TBANSACTIONS OF SECTION Q. 751 



The firemen have simply to watch the fire and clear the grate-hars when necessary, 

 the stoking being automatic, and the combustion is so complete that no smoke is 

 observed. 



In conclusion, the following- advantages have been secured : (1) An increased 

 efficiency ; (2) The poorest fuel can be employed eq ually with the richer kinds, 

 even in the state of dust ; (3) Automatic stoking ; (4) A complete consumption 

 of smoke. 



7. The Hopcraft Smokeless Furnace.^ 

 By Lieut. -Colonel W. J. Engmcdue, B.E. 



Sub-Section II. 



1. A Curve Banger. By Alex. P. Trotter. 



Railway curves are generally set out in the field by the method of tangential 

 angles. For this purpose a theodolite is used, with a book of tables of the angles 

 for curves of different radii. The assistance of two chainmen with a chain is re- 

 quired. For each point on the curve the table must be consulted to find the 

 tangential angle, and the vernier of the theodolite has to be set by the tangent 

 screw, and signals have to be made to the chainmen. 



The instrument brought before the Section is an application of the 2l8t propo- 

 sition of the thi)-d book of Euclid, viz., ' The angles in the same segment of a circle 

 are equal to one another.' 



A half-silvered mirror, such as is used in sextants, is mounted on an axis at 

 one end of a bar, the other being provided with a sight. The motion of the mirror 

 on its axis allows its inclination to the sight to be adjusted. 



To set out a curve, a pole or other mark is set up at each extremity, and the 

 mirror is suitably adjusted. "When the poles are seen, the one direct through the 

 xmsilvered part and the other by reflection in the silvered part of the mirror, in 

 apparent coincidence and in the middle of the field, as shown by the vertical line 

 engraved on the mirror, the instrument is then at a point on the curve required. 



The mirror being clamped in position, the observer walks in the direction of 

 the curve, and at suitable intervals places himself so tliat the poles at the extremities 

 of the curve are seen in apparent coincidence. Where accuracy is required in 

 small curves, a plumb-bob suspended from the axis of the mirror may be used to 

 indicate the exact spot on the ground. 



Only one adjustment is required for any one curve. No tables, assistants, 

 chain, or knowledge of trigonometry are required. No cumulative error can 

 occur in the use of this instrument, as is almost always the case with the method 

 of tangential angles. 



It frequently happens that a curve is required merely to be set out between 

 two points and pass through a third point. In this case" no calculation whatever 

 is required for setting the mirror. The poles being set up at the extremities, the 

 observer, standing over the third point, adjusts the mirror so that one of the poles 

 is seen direct, and the other by reflection. The angle between the incident and 

 the reflected ray at the mirror is the angle in the segment. 



When the radius and the length of the chord are knowTi, the mirror may be 

 adjusted by the use of a scale divided info equal parts, representinsr the ratio of 

 the chord to the radius. The arc may be greater or less than a .semicircle. 



When the mirror is inclined at an angle of 45° to the axis of the sight, the 

 reflected ray makes a right angle with the direct ray, and the nngle in a semicircle 

 teing a right angle, poles placed at the ends of a diameter vrill appear in coinci- 



' See Engineering, vol. xlviii., p. 482. 



