Chapter V: Appendix

A.—Decimal Arithmetic 459
B.—Algebraic formulæ 461
C.—Weights and measures 464
D.—Value of the Birmingham gauges 465
E.—Locomotive boilers 466
F.—Effect of grades on the cost of working 468
G.—Form for a locomotive specification 471
H.—Relative cost of transport by railroad and by stage 476
I.—Form for experimental trips with locomotives 478
K.—Proper weight for locomotives 479

ADDITIONS, ALTERATIONS, AND CORRECTIONS.

The reader is particularly requested to apply the following errata before perusing the work. They are partly mistakes in printing, and partly errors in the original MS. The only excuse the writer can offer for the number is, that, being engaged in Missouri, while his publishers were in Boston, he has been prevented from seeing a single proof-sheet in time for its correction.

Page 5, line 7, for “499.999,” read “499,999.”

— 5, l. 9, for “49.999,” read “49,999.”

— 10, l. 1, for “can be,” read “can never be.”

— 12 to 23, headings, for “reconnoitre,” read “reconnoissance.”

— 18, l. 24, for “36.9,” read “36.8.”

— 19, l. 6, for “table B,” read “table D.”

— 24, l. 1, for “any thing,” read “every thing.”

— 25, l. 17, for “horizontal line m m m,” read “line 1, 2, 3,” etc.

— 26, l. 2, for “land,” read “level.”

— 27, l. 1, for “at the place,” read “at the right place.”

— 28, l. 29, for “reconnoitre,” read “reconnoissance.”

— 30, l. 3, for “A _c d_ B,” read “A C D B.”

— 32, l. 2, the point _m_ in the cut, is one whole division above C;
it should be only three fourths of a division.

— 38, l. 10 from bottom, for “276,” read “268.”

— 39, l. 10 from bottom, for “142.13,” read “143.13”; and last line,
for “58.46,” read “48.46.”

— 40, l. 7, for “10310,667,” read “10,277,333.”

— 42, l. 9, for “Thus,” read “These.”

— 42, l. 8 from bottom, for “2°.81 or 2° 48′.6” read “2°.86 or
2°.51.6.”

— 43, l. 27, for “Hencke,” read “Henck.”

— 47, 48, 49, for “McCullum,” read “McCallum.”

— 47, l. 18, for “distance,” read “resistance.”

— 48, l. 6, for “infringing,” read “impinging”; line 9, for
“slacking,” read “shackling”; l. 8 from bottom, for
“increased,” read “increases.”

— 50, l. 17, for “110 + 15.60,” read “110 + 15.62.”

— 52, l. 15, for “45.59,” read “45.49”; also l. 17, for “1132,” read
“11.32.”

— 58, l. 10, for “of size,” read “and size.”

— 58, l. 5 from bottom, for “one cent,” read “/100 of a cent.”

— 61, l. 3, for “are necessary,” read “are not necessary.”

— 63, l. 28, for “stretches,” read “stretchers.”

— 65, l. 15, for “spanded,” read “spandrel.”

— 71, l. 6 from bottom, for “left,” read “let.”

— 73, l. 19, for “chains,” read “chairs.”

— 74, l. 5, for “across ties,” read “on cross-ties.”

— 74, l. 12, for “28 inches,” read “27 inches.”

— 75, l. 18, for “land,” read “haul.”

— 76, l. 8, for “top,” read “bottom,” and for “charred when,” read
“charred where.”

— 76, l. 11, for “twopenny,” read “tenpenny.”

— 78, l. 1 and 2, for “base,” read “basis.”

— 84, l. 13, for “as,” read “or.”

— 89, l. 6, for “Whenever,” read “Wherever”; l. 12, for “Letting,”
read “Setting.”

— 90, l. 4, for “cost,” read “cut.”

— 93, l. 6, for “37 and 38,” read “36 and 37.”

— 95, l. 1, for “beach,” read “bench”; l. 3, for “to so,” read “so
to”; l. 13, for “b being 10 ft. back of 2 is ... 100.00,” read
“b being 10 ft. back of 2 is 0.1 ft. higher than 2, or ...
100.10.”

— 102, l. 1, head of middle col., for “Slopes 1¼,” read “Slopes 1½.”

— 103, l. 4 from bottom, for “and ten feet,” read “and one end ten
feet.”

— 104, l. 9, for “any,” read “very.”

— 108, l. 9, for “Elwood,” read “Ellwood.”

— 115, l. 5, for “a loam,” read “a berm”; l. 16, for “a rent,” read
“a vent.”

— 117, l. 7, for “volcanic,” read “voltaic.”

— 117, l. 9, for “Round Drum,” read “Round Down.”

— 117, l. 18, for “Col. Puseling,” read “Col. Pasley.”

— 118, l. 2, for “Maillefaut,” read “Maillefert.”

— 118, l. 16, for “insert,” read “invert.”

— 118, l. 25, for “quointed,” read “grouted.”

— 119, l. 30, for “furnished,” read “finished.”

— 120, Table, for “Nochistingo,” read “Nochistongo”; for
“Supperton,” read “Sapperton”; and for “Black Rock, W. S.”
read “Black Rock, U. S.”

— 121, l. 19, for “Belchingly,” read “Blechingly.”

— 125, in table at bottom, for “90/69,” read “90/66,” and for “140,
20/140, 20/160 or 0.13,” read “111, 20/111, 20/131, or 0.15.”

— 126, l. 1, for “extensive,” read “extensile.”

— 127, l. 10, for “67,200,” read “65,251.”

— 127, l. 26, for “Hodgekinson,” read “Hodgkinson.”

— 128, l. 4, for “12000,” read “11000.”

— 128, l. 15 and 22, for “Hodgekinson,” read “Hodgkinson.”

— 129, l. 5, for “12000,” read “11000.”

— 129, l. 2 from bottom, for “Sun Wood,” read “Ironwood.”

— 130, l. 7, for “_WL^2_ = 4_Sbd^2_,” read “_WL_ = 4_Sbd^2_.”

— 131, l. 9, for “wood 143,” read “wood 133.”

— 134, in art. 164, for “700,” read “952.”

— 136, for example there given, place the following:—

Span 30 feet, Whence—
Length 34 feet, Length 34 feet,
Load 10 tons at centre. Span 30 feet,
Depth 25½ inches,
Lower flange 32.58 square inches,
Upper flange 5.34 square inches,

_a_ = (6 × 10 × 12 × 30)/(26 × (34 × 12)/16) = 32.58

and 32.58/6.1 = 5.34.

— 141, last line, Fig. 63 A was omitted; it is the same as fig. 102,
page 200, inverted.

— 142, last line, for “span,” read “spans.”

— 146, head of col. 7, for “Top Washer,” read “Thickness of Washer.”

— 150, after line 9, Figs. 67 D and 67 E (page 153) should be
inserted.

— 151, l. 3, for “_W_ = 2249,” etc., read “_W_ = 2240,” etc.

— 151, l. 18, for “opposite to 31,416, is the diam. 1⅝,” read
“opposite to 41,415, is the diam. 1⅞.”

— 151, l. 19, for “1⅝,” read “1⅞.”

— 154, last line, for “tubular,” read “tabular.”

— 156, l. 4 from bottom, for “washer band,” read “washer used.”

— 164, l. 10 to 14, inclusive. The first number of ratios should be
20 instead of 15.

— 166, l. 11, for “69 B,” read “69 A.”

— 171, head of col. 5 of table, for “Rod of Arch,” read “Rad. of
Arch.”

— 173, l. 25, for “ability,” read “stability.”

— 173, l. 32, for “Whence,” read “Where.”

— 175, l. 8, for “triangular,” read “diagonal.”

— 178, l. 3, for “article,” read “outside.”

— 184, l. 4 from bottom, for “barriers,” read “voussoirs.”

— 187, fig. 96 is upside down; also, fig. 97, page 188, and fig. 98,
page 189.

— 193, l. 4, col. 3 of table, for “.00000675,” read “.00000685”;
also, l. 16, col. 5, for “straining,” read “shearing”; l. 7
from bottom, for “15,000,” read “18,000;” and l. 6 from
bottom, for “75,000,” read “105,000.”

— 199, l. 7 from bottom, for “20,132,” read “20,312.”

— 200, l. 4, for “A C,” read “A G”; and l. 6, for “that on A R,”
read “that on A K.”

— 202, l. 7, for “on page 193,” read “on page 138.”

— 204, l. 5 from bottom, for “varied line,” read “versed sine.”

— 207, l. 5 and 6, for “F G, G E, in place of E F, E C,” read “G L,
G E, in place of F L, F C.”

— 210, in place of “_f′_ = (π_F_)/(4_ph_),” put “_D_ = √(¾[_V^2_ –
_d^2_]) – √(¾[_l^2_ – _d^2_]).

where _D_ = depression,
_l_ = half length of curve before elongation,
_V_ = half length of curve after elongation,
_d_ = half distance between points of suspension.” Omit
the remainder of the paragraph.

— 211, omit the 6th and 7th lines, and in place of formula there
given, use that on page 210, (as corrected,) _V_ being the
length of semi-curve as elongated by heat instead of by
tension; the elongations, both by heat and tension, being
found by table on page 193.

— 212, l. 2, for “510.69,” read “510.80,” which result, of course,
runs through the whole example.

— 213 and 214. The remarks under “Anchoring Masonry,” are evidently
wrong throughout: 1st, the whole tension should be divided by
_two_, instead of _four_, as half of the whole tension acts at
each point of suspension; 2d, no reduction should be made for
the direction of the pulling force. One half of the tension is
3,321,250 lbs.; which is resisted by a column of masonry of
3,321,250/160 = 20,758 cubic feet, or 20 × 20 × 52 feet, or by
a mass 15 × 15 × 91 feet.

— 214, l. 6, for “561,527,” read “562,542.”

— 215, l. 14 from bottom, for “STIFFENING TOWERS,” read “STIFFENING
TRUSSES.”

— 225, l. 14, for “194,” read “193.”

— 226, l. 3, for “see page 128,” read “see page 193.”

— 227, l. 4, for “detensional,” read “detrusional.”

— 228, in place of equations at l. 16, put “_R_ × _a_ = _R′_ × (2
_d_ × _t_)”,

whence _d_ = (_R_ × _a_)/(2_R′_ × _t_);
where _a_ = area of rivet,
_d_ = distance,
_t_ = plate thickness.

— 229, in art. 242, the strengths of “wrought iron,” have been taken
for those of “boiler plate”; that is, 11,000 for 7,500, and
15,000 for 12,740, which is wrong.

— 231, l. 21, for “chopped,” read “dropped.”

— 234, l. 4, for “joint,” read “just.”

— 235, l. 14, for “0.016 feet,” read “0.047 feet.”

— 236, l. 9, for “care,” read “ease.”

— 237, l. 3 from bottom, for “representing,” read “separating.”

— 241, l. 2, for “localities,” read “locality.”

— 242, l. 7, omit “and _c_ _e_, the parapets.”

— 243, l. 9, for “embankment,” read “abutment.”

— 244, l. 9, for “is thus,” read “is found thus.”

— 245, l. 17, for “latter,” read “batter.”

— 249, l. 23, for “common hydraulic,” read “common mortar,
hydraulic.”

— 249, l. 27, for “argyle magnesia,” read “argil, magnesia.”

— 251, l. 16, for “7½ to 2,” read “1½ to 2.”

— 254, last l., for “corners,” read “courses.”

— 256, l. 13, for “formed,” read “found.”

— 258, art. 276, in place of “20/2 × 15 × 1 × 100 × 20/3,” put “20 ×
15 × 1 × 100 × 2 × 20/3,” where 2 represents the ratio between
C^{_a_} 6, and 6–2; thus, 20 × 15 × 1 × 100 × 6.6/12 × 20/3 =
111,111, for the overthrowing force in place of 100,000. The
overthrowing force is thus large, because the maximum weight
of earth has been assumed to press against the wall with its
whole force, no allowance being made for friction. In
practice, 4/10 of the height has been found amply thick for
walls retaining ordinary earth.

— 262, last l. but one, for “superstratum,” read “substratum.”

— 264, in example, l. 5, for “26,667,” read “48,000.”

— 266, l. 25, for “Godwin,” read “Goodwin.”

— 266, l. 26, for “There, sands,” read “These sands.”

— 267, l. 22, for “bottom,” read “proper level.”

— 281, l. 4 from bottom, for “curve,” read “cone.”

— 282, l. 20, for “Daniel,” read “David.”

— 282, l. 4 from bottom, for “cup,” read “cap.”

— 284, l. 10, and 285, l. 8, for “compressed rails,” read “compound
rails.”

— 285, l. 5, for “extension,” read “extensile.”

— 289, invert col. 1 of table, so that it shall read—

At 100° place the rails in contact.
At 90° at a distance of .00136 feet, or 0.016 inches.
At 80° at a distance of .00272 feet, or 0.032 inches
Etc.

— 289, last l., for “levelled,” read “bevelled.”

— 291, last l., for “_a c_, 4.8,” read “_a c_, L 8.”

— 292, l. 9, for “_e h_ and _d k_,” read “_e L_ and _d k_”; same p.
l. 6 from bottom, for “_a_, 9 is three, etc.” read “_a b_ is
three,” etc.

— 293, l. 6 and 7, for “_i g_, _e h_, _b b_, 8, 9, _A s_ 79,” read
“_i g_, _e h_, _a c_, _b c_.”

— 296, l. 14, for “_R^2_ – (_R_ – 8)^2,” read “_R^2_ – (_R_ –
_g_)^2.”

— 303, art. 299, for “M. Leguire,” read “M. Seguin.”

— 306, l. 2, for “R. R. & G.,” read “R. K. and G.”

— 314, l. 2, for “D. R. Clark,” read “D. K. Clark.”

— 320, l. 1, for “Railroad, three pounds (Pennsylvania),” read
“Railroad (Pennsylvania), three pounds.”

— 320, l. 7, for “coal,” read “coke.”

— 331, near bottom, for “The area is, therefore,

Sides, twice length, etc., read “Sides, twice length by height, etc., Back, twice height, etc., Back, height by width, etc., Front, twice height, etc., Front, height by width, etc., Top, twice length, etc.,” Top, length by width, etc.”

— 334, l. 15, for “44.7 lbs.,” read “14.7 lbs.”

— 335, l. 7, for “Railway Mechanics,” read “Railway Machinery.”

— 335, l. 10, for “two velocities,” read “low velocities.”

— 336, last l., for “entering part,” read “entering port.”

— 341, l. 11, for “properties,” read “proportions.”

— 341, last l., for “Nollan,” read “Nollau.”

— 346, l. 17, for “part,” read “port,” and for “construction,” read
“contraction.”

— 355, l. 7, for “6300,” read “5170”; and l. 9, for “16,905,” read
“15,775.”

— 363, l. 17, for “44 × 2 = 80,” read “44 × 2 = 88.”

— 363, l. 18, for “54½ × 3 = 103½,” read “54½ × 3 = 163½.”

— 367, l. 16, for “15.0/10,” read “15.0/16,”

— 368, l. 15, for “_u_ = 135,” read “_n_ = 135,” etc.

— 370, l. 7, for “feet,” read “per cent.”

— 376, for “19090,” read “19050.”

— 384, in last part of example, for “5280/(4½ × 3.1416) × 4 =
37300,” read “25 × 5280/(4 × 3.1416) × 4 = 37348.”

— 421, bottom line, for “decision,” read “division.”

— 423 and 424, in table, for “count,” read “cost.”

— 427, l. 32, for “which,” read “we.”

— 428, l. 4, transpose “Dr. Lardner, (1850,)” to the end of line 3.

— 443, l. 28, for “valuation,” read “solution.”

— 446, l. 11, for “attained,” read “obtained.”

— 459, l. 20, for “Hectametre,” read “Hectometre.”

— 459, l. 21, for “Ridometre,” read “Kilometre.”

— 461, l. 7, for “less than _a_, or _o_,” read “less _a_, or 0.”

— 468, l. 30, for “fractions,” read “functions.”

— 474, l. 18, for “Balbett,” read “Babbitt.”

— 479, l. 10, for “one sixth, with much less,” read “one sixth; with
sand, much less.”

HANDBOOK

OF

RAILROAD CONSTRUCTION.