HYDRAULIC EQUIVALENTS.
| EQUIVALENTS OF POUNDS AVOIRDUPOIS. | |||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 10 | 100 | 1000 | 10,000 | 100,000 | |||||||||||||
| qr. | lb. | cwt. | qr. | lb. | ton | cwt. | qr. | lb. | ton | cwt. | qr. | lb. | ton | cwt. | qr. | lb. | |
| 1 | 0 | 10 | 0 | 3 | 16 | 0 | 8 | 3 | 20 | 4 | 9 | 1 | 4 | 44 | 12 | 3 | 12 |
| 2 | 0 | 20 | 1 | 3 | 4 | 0 | 17 | 3 | 12 | 8 | 18 | 2 | 8 | 89 | 5 | 2 | 24 |
| 3 | 1 | 2 | 2 | 2 | 20 | 1 | 6 | 3 | 4 | 13 | 7 | 3 | 12 | 133 | 18 | 2 | 8 |
| 4 | 1 | 12 | 3 | 2 | 8 | 1 | 15 | 2 | 24 | 17 | 17 | 0 | 16 | 178 | 11 | 1 | 20 |
| 5 | 1 | 22 | 4 | 1 | 24 | 2 | 4 | 2 | 16 | 22 | 6 | 1 | 20 | 223 | 4 | 1 | 4 |
| 6 | 2 | 4 | 5 | 1 | 12 | 2 | 13 | 2 | 8 | 26 | 15 | 2 | 24 | 267 | 17 | 0 | 16 |
| 7 | 2 | 14 | 6 | 1 | 0 | 3 | 2 | 2 | 0 | 31 | 5 | 0 | 0 | 312 | 10 | 0 | 0 |
| 8 | 2 | 24 | 7 | 0 | 16 | 3 | 11 | 1 | 20 | 35 | 14 | 1 | 4 | 357 | 2 | 3 | 12 |
| 9 | 3 | 6 | 8 | 0 | 4 | 4 | 0 | 1 | 12 | 40 | 3 | 2 | 8 | 401 | 15 | 2 | 24 |
TRIGONOMETRICAL FUNCTIONS.
RIGHT-ANGLED TRIANGLES.
Sin. A = a
b Sec. A = b
c Tan. A = a
c
Cos. A = c
b Cosec. A = b
a Cotan. A = c
a
Versin. A = b − c
b. Coversin. A = b − a
b.
| Given. | Required. | Formulæ. |
| a,b | A,C,c | Sin. A = a b Cos. C = a b c = √(b + a)(b − a) |
| a,c | A,C,b | Tan. A = a c Cotan. B = a c b = √a2 + c2 |
| A,a | C,c,b | C = 90° − A c = a × Cotan. A b = a Sin. A |
| A,b | C,a,c | C = 90° − A a = b × Sin. A c = b × Cos. A |
| A,c | C,a,b | C = 90° − A a = c × Tan. A b = c Cos. A |
OBLIQUE-ANGLED TRIANGLES.
s = ½(a + b + c)
| Given. | Formulæ. | |
|---|---|---|
| A,B,C,a | Area= | (a2 × Sin. B × Sin. C) ÷ 2 Sin. A |
| A,b,c | ½(c × b × Sin. A) | |
| a,b,c | √s(s − a)(s − b)(s − c) | |
| Given. | Required. | Formulæ. |
| A,C,a | c | c = aSin. C Sin. A |
| A,a,c | C | Sin. C = c Sin. A a |
| a,c,B | A | Tan. A = a Sin. B c − a Cos. B |
| a,b,c | A | Sin. ½A = √(s − b)(s − c) b × c |
| Cos. ½A = √s(s − a) b × c; |
||
| Tan. ½A = √(s − b)(s − c) s(s − a) |
||
COMPOUND ANGLES.
Tan. (A + B) = Tan. A + Tan. B
1 − Tan. A Tan. B.
Tan. (A − B) = Tan. A − Tan. B
1 + Tan. A Tan. B.
SLIDE RULE DATA SLIPS, compiled by C. N. Pickworth, Wh.Sc.
| ¹⁄₃₂ | 0·03125 |
| ¹⁄₁₆ | 0·0625 |
| ³⁄₃₂ | 0·09375 |
| ⅛ | 0·125 |
| ⁵⁄₃₂ | 0·15625 |
| ³⁄₁₆ | 0·1875 |
| ⁷⁄₃₂ | 0·21875 |
| ¼ | 0·25 |
| ⁹⁄₃₂ | 0·28125 |
| ⁵⁄₁₆ | 0·3125 |
| ¹¹⁄₃₂ | 0·34375 |
| ⅜ | 0·375 |
| ¹³⁄₃₂ | 0·40625 |
| ⁷⁄₁₆ | 0·4375 |
| ¹⁵⁄₃₂ | 0·46875 |
| ¹⁷⁄₃₂ | 0·53125 |
| ⁹⁄₁₆ | 0·5625 |
| ¹⁹⁄₃₂ | 0·59375 |
| ⅝ | 0·625 |
| ²¹⁄₃₂ | 0·65625 |
| ¹¹⁄₁₆ | 0·6875 |
| ²³⁄₃₂ | 0·71875 |
| ¾ | 0·75 |
| ²⁵⁄₃₂ | 0·78125 |
| ¹³⁄₁₆ | 0·8125 |
| ²⁷⁄₃₂ | 0·84375 |
| ⅞ | 0·875 |
| ²⁹⁄₃₂ | 0·90625 |
| ¹⁵⁄₁₆ | 0·9375 |
| ³¹⁄₃₂ | 0·96875 |
Circ. of circle = 3·1416 d.
Area „ „ = 0·7854 d2.
Sq. eq. area to cir., s = 0·886 d.
Circle eq. to sq., d = 1·128 s.
Sq. inscbd. in circ., s = 0·707 d.
Circsb. circ. of sq., d = 1·414 s.
Area of ellipse = 0.7854 a × b.
Surface of sphere = 3·1416 d2.
Volume „ „ = 0·5236 d3.
„ „ cone = 0·2618 d2 h.
Radian = 180°
π = 57·29 deg.
Base of nat. or hyp. log. = e = 2·7183.
Nat. or hyp. log. = com. log. × 2·3026.
g (at London) 32·18 ft. per sec., per sec.
Abs. temp. = deg. F. + 461° = deg. C. + 274°.
C.° = 5
9(F.° − 32°); F.° = 9
5C.° + 32°.
Cal. pr.—Ther. units per lb.: Coal, 14,300;
petrol’m, 20,000; coal gas per cu. ft., 700.
Sp. heat:—Wt. iron, 0·1138; C.I., 0·1298;
copper, brass, 0·095; lead, 0·0314.
Inch = 25·4 mil’metres; mil’metre = 0·03937 in.
Foot = 0·3048 metres; metre = 3·2809 feet.
Yard = 0·91438 metre; metre = 1·0936 yards.
Mile = 1·6093 kilomtrs.; kilomtr. = 0·6213 mile.
Sq. in. = 6·4513 sq. cm.; sq. cm. = 0·155 sq. in.
Sq. ft. = 9·29 sq. decmtr.; sq. decmtr. = 0·1076 sq. ft.
Sq. yd. = 0·836 sq. metre; sq. metre = 1·196 sq. yds.
Sq. ml. = 258·9 hectares; hectare = 0·00386 sq. ml.
Cu. in. = 16·386 c. cm.; c. cm. = 0·06102 cu. in.
Cu. ft. = 0·0283 c. metre; c. metre = 35·316 cu. ft.
Grain = 0·0648 gramme; gram. = 15·43 grs.
Ounce = 28·35 grams.; „ = 0·03527 oz.
Pound = 0·4536 kilogm.; kilogm. = 2·204 lb.
Ton = 1·016 tonnes; tonne = 0·9842 ton.
Mile per hr. = 1·466 ft., or 44·7 cm., per sec.
Lb. per cu. in. = 0·0276 kilogram per cu. cm.
Kilogram per cu. cm. = 36·125 lb. per cu. in.
Lb. per cu. ft. = 16·019 kilogm. per cu. mtre.
Grain per gall. = 0·01426 gramme per litre.
Gramme per litre = 70·116 grains per gall.
| Ultimate Strength | Lb. per Sq. in. | |
|---|---|---|
| Tens’n. | Comp’n. | |
| Wt. iron | 50,000 | 50,000 |
| Cast „ | 16,000 | 95,000 |
| Steel | 80,000 | 70,000 |
| Copper | 21,000 | 50,000 |
| Brass | 18,000 | 10,500 |
| Lead | 2,500 | 7,000 |
| Pine | 11,000 | 6,000 |
| Oak | 15,000 | 10,000 |
| Weight of Metals. | Cub. In. | Cub. Ft. | 12 Cu. In. |
|---|---|---|---|
| Wt. iron | 0·277 | 480 | 3·33 |
| Cast „ | 0·260 | 450 | 3·12 |
| Steel | 0·283 | 490 | 3·40 |
| Copper | 0·318 | 550 | 3·82 |
| Brass | 0·300 | 520 | 3·61 |
| Zinc | 0·248 | 430 | 2·98 |
| Alumin’m | 0.096 | 168 | 1·16 |
| Lead | 0.411 | 710 | 4·93 |
1. It will be recognised that n is the characteristic of the logarithm of the original number.
2. The special case in which the numerator is 1, 10, or any power of 10 must be treated by the rule for reciprocals (page 27).
3. The possible need for traversing the slide, to change the indices, when using the C and D scales, is not considered as a setting.
4. The reader may be reminded that cross-multiplication of the factors in any such slide rule setting will give a constant product, e.g., 20 × 94·5 = 27 × 70.
5. In this case cross dividing gives a constant quotient, e.g., 8 ÷ 3 = 4 ÷ 1·5. Since the upper scale is now a scale of reciprocals, the ratio is really
| O | ⅛ | ¼ |
| D | 1·5 | 3 |
6. These lines should not be brought to the working edge of the scale but should terminate in the horizontal line which forms the border of the finer graduations, their value being read into the calculation by means of the cursor (see page 55).
7. The same principle may be applied to the cursor.
8. Philosophical Transactions of the Royal Society, 1815.
“An extremely useful and much-needed little work, giving a complete explanation of the theory and use of logarithms, by a teacher of great clearness and good style.”—The Mining Journal.
Comprising “The Indicator: Its Construction and Application” and “The Indicator Diagram: Its Analysis and Calculation.” Complete in One Volume.
“Mr. Pickworth’s judgment is always sound, and is evidently derived from a personal acquaintance with indicator work.”—The Engineer.
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For a full and intelligent appreciation of the Slide Rule and its various applications an elementary knowledge of logarithms is necessary. All that is required will be found in this little work, which gives a simple, detailed and practical explanation of logarithms and their uses, particular care having been taken to elucidate all difficult points by the aid of a number of worked examples.
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| W. P. THOMPSON, | G. C. DYMOND, |
| F.C.S., M.I.Mech.E., F.I.C.P.A. | M.I.Mech.E., F.I.C.P.A. |
| W. P. Thompson & Co., | |
| 12 CHURCH STREET, LIVERPOOL, | |
| CHARTERED PATENT AGENTS. | |
| H. E. POTTS, | J. V. ARMSTRONG, |
| M.Sc., Hon. Chem., F.I.C.P.A. | M.Text.I., F.I.C.P.A. |
| W. H. BEESTON, R.P.A. | |
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The Centre Screw Spring Bow Half Set of Compasses, as illustrated, possesses the advantage of COMBINING IN ONE INSTRUMENT THE SET OF THREE SEPARATE SPRING BOWS hitherto in use, while the centre screw makes for ease and accuracy of manipulation, at the same time providing a radius of over 2 inches, or double that of the old pattern.
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Illustrated Booklet giving full particulars and prices of other Instruments and Cases of Instruments sent on application.
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| Page | Changed from | Changed to |
|---|---|---|
| 24 | the right, so the number of digits in the answer = 3 − 2 × 1 = 2 | the right, so the number of digits in the answer = 3 − 2 + 1 = 2 |
| 116 | grammes, we have the equation, x × Cl. Ag.Cl. × a s. Hence, the mark |
grammes, we have the equation, x = Cl. Ag.Cl. × a s. Hence, the mark |
- Typos fixed; non-standard spelling and dialect retained.
- Used numbers for footnotes, placing them all at the end of the last chapter.