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^30 THE LOCOMOTIVE. [September, paus or coils of pipe ; but in such cases dished heads are greatly to be preferred to flat ones, because their strength can be computed with greater nicety.* Rankine, Grashof, and Lame have each given a great deal of attention to the subject of flat heads, and have deduced rules for finding the thickness of them. Rankine's rule for flat, wrought-iron heads is: "Multiply the pressure on the head, in pounds per square inch, by the square of the radius of the flat part (in inches) ; divide the result -by the tensile strain, in pounds per square inch, that the material of the head will safely bear, and take the square root of the quotient." This gives the thickness of the head in inches. Mr. Samuel Nicholls, in his Theoretical and Practical Boiler-Mal-er, has put this rule into useful shape, but unfortunately there is an error in the rule as he gives it, and in the illustrative example also. It should read something like this : " To find the thickness that a flat, unstayed head should have, multiply the thickness of the shell to which the head is to be attached by the radius of the head (in inches), and take the square root of the product. This gives the thickness that the head must have in order to equal the shell in strength." This rule is identical with Rankine's, except that it is put in a different form. As an example, let us take the following: What thickness of plate shall we require for a flat unstayed dome top, the dome being 36 inches in diameter, and in. I thick, in order that the end may be equal in strength to the remainder of the dome? Here the radius is 18 inches; 18"x|"=6.75", and ^/G. 75=3. 6" (instead of 1.59 inches, as in Mr. Nicholls' example). Very few experiments have been made, relative to the strength of flat, wrought-iron heads, and our knowledge of them comes largely from theory. It is true that very care- ful experiments have been made on small plates y'g of an inch thick, yet the data so obtained cannot be considered satisfactory when we come to consider the far thicker heads that are used in steam engineering practice, although the results agreed well with Rankine's formula. Mr. Nicholls, being foreman of a boiler shop in England, has since made some experiments on larger heads, and from them he has deduced the following rule, which will probably work well with heads that do not differ very widely from those he experimented with: "To find the proper thickness for a flat unstayed head, multiply the area of the head by the pressiu-e per square inch that it is to bear safely, and multiply this by the desired factor of safety (say 8) ; then divide the product by ten times the tensile strength of the material used for the head."t His rule for finding the bursting pressure when the dimensions of the head are given is: "Multiply the thickness of the end plate in inches by ten times the tensile strength of the material used, and divide the product by the area of the head in inches." In Mr. Nicholls' experiments the average tensile strength of the iron used for the heads was 44,800 lbs. The results he obtained are given below, the bursting pressure being calculated in each case, both by Nicholls' rule and by Rankine's, for the purpose of comparison. 1. An unstayed flat boiler head is %^ inches in diameter and J_ inch thick. What is its bursting pressure? The area of a circle 34^ inches in diameter is 935 sq. inches; then ^\x 44,800x10=252,000, and 252,000-^935 = 270 lbs., the calculated bursting pressure according to Nicholls' rule. The head actually burst at 280 lbs. (Rankine's formula gives only 44 lbs. as the bursting pressure.) 2. An unstayed flat head is 34^ inches in diameter and | inch thick ; what is its bursting pressure? The area of the head being 935 square inches, as before, we have * See The Locomotive for February, 1890. + The formula from which this rule is taken is given on p. 146 of Mr. Nicholls' book. In this formula the denominator should be C X T.
1898.] THE locomotivp: 131 |x44,800x 10 = 168,000, and 168,000-^-935 = 180 lbs., which is the bursting pressure according to Nicholls' rule. This head actually burst at 200 lbs. (Hankine's formula jjives only 21 lbs. as the burstiii
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^ rtE.'pTWE © (§) THE LOCOMOTIVE.
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THE LOCOMOTIVE. [January, a o o M -
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6 THE LOCOMOTIVE. [January. In both
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3 THE LOCOMOTIVE. [Januahy, been em
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^Q THE LOCOMOTIVE. [January, ])rove
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42 THE LOCOMOTIVE. [January, Sit «
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14 THE LOCOMOTIVE. [January. After
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16 TlIK hOCOMO'J'i Vi.. Incorporate
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18 THE LOCOMOTIVE, [Februaky, stren
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20 THE LOCOMOTIVE. [February, could
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22 THE LOCOMOTIVE. [February, Natur
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24 THE LOCOMOTIVE. [Februart Paper
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28 THE LOCOMOTIVE. Pit *0tiim$tlt
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30 THE LOCOMOTIVE. [February, jured
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32 Incorporated 1866. THE LOCOMOTIV
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34 THE LOCOMOTIVE, [March, pressure
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36 T II E L () C O yi O T l\E. [Mar
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38 'i^il^ LOCOMOTl V i:. [Makcu, (1
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40 THE LOCOMOTIVE. [March, art & Co
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42 THE LOCOMOTIVE. [March, Ml ^^^'3
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^(3 THE LOCOMOTIVE. [March, power o
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48 Incorporated 1866. THE LOC (J MO
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50 THE L O C O 31 U T I ^' E , [Apr
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52 THE LOCOMOTIVE. [April, (This is
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54 THE LOCOMOTIVE. [April, Castle,
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56 THE LOCOMOTIVE. [April, sious ar
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58 ' THE LOCOMOTIVE. [April, Hit St
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,60 THE LOCOMOTIVE. L-^p«il, nortl
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62 THE LOCOMOTIVE. [Aprfl, these pi
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64t Incorporated 1866. THE LOCOMOTI
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66 THE LOCOMOTIVE. [May, much as we
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68 THE LOCOMOTIVE. [May, diameter o
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70 THE LOCOMOTIVE. [May, by tirlce
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72 THE LOCOMOTIVE. [May, Boiler Exp
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74 THE LOCOMOTIVE. [May, HARTFORD,
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76 THE LOCOMOTIVE. [Mat, weeks amou
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'^8 THE LOCOMOTIVE. [Ma\% coat-tail
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Page 132 and 133: 124 THE LOCOMOTIVE [August, hard en
Page 134 and 135: 126 THE LOCOMOTIVE. [August, The Bu
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: 180 THE LOCOMOTIVE. [December, In
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^82 THE LOCOMOTIVE. [December, that
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184 THE LOCOMOTIVE. [December, HART
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186 THE LOCOMOTIVE. [December, The
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188 THE LOCOMOTIVE [Decembeb, angle
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190 THE LOCOMOTIVE. [December, Such
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i92 Incorporated 1866. THE LOCOMOTI
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INDEX, Equivalent of heat, redeterm
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