to the coupled wheels.  The boiler is 11 ft. long by 4 ft. 2 in. diameter; the grate area is 16.25 square feet; and the heating surface is, tubes, 1,216.5 square feet; fire-box, 97.0 square feet; total, 1,313.5 square feet.  The boiler pressure is 140 lb., and the tractive power per lb. of steam pressure in the cylinders, 88 lb.  The weight in full working order is on the leading wheels, 10 tons 5 cwt.; driving wheels, 11 tons; trailing wheels, 9 tons 15 cwt.; total, 31 tons.

[Illustration:  FIG. 3.—­LONDON & NORTH-WESTERN RAILWAY.]

[Illustration:  FIG. 4.—­JOY’S VALVE GEAR.]

Turning now to the London and North-Western Railway, we find that between 1862 and 1865 the express trains were worked with a handsome type of engines, known as the “Lady of the Lake” class.  They have outside cylinders 16 in. diameter and 24 in. stroke, with single driving wheels of 7 ft. 6 in. diameter, and leading and trailing wheels 3 ft. 6 in. diameter, with a total wheel base of 15 ft. 5 in.  The frames are single, with inside bearings to all the wheels.  The boiler is 11 ft. long and 4 ft. diameter, and the heating surface is in the tubes, 1,013 feet; fire-box, 85 ft.; total, 1,098 feet.  The tractive power per lb. of steam pressure in the cylinders is 68 lb.  The weight in full working order is on the leading wheels, 9 tons 8 cwt.; driving wheels, 11 tons 10 cwt.; trailing wheels, 6 tons 2 cwt.; total, 27 tons.  The tender weighs 171/2 tons in working order.  These engines burn about 27 lb. of coal per mile with trains of the gross weight of 117 tons, which is not at all an economical duty.  About 1872, the weight of the heavier express trains on the North-Western had so increased, that a new standard type for this service was designed, and is now the standard passenger engine; it has inside cylinders 17 in. diameter and 24 in. stroke; the driving and trailing wheels are coupled, and are 6 ft. 6 in. diameter, and the leading wheels 3 ft. 6 in.  The frames of steel are single, with inside bearings to all the wheels, and the boiler, of steel, is 9 ft. 10 in. long and 4 ft. 2 in. diameter.  The steel used has a tensile strength of 32 to 34 tons per square inch, all the rivets are put in by hydraulic pressure, and the magnetic oxide on the surface of the plates where they overlap is washed off by a little weak sal-ammoniac and water.  In testing, steam is first got up to 30 lb. on the square inch, the boiler is then allowed to cool, it is then proved to 200 lb. with hydraulic pressure, and afterward to 160 lb. with steam.  The fire-box is of copper, fitted with a fire brick arch for coal burning, and the grate area is 15 square feet.  The heating surface is, in the tubes, 1,013 square feet; fire-box, 89 square feet; total, 1,102 square feet.  The wheel base is 15 ft. 8 in., and the tractive power 88 lb. for each lb. of steam pressure in the cylinders.  These engines, working the fast passenger trains at a speed of about 45 miles per hour, burn about 35 lb. of coal per mile, when