A wrought iron bar 22 feet long is heated from 70° to 300°. How much will it lengthen ?

22 X (300-70) X .00000686 = .0347116 ft. = .41654 in.

The following table gives the temperatures and latent heats of fusion and of vaporization of a number of substances:

How many units of heat are required to melt 10 pounds of zinc from a temperature of 60° F? The specific heat of zinc from the preceding table is .0956. Hence, the number of heat units necessary to raise it to the melting point is 10 X (680—60) X.0956 592.72.

Latent heat of fusion = 50.63 heat units. Hence, the total number of heat units required is 592.72 + 10 x 50, 63 = 1099.02.

To Develop the Dome of a Boiler.

A side view of the dome, together with a section of the boiler, is shown in figure A. Draw Fig. B, the end view of the dome and of the boiler. Above the dome draw a circle in e'' m, of ""

the same diameter as the dome. Divide the lower half of this circle, as n e' m, into any number of equal parts, as m c', c'' d'', d" e'', ''f" and f" g". The greater the number of these divisions the more accurate will be the results. From the points of divisions c'', d'', e'', ƒ'' and g'', draw lines parallel to the vertical center line of the boiler as c'' c', d'' d', f" f' and g' g'.

We are now ready to draw the template of the dome as shown in Fig. C. Draw a straight line of indefinite length, and on it lay off a distance h i equal to the circumference of the dome. (The circumference of the dome is found by multiplying the diameter ab of the dome by 3.1416.) Divide the distance hi into twice the number of equal parts that the semicircle above the dome in Fig. B has been divided into. In the figure it has been divided into six equal parts, therefore, divide this line into 2 × 6

= 12 equal parts also, as bg, gf, fe, ed, etc., and through these points of division draw lines at right angles to the line hi, as shown; make the length of each of these lines the same as the length of the line which corresponds to it in Fig. B. Thus e e' is equal to e e' in Fig. B, d d' is equal to d d' in Fig. B, a a' is equal to a a' in Fig. B, etc. After having laid off the lengths of these lines, draw the curved line i'e' h'. This being done, we have the template of the dome on the seam. The lap for riveting must be allowed as shown by the dotted lines around the template.

To Develop the Slope Sheet a b c d of a Boiler Shown at A, in the Figure Below.

JK lay off the distances i m, no and Kp, equal to the distances h 1, i 2 and bf, respectively, and pass the dotted curve J mop through the points. Now draw Fig. C. Draw the straight line kq and through the point J, draw ec perpendicular to it. Lay off on the line k q on each side of the line c e, points m' and m' at distances from it equal to the length of Jm in Fig. B. Lay off also points o and o' at distances from m' and m' equal to mo in Fig. B; also, points p' and p' at distances from o' and o' equal to op of Fig. B. Through the points thus laid off, draw lines parallel to c e. Lay off the points cand e from J, in Fig. C, equal to Jc and Je, respectively, in Fig. B; the points 1''' and 1'' from m' equal to i 1'' and i 1′ in Fig. B; points 2''' and 2" from o' and o equal to n 2" and n 2', and the points 3"" and 3" from p' equal to K3" and Kp of Fig. B. Through the points thus laid off draw the curved lines 3"" c 3"" and 3" e 3". With the points 3" as centers and a radius a d, Fig. B, describe the arcs r and r. With the points 3" as centers and a radius 3' a, Fig. B, describe the arcs 8 and 8. From the points of intersection of these arcs draw lines to the points 3"" and 3". This being done, we have the template of the slope sheet on the seams. The laps for riveting must be allowed as shown by the dotted lines around the template.

To Develop the Slope Sheet 1 m n o of a Boiler, Shown at A, in the Figure on Following Page.

Draw the two views of the sheet as shown in Figs. B and C. Suppose the seam to be at on Fig. A, and the sheet to be made in one piece. Divide the semicircles a d g and a' d' g' Fig. C, into any number of equal parts; the greater the number of these divisions the more accurate will be the results. Join the points b and b', c and c', d and d', e and e', and ƒ and ƒ by full lines, and join the points b and a', c and b', d and c', e and d', ƒ and e', and g and f' by dotted lines, as shown. Then draw Figs. D and E. Draw at right angles to one another the lines w a and w x, also the lines z a' and zy. Make the length of the line w x equal to r Fig. B, and the length of the line w a equal to a a' Fig. C. From w lay off on the line w a, Fig. D, distances w b, w c, w d, we, w f and w g, respectively equal to the lengths of the full lines, b b', c c', etc., of Fig. C, and draw the