degree y, whose coefficients are rational functions of the different functions Ax (u, u2 • • Uz) λk (V1 V2 . . X) and of the corresponding values of those roots (y) which we have introduced into the equations (2).

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X' (Y1) X′ (Y2) X'(Y3) • x' (Yn) 0, the first member of which, as we know, can be expressed by an entire function of (x). Each of its roots enjoys the property of rendering equal two of the roots (y) of the equation x (y)=0. Suppose then that y) becomes equal to another root y for the different values xa, a", a," . . . a ̧(~‚), And in the same way that y=Y[2] for

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Riemann himself contributed a paper entitled "Ueber das Verschwinden der Functionen,' in the sixty-fifth volume of Crelle's 'Journal.' 'Ueber die dritte Gattung der Abelschen Integrale erster Ordnung,' by Roch, also in the sixty-fifth volume; Ueber diejenigen curven deren Co-ordinaten sich als hyperelliptischen Functionen eines Parameters darstellen lassen,' by Brill, in the same volume. This memoir is interesting from its connection with the investigations of Rosenhain. 'Bestimmung von d log(0, 0, 0...) durch die Classen moduln,' Thomæ, Crelle, 66; Ueber Theta Functionen vielfacher Argumente, Gattung,' Roch, Crelle, 68; 'Ueber das Additions-Theorem by Roch, in the same volume; Ueber Abelsche Integrale dritten der Abelschen Functionen,' Weber, Crelle, 70; 'Zur theorie der Umkehrung der Abelschen Integrale,' Weber, in the same volume; Beitrag zur Bestimmung von 0 (0, 0, 0..),' Thomæ, Crelle, 71.

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From this arises this important property of the inverse functions, which consists in the coexistence of a series of indices of periodicity for all the arguments, and which shows an extension of that remarkable property which Jacobi long ago discovered the Abelian integrals to possess. Consider the equation:later results of Graham are noticed under GASES, E. C. S. col. TRANSPIRATION [E. C. vol. viii. col. 331]. Some of the 1113, as also those referred to under AIR PUMP (SPRENGEL'S), E. C. S. col. 75. Löwenthal ('Journal Chem. Soc.' 1872, p. 219) with reference to liquid transpiration, and its practical use in scientific and technical chemistry, employs an apparatus somewhat different from that used by Graham. He uses a vessel for condensed air of a capacity of not less than 1800 cubic cent., and two capillary tubes with two stop-cocks of exactly equal dimensions, so that two experiments may be carried on at the same time. Instead of placing the tubes in water at a known temperature, the air of the room is kept at a constant point during the experiments. The tubes employed vary in capacity from 2.5 to 5.7 cub. cents., some having one, some having two bulbs. The time which the liquid takes to pass through the capillary tube is noted by a method similar to that employed by Graham. It is shown that the fatty oils used in the arts have very different rates of transpiration, and that this is also the case with milk, beer, wine made from fruits, grape-wine, and various other substances, a fact which it is proposed to turn to practical account in testing such compounds. In the case of some liquids there exists a relation between their respective diffusion and transpiration rates. Graham gives the diffusion of HCl solution to NaCl solu

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and let us denote by the letter (m) entire numbers positive or tion as 1: 0.7; but Löwenthal gives their respective rates of trannegative. If we then assume:

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spiration as 1 0·732. So the diffusion of NaCl to sugar is as 2:33: 7, their transpiration rates as 2·33: 5.83.

TRAUMATIC (from Tpavua, a wound), in Surgery, a term applied to diseases arising out of wounds or mechanical injuries; as T. erysipelas, T. tetanus, &c.

TRAWLING, a mode of fishing in deep waters, by dragging a net along the bottom of the sea. The trawl-net is a kind of triangular bag, 70 feet long by 40 wide, and ending nearly in a point at the bottom; the meshes vary in size from 4 inches to 1 inches square; the mouth is kept open by a long beam which rests on two upright iron frames. The net is towed by a rope, in such a way that the lower edge of the mouth shall be in close contact with the sea-bed. This, the beam-trawl, has superseded a less effective pole-trawl, formerly in use. It is only on a 6 T

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smooth sea-bed that the trawl-net can be advantageously used. The trawlers catch cod, haddock, soles, and some other kinds of white and flat fish ; but not herrings or mackerel, which are more usually caught by drift-nets and seine-nets. The German Ocean is the chief scene of trawl-fishing. The trawl-net is much used by naturalists and in deep-sea dredging.

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l2 a2 + m2 63 + n2 y2 — 21m a 6 - 2m ne y Take the triangle formed by the tangents a, 6, and the chord of contact la+me - ny=0, and complete the parallelogram, so that la+meny=0 may be one of the diagonals, then the other diagonal will bisect this chord of contact, and therefore since it passes through the intersection of the tangents, (a) it will also pass through the centre of the ellipse.

This

To find the equation to a straight line drawn parallel to €, and passing through the intersection of la+ me—ny and ɑ. straight line will be a side of parallelogram. The equation to this straight line must be of the form += 0, which may be writtena t 6 + 1/2/1/ 2 )

TREASURER (from enoavpós, Latin, Thesaurus, a treasurer, or treasury), an officer to whom is committed the care of the revenues and the wealth, whether in the form of money or of other valuables, belonging to empires, nations, counties, corporations, or individuals. The use of the word is modified in different countries by its relative extent and dignity, and has been found in such combinations as Arch-Treasurer, Grand Treasurer; and, in England, as Lord High Treasurer, Treasurer of the Household, Treasurer of the Navy, Treasurer of War, Treasurer of the Exchequer, and others, some of which, by a change of form or by a change or suppression of function, have become obsolete. The Treasury is the department of the English Government which has to do with the receipt of all taxes and fines, and the payment of all moneys; and the chief of this department was formerly styled Lord High Treasurer. In the year 1612, however, it was thought advisable to place the office in commission, that is, to distribute the duties This must pass through a=0, me—ny=0, which leads at once to and responsibilities of the office among several styled Lords Commissioners of Her Majesty's Treasury. The Chancellor of the Exchequer stands next in importance, as a Lord of the Treasury, to the Prime Minister, who usually appropriates the office of First Lord.

persons,

who are

In an ecclesiastical sense, the office of Treasurer in cathedral

6 + μ

the condition

a

(

2A

b 2A

с

2A

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= 0.

= γ 0. Similarly the equation to the side of the parallelogram opposite (a) will be:

and collegiate churches involved the charge of the vestments, and therefore the equation to the side of the parallelogram opplate, jewels, altar-ornaments, relics, muniments, and other posite will be valuables belonging to the foundation, and the proper care of everything necessary to the ordinary or extraordinary celebration of the Divine service and sacraments. The simpler faith and worship of the Reformation in this country, brought about either the total abolition or the relative degradation of the Treasurer; who, in cathedrals of the new foundation, is merely the bursar, and is annually elected from the residentiary canons. (Frederick Wicks' British Constitution and Government; Walcott's Sacred Archæology; Moroni's Dizionario Ecclesiastico.)

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TREFOIL, in Gothic Architecture, a figure of three leaves or lobes formed by as many cusps. It is of frequent occurrence in the tracery of windows, panels, and tombs, and, indeed, wherever tracery is employed. In Heraldry the trefoil (shamrock or clover leaf) is usually blazoned on a stalk, when it is or, as we may write it : termed a trefoil slipped. When a charge is bordered or spotted over with trefoils it is said to be treflée.

TREHALOSE [MYCOSE, E. C. S., col. 1582].

TRENAILS, or TREENAILS, wooden nails or pegs used in fastening the timbers of ships; they are usually of oak or of locust-wood, 15 to 18 inches long by 1 to 14 inches diameter, and are driven into holes bored by means of an auger.

TRIBUNALS OF COMMERCE [COMMERCE, TRIBUNALS OF,
E. C. S. col. 592].

TRICARBALLYLIC ACID, Carballylic acid, C¡Í ̧O =
CH,(COHO)

CH, COHO), an acid formed by the action of potassic hydrate
CH2(COHO)

on allylic tricyanide, and of sodium amalgam on aconitic acid or
ethylic aconitate. The colourless crystals melt at 158°, and are
easily soluble in water or alcohol, but only sparingly so in

ether.

TRICHLOROPHENOMALIC ACID [PHENOMALIC ACID, E. C. S., col. 1677].

TRICLINIUM [HOUSE, E. C. vol. iv. col. 747]. TRILINEAR CO-ORDINATES. This method has been explained in the article GEOMETRY, ANALYTICAL, OF TWO DIMENSIONS, E. C. S. col. 1128. Since, however, that article was written we have been desirous to explain certain principles which have been developed in Mr. Ferrers' treatise on Trilinear Co-ordinates,' an excellent work containing much to interest the If as before

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a + be

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aа + be 0, aa + cy O, be + cy = 0. For more information we refer to Mr. Ferrers' work. TRINITROCELLULOSE [GUN COTTON, E. C. S., col. 1204]. TRINITY, Representation of in Art. The representations in art of this sacred subject have been in common use from the earliest ages of the Christian church. The simplest in form and oldest in date is the triangle, which sometimes contains within it the monogram of the name of Christ, or two triangles interlaced. This symbol is frequently found on the tombs of the primitive Christians, in the Catacombs at Rome, and it is the one which has been most constantly and universally employed down to the present day. Another early symbol of the mystic union of the three persons in one Godhead was a Latin inscription placed in three geometric lines, forming a triangle and having at each angle the names of the Father, Son, and Holy Spirit, the connecting lines consisting of the words non est, so as to present to the eye the doctrine of that portion of the

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