34 L U B L U B school (gymnasium) is situated in the spacious buildings of St Catharine, formerly the house of the Franciscans. The charitable institutions enjoy a large, well-administered property, chiefly the lands of the monastery of St John and the hospital of the Holy Ghost. Since 1789 there has existed a " Gesellschaft zur Befb r- derung Gemeinniitziger Thatiglceit, " with a branch union for the history and the antiquities of Liibeck, which has collected a valu able museum and promotes important historical publications, the materials of which are kept in the most unique municipal archives in existence. The income and expenditure of the Liibeck budget of 1881 balance with 2,739,382 marks; the public debt amounts to 23,804,913 marks. The manufactures of the town are numerous, but not large or im portant (woollen, linen, cotton, and silk goods, leather wares, hard ware, tobacco, and preserves). The commerce, on the other hand, is considerable, the chief exports being corn, cattle, wool, timber, and iron ; while wines, silks, cottons, hardware, colonial products, and dye-stuffs are imported. There is regular steamship communi cation with Copenhagen and the Baltic ports, and four lines of railway converge in Liibeck. Since the deepening of the Trave (1850-54) sea-going ships can come up to Liibeck itself; formerly they required to unload at Travemiinde. In 1878 the local ship ping of Liibeck amounted to 46 vessels of .10,223 aggregate tonnage (27 steamers, 1504 horse-power, 6463 tons). In 1877 2302 vessels (981 steamers) with a tonnage of 301,910 entered, and 2332 vessels (979 steamers) with a tonnage of 307,567 cleared the port. See Codex Diplomatics Lubecensi*, 6 vols., 1843-81 ; C. W. Pauli, Liibeckisclie Zustcinde zum Anfang des vienehnten Jahrhunderts, 1847; Waitz, Liibeck unter Jiirgen, Wullenwever, 3 vols., 18.55, 1856 ; W. Hansel s " Liibeck," in Bluntsclili nnd Prater, Deutsches Staafsiforterbuch, iv. p. 731 ; Wehrmann, Die d tercn Liibeck schen Zunftrolle.n, 1S72 ; D. Schafer, Die Hansestadte nnd f onig Wa de- mar von Danemark, 1879. (R. P.) LUBLIN, a town of Russian Poland, capital of the province of same name, 60 miles south-east of Warsaw, on the Bistrzyca, a tributary of the Wieprz. It is the most important town of Poland after Warsaw and Lodz. It has an old citadel, many churches, and several educational and charitable institutions, and it is the see of a bishop. Lublin is one of the chief centres of the manufacture of thread-yarn and of linen and hemp goods (to the value of more than 250,000), as well as of woollen stuffs: there is also an active trade in corn and cattle. The three annual fairs have a certain importance for the neighbouring district. The population in 1873 was 28,900, and is rapidly increasing. The date of the foundation of Lublin is unknown, but it was in existence in the 10th century, and has a church which is said to have been built in 986. During the time of the Jagellons it was the most important city between the Vistula and the Dnieper, hav ing 40,000 inhabitants (70,000 according to other authorities), and keeping in its hands all the trade with Podolia, Volhynia, and Red Russia. Indeed, the present town is surrounded with heaps of ruins, which prove that it formerly covered a much larger area. But it was frequently destroyed by the inroads of Tartars and Cossacks. In 1568 and 1569 it was the seat of the stormy con vention at which the union between Poland and Lithuania was decided. In 1702 another convention was held in Lublin, in favour of Augustus II. and against Charles XII., who carried the town by assault, giving it over to his army to be plundered, and stayed for six weeks at Jacobowice, the estate of Prince Lubomirsky, in the immediate neighbourhood. In 1831 Lublin was taken by the Russians after a battle. The whole surrounding country is rich in historical reminiscences of- the struggle of Poland for inde pendence. LUBRICANTS are fluids which are interposed between solid machine surfaces that a c required to slide on each other. The object is to lessen the friction, which is injurious both in wearing away the surfaces, and thus destroying the fit between them, and in dissipating and rendering useless pirt of the energy transmitted through the machine. The difference between the wear on unlubricated and that on lubricated surfaces is so serious that a comparison b2tween the cost of lubrication and the money saving in avoidance of repairs is superfluous. But the difference in wear when two different lubricants are used is not very great, and the proper choice between the two lubricants depends on a comparison of their cost with the amount of working power they save from dissipation. If the price of oil per gallon, inclusive of wages for its application to the journals, &c., be p ; if, in order to lubricate as well as can be done with this oil any one working surface or set of such surfaces, .it is necessary to use the fraction g of a gallon of oil per hour ; if, with the use of this quantity of the oil, there is still wasted in friction at these surfaces H horse-power; and if the cost in fuel, water, wages, repairs, &c., of the working energy is P per hour per horse-power ; then the money loss per hour caused by the friction is py + PR. By comparing the values of this quantity for two oils, it can be determined which it is more advantageous to use. Of the commonly used oils, the higher priced are much more efficient as lubricants. If two oils of which the same amount requires to be used have the prices p^ and p 2 , and allow I^ and H 2 horse-power to be wasted, then the money advantage to be gained per hour by using the first (the higher priced) rather than the second is P(H 2 - H 1 ) - (p l p.^y. This is positive if If this inequality is found not to be true in any special comparison, then the cheaper oil should be used. P varies from fd. to over IJd., according to the class of engine and boiler and to the good or bad management of the works, while p l p 2 , in comparing the extremes of cheap and expensive commercial lubricants, amounts to 2s. 6d. or more. To compare the advantages of using a larger or smaller amount of the same oil, let g l and g be the quantities used, and the resulting wastes of horse-power be H t and H 2 . Then the use of the larger quantity y l will be economical if P(H 2 - H,) -p( fjl -g. 2 )>0- or Considering the meaning of this inequality in the two cases of a high-priced and of a low-priced oil, in the former case has a larger value, while - - - - has also a J* ffl-ff 2 larger value than in the latter case. In both cases this latter fraction decreases with increase of ff l ; but it de creases more rapidly in the case of a high-priced than in that of a low-priced oil, because the former is a better lubricator. Thus with the dearer oil the limit beyond which it is uneconomical to increase the consumption of oil is reached sooner than with the cheaper, and it follows that of the cheaper oils it is best to use a large quantity, while of the dearer a smaller amount is what is most use fully employed. If the law according to which H varies with g be found for any oil, by experiment or otherwise, then the exact most economical quantity can be found by differentiating pg 4- PH with respect to g, and equating the differential coefficient to zero ; thus dTL dR dg" when is expressed in terms of </, gives this most econo mical value of g. An example of the actual values of the quantities involved in these formulas is given by an experiment by Van Cleve on a journal G inches in diameter by 7 inches long, in which the coefficient of friction was found to be about 077, and there was wasted 3 -4 horse power when 023 of a gallon was used per hour. Of the animal oils and fats suitable for lubrication those commonly used are sperm, lard, neats-foot, tallow, and common whale oil. Of vegetable oils olive, cotton-seed, and rape-seed are extensively employed, the first mostly in those countries where the olive is grown, and generally in the pure condition, while the last two are more used for mixing with higher class and more expensive oils. Various
full oils are also much used, and mineral oils now form a