two trucks with four low wheels each, which trucks could turn independently at each end, while large driving wheels without flanges may be placed between the trucks.

Estimates the altering of carriages to the 6 feet gauge at less than £30 each, and the engine and tender at £350 to £400 each.

Extract from a Return to the House of Lords, of the WORKING STOCK of Existing Railways.

Glasgow, Paisley, Kilmarnock, &c.... 31.........133.......................1334

Grand Junction-including Liverpool

Cost of EUROPEAN RAILWAYS PER MILE, extracted from a Report published by order of the House of Commons.

14,334

York and North Midland, &c........................ ........................... ......... 25,924

Problems, and one which is most generally used.

For example, supposing we wish to find out the variation from a straight line on a curve of 400 feet radius with a locomotive whose extreme centre of wheels are 20 feet. We wish to know this to find the width of tire to be put on the forward driving wheels to prevent falling off the rails. We are supposing now an 8-wheel engine, 4 drivers, and 4 wheels in a truck.

Now we have the radius, a b, 400 feet, and the chord, a c, 20 feet, which is the distance the wheel centres are apart; from b, as a centre, we describe the arc, a d c, with b a, as radius. Bisect the chord, a c, at f; then a ƒ will equal 10 feet, and ƒ c equal