Vi = cos m (4-4) n (2n+1) ≥ bu, m Qn, mσo -fdop V., which gives the potential for any interior with precisely similar expressions for ; and the corresponding point, when the potential at the surface is known. A similar equation is true for the potential at an exterior point, namely, V. -doV.; but for the full explanation of this formula we refer to Green's original work. A variety of applications are made of these fundamental theorems. We can only find room for one of them. Let V, =b be the equation to a closed surface, where V. satisfies the equation & V1 = 0. Let p be the density of the electricity, supposed in equilibrium, and distributed over this surface. Then since the interior potential for electricity in equilibrium on the surface must be constant, we have, p h dVe where hVe 4π dw' is the exterior potential, h being a constant depending on the quantity of electricity. = density. When this spheroid supposed oblate, tends to become a circle by the continued diminution of oo, the resulting series when vanishes admits of several modes of summation given by Lipschitz. Thus he is able to obtain expressions for the distrisubsequent paper extends his researches to the segment of a bution of electricity in the circle, which hence arises, and in a sphere bounded by circular arcs. The equation Assume VN dx = {y2 + (x 0, This expression for (p) gives the density at any point on the surface, of electricity distributed on a spheroid, when in equilibrium, proportional to the perpendicular from the centre of the spheroid to the tangent plane drawn through that point. We now proceed to explain some recent applications of Laplace's coefficients to the theory of electricity due to Lipschitz, which will be found in the 58th volume of Crelle's Journal.' Let va be a potential function for the space exterior to a surface coinciding at the surface with and a potential function inside the surface coinciding at the surface with v. Also let va vanish at an infinite distance from the surface. √ √1-μ cos (-), and Lipschitz makes continual use of this remarkable integral in his researches. In giving the investigations of Sir W. Thomson, we define surfaces for which the potential is constant as surfaces of equilibrium. Then (1). The attraction of the matter spread over E, on an external point, where E is a surface of equilibrium, enclosing an attracting mass, is equal to the attraction of M on the same point multiplied by 4, provided that the matter be distributed on E so that its density at any point P is equal to the attraction of M on P. (2). The attraction of the matter spread over E on an internal point is zero. Let u (as defined at the beginning of this article) be the potential of M on the point P(x, y, z) in E. Then the components of the attraction of M on P in the directions of x, y, z, vector there given between points situated in confocal spheroids, where the integrals extend over the entire surface. Now n, m Σ (2n + 1) Σm b3n, m Pn, m (0) Qn, m (σ ̧) Pn, m μ Pn, w μy እ 0 cos m (4-4), and supposing the surface we have been considering to become a spheroid, it appears that uq u'c. v" + v' = u'p For the determination of these constants, we refer the reader to Sir W. Thomson's papers in the third volume of the 'Canbridge Mathematical Journal' (old series), p. 193. By supposing the surfacing E' removed to an infinite distance, we find v"=4πu'. We also find p−4′′, q=0, or q= −4, according as P' is without or within E, c=-4, or c=0, according as P is without or within E. Hence v' = 4ru' when P' is without E. v' = date [ENVELOPE MAKING, E. C., vol. iii., col. 899]. For recent statistics of stationery, and other particulars, see PAPER MANUFACTURE AND TRADE, E. C. vol. vi., col. 354; and E. C. S. col. 1643. STEAM-CULTURE. The termination of a number of successful patents, dated 1855-58, especially those of D. and T. Fisken, W. Smith, Woolston, and Fowler and Co., is giving a fresh stimulus to the cultivation of land by steam. The other plans in use at the date of E. C. have been given up (E. C. vol. i. col. 145, and vol. viii. col. 247). Mr. Smith continues to work profitably the turning-cultivators and tackle on the "round-about system," which he introduced in 1856; but the other two, although both in the field with their respective systems, have greatly improved them, the alterations made amounting to a change of principle in the mode of laying down the tackle and hauling the implements. It is worthy of record that the improvements now being made (1873) were in principle anticipated by two prior patents, McRae's, No. 8329, 1839, and Osborn's, No. 11,304, 1846. Both patentees were planters in British Guiana, and both had their projects reduced to practice in this country-McRae at Glasgow and Osborn in London,— and as they were differently reduced to practice from what they are patented, and immediately shipped for the above colony, the merits of the improvements made have been lost sight of by subsequent patentees and the agricultural public. Thus McRae's steam-plough (seen by the writer in 1840) had two central wheels, like Fowler's, and a partial balance movement, which took his ploughs half way out of the ground at land's-end, the other half was done by springs, on the principle of one of Howard's steam ploughs, a friction drum and slack rope drum like Fowler's, are also specified. As patented the implement has four wheels, but springs are not specified-an important differAn illustrated description as patented will be found in the Repertory of Arts,' vol. xiv. (new series) p. 212; and the field trials at Possil, near Glasgow, were favourably reported the Glasgow Herald,' 1840. Osborn patented what is now termed the "double-twin system," subsequently described and illustrated, fig. 1, the engines being right and left, as fig. 3 and fig. 4, each carrying two drums on vertical axes, as patented by the late Mr. Fowler, of London, in 1856, and as now being made by Fowler and Co., Leeds, 1873, with the exception that Messrs. Fowler place their drums below the boiler, as in fig. 3 and fig. 4; whereas Osborn had them on the framing at the side. It is only in the principle of construction that they agree, in other respects the double-drum engines of Aveling and Porter and Fowler and Co. are greatly improved. In reducing his project to practice, Mr. Osborn unfortunately adopted the friction drum principle, which has since been given up. Osborn's steam culture system, as patented, will be found described with engravings in the Farmer's Magazine,' vol. xv. (second series) p. 559, 1847, and as reduced to practice in London, and tried on Taylor's Farm, Essex, in 'Farmer's Mag.,' vol. xix. (second series) p. 47, also with illustrations. Osborn's cultivator resembled in principle Howard's, fig. 1 and fig. 2. Osborn also was the first who used wire rope for hauling his im ence. From the first of these equations it follows that the attraction of E on a point without it is the same as that of M multiplied by 4, and since the second shows the potential of E on an in-plement. He also used an engine moving along one headland, ternal point to be constant, we infer that the attraction of E on an internal point is nothing. In a subsequent paper in the third volume of the Journal, Sir W. Thomson has extended these researches. A series of papers by the same author on Statical Electricity treated geometrically, will be found in the Cambridge and Dublin Mathematical Journal,' vols. i., ii.; v.; and Professor Plana has carried on the investigations of Poisson relative to two spheres in vol. vii. of the 'Turin Memoirs.' STATIONERY is a general name for manufactures in paper, especially those kinds used in writing, together with other materials and apparatus for the writing-desk and the countinghouse. Account-book making is an important item in these manufactures the strength required in books so much in use calls for the use of good stitching and covering, while the ruling of the sheets of paper, by some among the many kinds of apparatus employed for this purpose [RULING MACHINE, E. C. S. col. 1854], must vary with the purposes to which each book is applied. Several kinds of cutting machine are employed in giving definite size and shape to ordinary writing and note papers; while stamping presses and dies are extensively used for embossing or imprinting monograms, residential addresses, &c., on the paper and envelopes. Ingenious envelopemaking machines were shown at work in the International Exhibition of 1872, differing in many ways from those of older and another moving along the opposite headland, and an implement hauled to and fro between. This is another of the modern plans to be subsequently noticed. It will be unnecessary to go into further details of these old practices. Enough has been said to connect the present progress of steam culture with them. The different plans of using steam power in the cultivation of land are designated "systems," purposely to distinguish the one from the other. The classification is perhaps more convenient than correct, but for the sake of brevity and perspicuity the several systems will be noticed separately. 1. Fisken's system. The chief peculiarity of Fisken's mode of steam culture, is a light hemp or manilla rope driven by a portable engine (STEAM ENGINES, AGRICULTURAL, E. C. S.) at a velocity of from 20 to 30 miles per hour, for actuating two windlasses on opposite headlands. When first brought out in 1855, friction drums worked along a wire rope anchored at both headlands; but this plan has been abandoned for two winding drums, as above, one at each headland. The light rope passes round a groove in the fly-wheel of the engine, and from thence goes round the field supported by carriers, and in passing the two single drum windlasses, it takes a turn round a rigger on each, its tension being adjusted by a movable pulley at the engine in the usual way. All sorts of implements are hauled to and fro between the windlasses by means of two wire ropes, as 2. Double-twin system. The annexed engraving (fig. 1) represents the double-twin system of steam culture, as produced in 1871, by the Messrs. J. and F. Howard, of Bedford. It consists, as will be seen, of two locomotive engines, moving along opposite headlands, each engine carrying two winding drums. The four ropes from the four drums are yoked to the opposite ends of two Osborn-cultivators. The implements turn midland, and are always hauled directly to the winding drums. In examples where two different kinds of implements are used, as a plough followed by a cultivator or harrow, or a cultivator by a roller or harrow, the implements do not turn midland, but are hauled from engine to engine, and this is the best plan of working the double-twin system, as some difficulty is experienced in making good work in turning midland and in avoiding delays. In like manner, when a double turn of the cultivator, harrow, or roller is required, turning midland is not necessary. 3. The Round-about system. This is sometimes termed the "Woolston system," from its having been introduced by Mr. Smith, of Woolston, in 1856, and successfully followed by him. ever since. With the exception of Fisken's, it is the oldest practice now in use. Mr. Smith only uses a cultivator. With this simple implement he "smashes up," as he terms it, his stubbles in autumn, leaving the land in a rough and cloddy state, exposed to the weather, and so successful has his practice proved, that it is now almost universally followed in preference to ploughing and digging. His patent only covered a peculiar turn-bow for turning his implement at land's-end, by the trailing rope when it became the hauling rope. His windlass, a common one with two winding drums, was actuated by a common portable engine used for threshing, &c. Fig. 2 represents one of Howard's round-about systems, consisting of a portable engine improved windlass, and guide snatchblocks, seen immediately in front of the windlass, a fixed snatchblock anchor at the opposite headland, and two movable snatchblock anchors, between which a to-and-fro cultivator works. The movable snatchblock anchors are shifted by two anchormen, represented at their respective anchors in the engraving. The movable rope porters are shifted by a boy; in all five hands, exclusive of a man at the water cart, are engaged. The engine and windlass are represented as placed in the gateway; but if there is a pond near, they may be set down close to it, and thus save a water-cart. This is a cheap and popular system, the chief objection to it being the number of hands required to work it. 4. The twin Engine and single Implement system closely resembles the double-twin system, fig. 1, the difference being that there is only one implement and one winding drum on each engine. The two engines work along opposite headlands, each hauling the implement alternately the length of the field directly towards it, as the other pays out rope and gets into position for the returning bout. The annexed engravings, figs. 3 and 4, show two steam ploughing engines of the Messrs. Aveling and Porter, Rochester, Kent, expressly made for the twin engine and single implement system. They carry, each below the boiler, a single winding drum, with coiling apparatus for reeling the wire rope evenly on to the barrel. They are made in pairs, with the flywheel and driving gear on the right-hand side of the one, and on the left-hand side of the other; so that both drive and pull from the land side, i. e., the side next the implement. This mode of construction, which is under a recent patent, has effected a great reduction of wear and tear on the working parts, including the wire rope itself, as compared with the old engines not thus made in pairs. Another improvement in the construction of these engines is the extending the side plates of the fire-box upwards, in one piece on each side, as shown in both engravings, so as to carry the bearings of the crank shaft, countershaft, and driving axle. By this plan the centres preserve their respective positions, and work truthfully, effecting a maximum result with a minimum wear and tear. It was otherwise when the bearings rested on brackets bolted to the boiler-plate, for then unequal expansion put the centres out of position, thereby increasing the wear and tear of the working parts, reducing the effect produced, straining the boiler-plate, and eventually springing the bolts. The steam-jacket of the cylinder is in direct communication with the boiler, and steam is supplied to the cylinder from the dome with which the jacket is surmounted, and as it is taken from the forepart of the boiler it is dry, producing the greatest effect at the smallest expenditure of fuel. Priming is also prevented, steerage and the other lever movements, are convenient to the engine-driver, so that he has perfect control of his engine on the headlands, and in going from field to field. The steerage is best shown on fig. 4. Indeed, as the corresponding sides of the two engines are alike, the two sides shown illustrate both sides of each, so that what cannot be seen in the one is shown on the other. Thus the flywheel and gearing not seen in fig. 4, are shown on fig. 3, and so on. Messrs. Fowler of Leeds, and Aveling and Porter, have recently entered into arrangements for working each other's patents separately or combined; so that figs. 3 and 4 now (1873) represent the single drum ploughing engines of both those of Osborn. In one example the Howards place their boiler across the carriage frame, with a winding drum on each side. In another the drums are placed one at each end, as subsequently described. 5. The single Engine system, sometimes termed the "direct system," in contradistinction to the "round-about system," fig. 2 may be defined as half the double-twin system, fig. 1 Thus, if a self-moving anchor, subsequently described (fig. 6), is substituted for one of the engines (fig. 1), it would be termed a single engine set of tackle. If, therefore, a large farmer or contractor has a double-twin set, he can by means of two selfmoving anchors and the necessary length of rope and number of rope porters, divide it into two single engine systems. This is a practical advantage possessed by the double-twin set, fig. 1, already been superseded by the latter, and the latter, in its turn, is now being supplanted by winding drums, as shown in figs. 3 and 4. The practice has sometimes been termed "the endless rope system," such being the principle of hauling the implement. Thus a clip-drum consists of a series of clips on the periphery of a drum, so constructed as to form a groove, in which the pull of the wire rope, by the rotation of the drum, makes the clips "bite," thereby preventing the rope from slipping, as was experienced with grooved drums. The clip-drum is placed below the boiler, as the winding-drum in fig. 3, and driven in the same way by gearing from the crank shaft. Below the clip-drum is a winding drum for winding up, and carrying the rope at the close of the work or when shifting from one field to another. The engine moves along one headland, the two hauling ropes may go directly to the two movable anchors, one to each, and be yoked to the implement; but in horizontal drums, as Howard's, snatchblock or guide pullies are required to direct the rope to the anchors. The two anchors for the implement may be either snatchblock anchors, as shown fig. 2, or self-moving anchors, fig. 6. In like manner the two engines of the double-twin system (fig. 1) may remain stationary, and the tackle be laid down on the roundabout-system, to meet the requirements of hilly and wet land. Two single or doubledrum engines, stationary at opposite headlands, with selfmoving anchors, could work sowing machines, hoeing machines, mowing and reaping machines, and such like, successfully, when moving along the headlands, is impracticable, owing to the land being under crop. True, hoeing, mowing, and reaping machines have not yet been worked successfully by steam power; but it tion from figs. 3 and 4, or from any other now in use. Its chief peculiarity is its carrying the engine and working parts on the tender, separate from the boiler. These are usually carried on the top of the boiler by brackets bolted to the boiler plate. In figs. 3 and 4 the flywheel and countershaft are placed on the firebox-plate behind the boiler; but the cylinder and connecting rods, &c., are on the top of the boiler as usual. In fig. 5 the whole is placed on the tender behind the furnace, supported by the two main road wheels. This arrangement of the working parts effects a threefold improvement; first, the centres work more cool and truthful to each other than when placed on the boiler or firebox-plates. Second, by placing the engine on the tender the boiler will do duty longer, and when worn out can be renewed or repaired without interfering with the engine itself. Third, the removal of the working parts from |