COLLEGE OF AGRICULTURE DAVIS, CALIFORNIA LIBRARY THE MECHANIC'S TEXT-BOOK . AND ENGINEER'S PRACTICAL GUIDE: CONTAINING A CONCISE TREATISE DN THE NATURE AND APPLICATION OF MECHANICAL FORCES ; ACTION OF GRAVITY; THE ELEMENTS OF MACHINERY; RULES AND TABLES FOR CALCULATING THE WORKING EFFECTS OF MACHINERY; OF THE STRENGTH, RESISTANCE, AND PRESSURE OF MATERIALS; WITH TABLES OF THE WEIGHT AND COHE- SIVE STRENGTH OF IRON AND OTHER METALS. COMPILED AND ARRANGED BY THOMAS KELT, "GLOUCESTER CITY MACHINE COMPANY, TO WHICH IS ADDED, VALUABLE HINTS TO THE YOUNG MECHANIC ON THE CHOICE OF A PROFESSION; MISDIRECTION OF INDUSTRY; INTELI.ECTUAL CULTIVATION, AND THE STUDIES AND MORALS OF THE MECHANIC, ETC., ETC. BY JOHN FROST, LL. D. BOSTON: PHILLIPS, SAMPSON, AND COMPANY. 1857. Entered according to Act of Cougrws. in the year 1855 BY PHILLIPS. SAMPSON * CO, In the Clerk's Office of the District Court of Massachusetts CONTENTS. PRACTICAL GEOMETRY. Theorems. ***** To erect a perpendicular on a right line, 9 To erect a perpendicular at tlio end of a line,.. 9 To bisect a gi ven ann CHAPTER XI. The Mer.ha?dc's Studies continued, 329 CHAPTER XII The Mechanic's Studies continued, ......... 340 CHAPTER XIII. Tke Mechanics Studies continued, 359 CHAPTER XJV. The Morals of the Mechanic, . . 381 THE WORKSHOP COMPANION. \ PRACTICAL GEOMETRY. GEOMETRY is the science which investigates and demonstrates the properties of lines on surfaces and solids; hence, PRACTICAL GKOMKTKY is the method of applying the rules of the science to practical pur poses. 1. From any given point, in a straight /{we, to erect a perpendicular ; or, to make a line at right angles with a given line. On each side of the point A, from which the line is to be mads, take equal distances, as A 6, A c , and from 6 and c as centres, with any distance greater than b A, or c A, describe arcs cutting each other at d; then will the line A d be the per- pendicular required. 2. When a perpendicular is to be made at or near th* end of a given line. With any convenient radius, and with any distance from the given line A 6, describe a portion of a circle, as b A c, cutting the given point in A ; draw, through the centre of th^ circle w, the line b n c ; and a lin^ from the p)int A, cutting the intersections at c, is the perpendicular required. f 10 PRACTICAL GEOMETRY. 3. To do the same otherwise. From the given point A, with any convenient radius, describe the arc d c b ; from d, cut the arc in c, and from c, cut the arc in b ; also, from c and b as centres, describe arcs cutting each other in / ; then will the line A t be the perpendic- . ular as required. Note. When the three sides of a triangle are in the propor- tion of 3, 4, and 5 equal parts, respectively, two of the sides form a right anirle; and observe that in each of these or the preceding problems, the perpendiculars may be continued be- low the given lines, if necessarily required. 4. To bisect any given angle. From the point A as a centre, with any radius less than the extent of the angle, describe an arc, as c d; and from c and d as centres, describe arcs cutting each other at b ; then will the line A 6 bisect the angle as re- quired. 5. To find the centre of a circle, or radius, that shall cut any three given points, not in a direct line. From the middle point 6 as a centre, with any radius, as b c, b d, describe a portion of a circle, as c s d; and from r and t as centres, with an equal radius, cut the por- tion of the circle in c s and d s; draw lines through where the arcs cut each other ; and the intersection of the lines at s is the centre of the circle as required. PRACTICAL GEOMETRY. II 6. To find the centre of a given tircle. Bisect any chord in the circle, as A B, by a perpendicular, C D ; bi- sect also the diameter E D in f; and the intersection of the lines at / is the centre of the circle re- quired. 7. To fnd the length of any given arc oj a circle. With the radius A C, equal to |th the length of the chord of the arc A B, and from A as a centre, cut the arc in c; also from B as a centre, with equal radius, cut the chord in b; draw the line C b; and twice the length of the line is the length of the arc nearly. 8. Through any given point, to draw a tangent to a circle. Let the given point be at A; draw the line A C, on which describe the semicircle ADC; draw the line A D B, cutting the circumference in D, which is the tangent as required. 9. To draw from or to the circumference of a circle lines tending towards the centre, when the centre is inac cessible. Divide the whole or any given portion of the cir- cumference into the desired number of equa parts' then, with any radius less than the distance of tw 2 PRACTICAL GEOMETRY. divisions, describe arcs cutting each other, as A 1 B 1, C 2, D 2, &c.; draw the lines C 1, B 2, D 3, &c., which lead to the centre as required. To draw the, end lines. As A r, F r, from C describe the arc r, and with the radius C 1, from A or F as centres, cut the former arcs at r, or r, and the lines A r, F r, will tend to the centre as required. 10. To describe an arc, or segment of a circle, oj large radii. Of any suitable material, construct a triangle, as A B C; make A B, B C, each equal in length to the chord of the arc D E, and height, twice that of the arc B b. At each end of the chord D E fix a pin, and at B, in the triangle, fix a tracer, (as a pencil,) move the triangle along the pins as guides ; and the tracer will describe the arc required. 11. Or otherwise. Draw the chord A C B ; also draw the line H D I, parallel with the chord, and equal to the height of the segment ; bisect the chord in C, and erect the perpen- dicular C D ; join A D, D B ; draw A H perpendicular to A D, and B I perpendicular to B D , erect also the perpendiculars A n, B n ; divide A B and H I into any PRACTICAL GEOMETRY. J3 number of equal parts ; draw the lines 1 1, 2 2, 3 3, fee. ; likewise divide the lines A ?i, B n, each into half the number of equal parts ; draw lines to D from each division in the lines A ?i> B n, and, through where they intersect the former lines, describe a curve, which will be the arc or segment required. 12. To describe an ellipse, having the two diameters given. On the intersection of the two diameters as a centre, with a radius equal to the difference of the semi-diameters, describe the arc a b ; and from b as a centre, with half the chord 6 c a, describe the arc c d ; from o, as a centre, with the distance o d, cut the diameters in d r, d t ; draw the lines r, s, s, and , 5, s ; then from r and t describe the arcs s, s, s, s ; also from d and d, describe the smaller arcs s, s, s, s, which will complete the ellipse as required. 13. To describe an elliptic arch, the width and rise of span being given. Bisect with a line at right angles the chord or span A B ; erect the perpendicular A g, and draw the line q D equal and parallel to A C; bisect A C and A q in r and n ; make C / equal to C D, and draw the line Irq; draw also the line n s D ; bisect 8 D with a line at right angles, and meeting the line C D in g ; draw thejine g q, make C P equal to C &, and draw the iine g P*i; then from g as a centre, with the radius g- D, describe the arc s D i ; and from k and P as cen- tres, with the radius A k, describe the arcs A 8 and B ^ which completes the arch as required. O, 14 PRACTICAL GEOMETRY. 14. Bisect the chord A B, and fix at right angles any straight guide, as b c ; pre- pare, of any suitable mate- rial, a rod or staff', equal to half the chord's length, as d e f; from the end of the stafij equal to the height of the arch, fix a pin e, arid at the extremity a tracer/; move the staff, keeping its end to the guide and the fixed pin to the chord ; and the tracer will describe one half the arc required. 15. To describe a parabola, the dimensions being given. Let A B equal the length, and C D the breadth of the required parabola ; divide C A, C B into any num- ber of equal parts ; also divide the perpendiculars A a and B 6 into the same number of equal parts; then from a and 6 draw lines meeting each division on the line A C B ; and a curve line drawn through each inter- section will form the parabola required. 16. To obtain by measurement the length of any direct line, though intercepted by some material object. Suppose the distance be- tween A and B is required, but the right line is intercepted by the object C. On the point d, with any con- PRACTICAL GEOMETRY. 15 renient radius, describe the arc c c, make the arc twice Che radius in length, through which draw the line d c e t and on e describe another arc equal in length to once the radius, as eff; draw the line efr equal to efd; on r describe the arc jj, in length twice the radius; continue the line through rj, which will be a right line, and d e, or e r, equal the distance between d r by which the distance between A and B is obtained as required. 17. Jl round piece of timber being given, out of which to cut a beam of strongest section. Divide into three equal parts any diameter in the circle, as Ac/, e C ; from d or e, erect a perpendicular meeting the circumference of the circle, as d B ; draw A B and B C, also A D equal to B C, and D C equal to A B, and the rectangle will be a section of the beam as required. 18. To measure the distance between two objects, both being inaccessible. From any point C draw A any line C c, and bisect it in D ; take any point E in the prolongation of A C, and draw the line E e, making D e equal to D E ; in like manner take any point F in the prolongation of B C, and make D / equal to F D. Produce A D and e c till they meet in a, and also B D and fc till they meet in 6; then a b equal A B, or the distance between the objects as required. 2* 16 PRACTICAL GEOMETRY. 19. To ascertain the distance, geometrically, of anj inaccessible object on an equal plane. Let it be required to find the distance between A and B, A being inaccessible; produce the line in the direction of A B to any point, as D ; draw the line D d at any angle to the line A B ; bisect the line D d, through which draw the line B b, making c 6 equal to B c , draw the line d b a ; also through c, in the direction c A, draw the line a c A, intersect- ing the line d b a ; then b a equal B A, the distance required. 20. Otherwise. Prolong A B to any point D, making B C equal to C D ; draw the line D a at any angle with D A, and the line C b similar to B c; draw also the line .D E F, which inter- sects the line D a ; then a b a- equal B A, or the distance required. 21. To find the proper position for an eccentric, in relation to the crank in a steam engine, the angle oj eccentric rod, and travel of the valve, being given. Draw the right line A B, as the situation of the crank at commencement of the stroke ; draw also the line C d, as the proper given angle of eccentric rod with the crank; then from C as centre, describe a circle equal to the travel of the ^alve ; draw the line e f at right angles to the lino PRACTICAL GEOMETRY. 17 C J, draw also the lines 1 1, and 2 2, parallel to the line e f; and at a distance from e /on each side, equal to the .ap and lead of the valve, draw the angular lines C 1, C 2, which are the angles of eccentric with the crank, for forward or backward motion, as may be required. 22. The throw of an eccentric, and the travel of the valve in a steam-engine, also the length of one lever for communicating motion to the valve, being given, to deter- mine the proper length for the other. On any right line, as A B, describe a circle A D, equal to the throw a of eccentric and travel of valve ; then from C as a centre, with a ra- dius equal to the length of lever given, cut the line A B, as at d, on which describe a circle, equal to the throw of eccentric or travel of valve, as may be required ; draw the tangents B a, B a, cut ting each other in the line A B, and d B is the length of the lever as required. Note. The throw of an eccentric is equal to the sum of twice the distance between the centres of formation and revolution, as a b, or to the degree of eccentricity it is made to describe, as c d. And The travel of a valve is equal the sum of the widths of the two steam openings, and the valve's excess of length more than just sufficient to cover the openings. 23. To inscribe any regular polygon in a given circle Divide any diameter, as A B, into so many equal parts as the polygon is required to have sides ; from A and B as centres, with a radius equal to the diametej, describe arcs cutting each other in C ; draw the line C D through the second point of division on the diameter e, and the line D B is one side of the polygon required. 18 PRACTICAL GEOMETRY. 24. To construct a square upon a given right line. From A and B as centres, with the radius A B, describe Jie arcs A c 6, B c d, and from c, with an equal radius, describe the circle or portion of a circle d [ t d, A B, 6 c ; from b d cut the circle at e and c ; draw the lines A e, B c, also the line s t, which completes the square as required. a given 25. To form a square equal in area to triangle. Let A B C be the given tri- angle ; let fall the perpendicu- lar B d, and make A e half the height d B ; bisect e C, and de- scribe the semicircle e n C ; erect the perpendicular A s, or side of the square, then A 5 t x is the square of equal area as required. 26. To form a square equal in area to a given rec- tangle. Let the line A B equal the length and breadth of the given rectangle ; bisect the line in e, and describe the semi- circle A D B; then from A with the breadth, or from B with the length, of the rec- tangle, cut the line A B at C, and erect the perpendicular C D, meeting the curve at D, and C D equal a side of the square required. 27. To find the length for a rectangle whose area shall be equal to that of a given square, the breadth of the rec- tangle being also given. Let A B C D be the given square, and D E the given breadth of rectangle ; continue the line B C to F, and PRACTICAL GEOMETRY. 19 3SI draw the line D F ; also, continue the line D C to g, and draw the line A g parallel to D F ; from the intersection of the lines at g, draw the line g d parallel to D E, and E d parallel to D g-; then E D dg is the A I rectangle as required. 28. To bisect any given triangle. Suppose ABC the given triangle ; bisect one of its sides, as A B in e, from which describe the semicirche A r B ; bisect the same in r, and from B, with the distance B r, cut the diameter A B in v ; draw the line v y parallel to A C, which will bisect the triangle as required. 29. To describe a circle of greatest diameter in a giv- en triangle. Bisect the angles A and B, and draw the intersecting lines A D, B D, cutting each other in D ; then from D as centre, with the dis- tance or radii D C, de- scribe the circle C e y, as required. 30. To form a rectangle of greatest surface, in a given triangle. Let ABC be the given triangle ; bisect any two of its sides, as A B, B C, in e and d ; draw the line e d; also at right angles with the line e d, draw the lines ep, dp, and epp d is the rec- tangle required. 20 DECIMAL ARITHMETIC DECIMAL ARITHMETIC is the most simple and ex plicit mode of performing- practical calculations, on account of its doing away with the necessity of frac tional parts in the fractional form, thereby reducing long and tedious operations to a few figures arranged and worked in all respects according to the usual rules of common arithmetic. Decimals simply signify tenths ; thus, the decimal of a foot is the tenth part of a foot, the decimal of that tenth is the hundredth of a foot, the decimal of that hundredth is the thousandth of a foot, and so might the divisions be carried on and lessened to infinity ; but in practise it is seldom necessary to take into account any degree of less measure than a one-hundredth part of the integer or whole number. And, as the entire system consists in supposing the whole number divided into tenths, hundredths, thousandths, &c., no peculiarity of notation is required, otherwise than placing a mark or dot, to distinguish between the whole and any part of the whole ; thus, 34-25 gallons signify 34 gallons 2 tenths and 5 hundredths of a gallon; 11-04 yards sig nify 1 1 yards and 4 hundredths of a yard, 16-008 shil- lings signify 16 shillings and 8 thousandth parts of a shilling ; from which it must appear plain, that ciphers on the right hand of decimals are of no value whatever ; but placed on the left hand, they diminish the decimal value in a tenfold proportion, for -6 signify 6 tenths ; 06 signify 6 hundredths; and -006 signify 6 thou- sandths of the integer, or whole number. REDUCTION. Reduction means the construing or changing of vul- gar fractions to decimals of equal value ; also finding the fractional value of any decimal given. Rule 1. Add to the numerator of the fraction any number of ciphers at pleasure, divide the sum by the denominator, and the quotient is the decimal of equiva- lent value. DECIMAL ARITHMETIC. 21 Rule 2. Multiply the given decimal by the various fractional denominations of the integer, or whole num ber,. cutting off from the right hand of each product, foi decimals, a number of figures equal to the given number of decimals, and thus proceed until the lowest degree, or required value, is obtained. Ex. 1. Required the decimal equivalent, or decimal of equal value, to ^ of a foot -25, the decimal required. Ex. 2. Reduce the fraction J of an inch to a deci inal of equal value. - '125, the decimal required. 8 Ex. 3. What is the decimal equivalent to 5 of a gal Ion? - ~-875, the decimal equivalent. Ex. 4. Required the fractional value of the decimal 40625 of an inch. 40625 Multiply by J __ 8 3-25000 50000 A _ ? 1-00000 i and fa of an inch, the value required. Ex. 5. What is the fractional value of -625 of a cwt? 625 Multiply by 4 qrs, 4 2-500 X 28 Ibs. 28 14-000 = 2 quarters and 14 Ibs., the value required. 22 DECIMAL ARITHMETIC. Ex. 6 Ascertain the fractional value of -875 ot ait imperial gallon. 875 Multiply by 4 quarts 4 3-500 X 2 pints_ ].()00 = 3 quarts and 1 pint the value required. Ex. 7. What is the fractional value of -525 ot d . sterling ? 525 Multiply by 20 sh._ 10-500 X 12 pence j*j 0-000 = 10 shillings and fi pence* the value required. Independent of the mark or dot which distinguishes between integers and decimals, the fundamental rules, viz., Addition, Subtraction, Multiplication, and Division, are in all respects the same as in Simple Arithmetic ; and an example in each, illustrative of placing the separating point, will no doubt render the whole system sufficiently intelligible, even to the dullest capacity. Ex. 1. Add into one sum the following integers and decimals. 16-625; 11-4; 20-7831; 12-125; 8-04; and 7>00a 1O625 114 207&31 12-125 8-04 7.002 75-9751 = the sum required. DECIMAL ARITHMETIC. 23 Ex. 2. Subtract 1 19-80764 from 234-98276 234-98276 119-80764 115-1 75 12 z= the remainder Ex. 3. Multiply 62-10372 by 16-732. 62-10372 16-732 12420744 1822:*2 6210372 1039-1 1944304 the product required Observe that the number of figures in the product from the right hand, accounted as decimals, are equal to the number of decimals in the multiplier and multi- plicand taken together. Ex. 4. Divide 39-375 by 9-25. l)-25 ) 39 375 (4-256 = the quotient required. 3700 2375 -Observe that the number of dec! 1850 male, in the divisor and quotient together, must be equal to the number in the dividend. 6250 5550 " 700 Aiv le. The operation might be still continued, so as to reduce the quotient to a degree of greater exactitude ; but in practice it is quite unnecessary, being even now reduced to a measure of greater nicety than is commonly required. 3 DECIMAL ARITHMETIC. DEFINITIONS OF ARITHMETICAL SIGNS EMPLOYED IN THE FOLLOWING CALCULATIONS, WHICH OUGHT TO BE PARTICULARLY ATTENDED TO -9 i Tt SO 8 + 2 o * I x -I * fc 00 *# i * s - * -S .S .1 J! Ir U "PI ii ^ e. $ II I :i 5 " - i til ti - is s -a - 8--S "3 ? ti " ?? rt O 5 o HP co g ! *s . U ~ e X O I s - 28^1. 7 -J 2 |S 5 5 8 3 2 2 II Tf - - X 1 I + I X -I- " u> a* 1 lo 15 DECIMAL APPROXIMATIONS. POR FACILITATING CALCULATIONS IN MENSURATION. Uneal feet multiplied by -00019 = yards " -000568 = Square inches " -007 = " yards -0002067 = Circular inches " -OOaW5 = Cylindrical inches -0004545 =. " feet " -02909 = Cubic inches " -00058 = miles. square feet, acres, square feet, cubic feet, cubic yards, cubic feet. " feet 03704 = cubic yards. tt a tt 6-232 imper ial gallons u inches tt 003607 = " M Cylindrical feet tt 4-895 = n a " inches u 002832 = tt tt Cubic inches 263 = Ibs. avs. of cast iron tt tt 't 281 tt wrought do. tt tt it 283 as tt steel.V tt u tt 3225 = u copper. u tt u 3037 sai tt brass. it tt tt 26 S3 tt zinc. tt tt tt .4103 ss tt lead. it tt tt 2636 = tin. t tt tt 4908 = u mercury. Cylindrical inches tt 2065 SS tt cast iron a tt 2168 =r tt wrought iron u tt 2223 =r tt steel. u tt '2533 =r " copper. w tt 2385 = brass. a tt 201-2 zinc. tt tt 3223 ss tt lead. * r * 207 as tt tin. tt ft 3854 = tt mercury. Avoirdupois Ibs. tt 009 as cwts. tt tt 00045 tt tens. DECIMAL EQUIVALENTS. DECIMAL EQUIVALENTS TO FRACTIONAL PARTS OF LINEAL MEASURES. One inch, the integer, or whole number. U6875 J & fa 625 ^ 28125 & ^ 9375 1 & T \j 59375 | & -rfe 25 ^ 90625 I & T& 5625 -| & T J F 21875 ^ & 7^ 875 o F 53125 o 8 & T-fV 1875 o |& T ^ 84375 - J & $2 5 ^ ? 15625 "3 4- & -JJ2- 8125 | f & A 46875 4- & 7^75- Oi * O 4 - O ^ 125 1" 78125 4 & I$V '4375 g ^ &T V 09375 | ^. .75 B 40625 ^ & ^j 0(525 T ! F 71875 | & JJ 3 J 375 f 03125 ^ 6875 | & T5 34375 | & gV 65625 | & -2 3125 1 & T ^ One foot, or 12 inches, the integer. 9166 11 inches. 6333 - 10 * 4166 5 inches. 3333 ^ 4 0625 c | of inch. 0528 | " 75 1 9 " 25 3 " 04 166 | " 6666 Sf 8 " 1666 S" 2 " 03125 v " 5833 7 " 0833 1 " 02083 | | " 5 6 07291 d | 01041 ^ " One yard, or 36 inches, the integer. 972S a> inches. 6389 23 inches. 3055 11 inches. 9445 34 " 61 11 22 " 2778 10 9167 33 " 5833 21 " '25 9 8889 c 32 " 5556 o 20 " 2222 o 8 8611 ~ 31 " 5278 ^19 " 1944 ^ 7 { 8333 | 30 " 5 = 18 " 1666 3 6 " 8056 5" 29 " 4722 17 " 1389 S" 5 " 7778 28 " 4445 | 16 1111 4 " 75 * 27 " 41% 15 -0833 * 3 7232 26 " 3889 H ' 0555 2 " 6944 25 " 3611 13 i 0277 1 ' 6667 24 " 3333 12 j 27 MENSURATION. MENSURATION is that branch of Mathematics which IP employed in ascertaining the extension, solidities, and capacities "of bodies, capable of being measured. 1. MENSURATION OF SURFACE. To measure or ascertain the quantity of surface in any right-lined figure whose opposite sides are parallel to iach other, as a Square, Rectangle, Rhomboid, &c. Rule. Multiply the length by the breadth ; the pro- duct is the area or superficial contents. Application of the Rule to practical Purposes. 1. The side of a square piece of board is 8 T 3 ^ inches fli length ; required the area or superficies. Decimal equivalent to the fraction ^ = -1875, (see page 26 ;) and 8-1875 X 8-1875 = 67-03515625 square inches, the area. 2. The length of the fire grate under the boiler of a steam engine is 4 feet 7 inches, and its width 3 feet 6 inches ; required the area of the fire grate. 7 in. = -5833 and 6 in. = -5, (see Table of Equivalents, p. 26;) hence 4-5833 X 3-5 = 16-04155 square feet, the area. 3. Required the number of square yards in a floor whose length is 13, and breadth 9| feet 13-5 x 9-75 = 131-625 -f 9 = 14-625 square yards. Note 1. The above rule is rendered equally applicable to figures whose sides are not parallel to each other, by taking 28 MENSURATION. the mean breadth as that by which the contents are to be esti- mated. 2. The square root of any given sum equals the side of square of equal area. ^3. Any square whose side is equal to the diagonal of another square, contains double the area of that square. 4. Any sum or area, (of which to form a rectangle.) divided by tho breadth, the quotient equals the length ; or divided by the length, the quotient equals the breadth of the rectangle, required. TRIANGLES. JJni/ two sides of a right-angled triangle being gwtn^ to full the third side. Rule 1. Add together the squares of the base and perpendicular, and the square root of the sum is tho hypotenuse or longest side. Rule 2. Add together the hypotenuse a % nd any one side, multiply the sum by their difference, and the square root of the product equals the other side. Application to practical Purposes. 1. Wanting to prop a building with rakingf shores, the top ends of which to be 25 feet from the ground, and the bottom ends 16 feet from the base of the building ; what must be their length, independent of any extra length allowed below the surface of the ground ? 25 2 + 16 2 = V 881 = 29-6316 feet, or -6816x12 = 8 inches} consequently, 29 feet 8 inches nearly. 2. From the top of a wall 18 feet in height, a line was stretched across a canal for the purpose of ascer- taining its breadth ; the length of the line, when meas- ured, was found to be 40 feet; required the breadth from the opposite embankment to the base of the wall. 40 18 = 22, and 40 -f 18 x 22 = V 1276 = 55-72, or 35 feet 9 inches nearly, the width of the can il. Triangles similar to each other are proportional to each other; hence their utility in ascertaining tlia heights and distances of inaccessible objects. MENSURATION. Thus, suppose the height of an inaccessible object I) is required ; I find by means of two staffs, or otherwise, the height of the perpendicular B C artd the length of the base line AB; also the dis- tance from A to the base of the object G D ; then AB: BC::AG.GD. And suppose A B = 6 feet. B C = 2 feet, and A G = 150 6 : 2 : : 150 : 50 feet, the height of D from G. Again, suppose the inaccessible dis- tance A be required ; make the line B A, B C, a right angle, and B C of three or four equal parts of any convenient dis- tance, through one of which, and in a line with the object A, determine the triangle CDF; then the proportion will be as C F : C D : : B F : B A. Let C F = 10 yards, C D = 53, and B F = 30, 10 : 53 : : 30 : 159 yards, the distance from B. To fnd the area of a triangle when the base and per- pendicular are given. Rule. Multiply the base by the perpendicular weight, and half the product is the area. 1. The base of the tri- anglo A D B is 11-3- inches in length, and the height D C, 3 1 inches ; required the jirea. J hence -09375 and f = -375, (see page 26 :) 11-09375 X 3-375 -- ^ - = 18-72075 square inches, the area. 30 MENSURATION. 2. The base of a triangle is 53 feet 3 inches, and the perpendicular 7 feet 9 inches ; required the area or su- perficies. 53-25 x 7-75 _ ^.g^g B q Uare feet, the area. Wlien only the three sides of a triangle can be given to find the area. Rule. From half the sum of the three sides subtract each side severally ; multiply the half sum and the three remainders together, and the square root of the product is equal the area required. Required the area of a triangle, whose three sides are respectively 50, 40, and 30 feet 50 4. 40 -f 30 = 60, or half the sum of the three sides. 60 30 = 30 first difference, 60 40 = 20 second difference, 60 50= 10 third difference, then 30 X 20 X 10 X 60 = V3&XXX) = 600, the area required. Triangles are employed to great advantage in deter- mining the area of any recti- lineal figure, as the annexed, and by which the measure- ment is rendered compara- tively simple. POLYGONS. Polygons, being composed of triangles, may of course be similarly measured; hence, in regular polygons, multiply the length of a side by the perpendicular height to the centre, and by the number of sides, and half the product is the area. MENSURATION. I g I * ooo^cx) tico fit cS TO S a& ob 50 25 i^ IO ^? X) r-t *O !X * ro 10 oo 'i'g J (M & r,^ C^ lO O? f^ IO !"* -to J.OtO OOt^C^t^ 10 1^ 00 ^ ?p "^ Cp l> i-^ 11 r-i rH o666AAA.A^ I^S ^ ^ 3 - ^ - -^ s - - - - w!t ~ < g ;"1 !!**"!!! fl fi ^* " g o cs g g & |> 1 | | I I f fill I 32 MENSURATION. Application of the Table. 1. The radius of a circle being 6^ feet, required the side of the greatest heptagon that may be inscribed therein. 86.7 X 6-5 = 5-6355, or 5 feet 7 inches nearly. 2. Each side of a pentagon is required to be 9 feet required the radius of circumscribing circle. 852 X 9 = 7-668, or 7 feet 8 inches. 3. A perpendicular from the centre to either side of an octagon is required to be 12 feet; what must be the radius of circumscribing circle? 1-08 X 12 = 12-96, or 12 feet 1 1J inches. 4. Each side of a hexagon is 4<| yards ; required its superficial contents. 4i X 2-598 = 52-6095 square yards. THE CIRCLE AND ITS SECTIONS. Observations and Definitions. 1. The circle contains a greater area than any other plane figure bounded by the same perimeter or out- line. 2. The areas of circles are to each other as the squares of their diameters; any circle twice the diam- eter of another contains four times the area of the other. 3. The radius of a circle is a straight line drawn from the centre to the circumference, as O B. 4. The diameter of a circle is a straight line drawn through the centre, and terminated both ways at the circumference, as C O A. 5. A chord is a straight line joining any two points of the circumference, as D F. 6. The versed sine is a straight line joining the chord and circumference, as E G. MENSURATION. 33 7. An arc is a ^y part of the circumference, as C D E. 8. A semicircle is half the circumference cut oif by a diameter, as C E A. 9. A segment is any portion of a circle cut off by a chord, as D E F. 10. A sector is a part of a circle cut off by two radii, as A O B. General Rules in Relation to the Circle. 1. Multiply the diameter by 3-1410, the product is the circumference. 2. Multiply the circumference by -31831, the product is the diameter. 3. Multiply the square of the diameter by -7854, the product is the area. 4. Multiply the square root of the area by 1-12837, the product is the diameter. 5. Multiply the diameter by -8862, the product is the side of a square of equal area. 6. Multiply the side of a square by 1-128, the prod- uct is the diameter of a circle of equal area. Application of Hie Rules as to Purposes of Practice. 1. The diameter of a circle being 7 T \ inches, re quired its circumference. 7-1875 X 3-1416 =22-58025 inches, the circumference. Or, the diameter being 30 feet, required the circum- ference. 3-1416 X 30-5 = 95-8188 feet, the circumference. 2. A straight line, or the circumference of a circle, oeing 274-89 inches, required the circle's diameter cor- responding thereto. 274-89 X '31831 = 87-5 inches diameter. -Or, what is the diameter of a circle, when the cir- cumference is 39 feet ? 31831 X 39 = 12-41409 feet, and 41409 X 12 = 4-96908 inches, or 12 feet 5 inches, very nearly the diameter. 34 MENSURATION. 3. The diameter of a circle is 31 inches ; what j" its area Jr. square inches ? 3-75' = 14.-M25 X -7&H = 1 1-044, &c., inches area. Or, suppose the diameter of a circle 25 feet G inc.bes t required the area. 2.V5'-' = fioO-25 X -7854 = 510-706, &c., fe^t. the arna. 4. What must the diameter of a circle be, to contain an area equal to 7U(rri(J square inches ? V 706 : 86~= 26-5U> X H2837 = 29-998 or 30 inches, the diam- eter required. 5. The diameter of a circle is 144 inches; what must I make each side of a square, to be equal in area to the given circle ? 14--25 X -8862= 12-62335 inches, length of side required. ./?n?y chord and versed sine of a circle being given, to find tJte diameter. Rule. Divide the sum of the squares of the chord and versed sine by the versed sine, the quotient is the diameter of corresponding circle. 1. The chord of a circle A B equal ty feet, and the versed sine C D equal 2 feet, required the cir- cle's diameter. 6-0* 4- 22 = 46-25 -f. 2 = 23-125 feet, the diameter. 2. In a curve of a railway, I stretched a line 72 feet m length, and the distance from the line to the curve 1 found to be l\ ft. ; required the radius of the curve. 722 -f 1-252 = 5185-5625, and i'^O X -^ Tojind the length of any given arc of a circle. Rule. From eight times the chord of half the arc subtract the chord of the whole arc, and one third of {he remainder is equal the length of the arc. MENSURATION. 35 Required the length of the arc ABC, the chord A B of half the arc being 4 feet 3 inches, and chord A C of the whole arc 8 feet 4 inches. = 34,andM 8-333== - = 8-555 feet, the length of the arc. To find the area of Hue sector of a circle. Rule. Multiply the length of the arc by its radius, and half the product is the area. The length of the arc ACS, equal 9 feet, and the radii F A, F B, equal each 7 feet, required the area. 9-5 X 7 = 65-5 -f 2 = 32-75, the area. Note. The most simple means where- by to find the area of the segment of a circle is, to first find the area of a sector whose arc is equal to that of the given segment 5 and if it toe less than a semicircle, subtract the area of the triangle formed by the chord of the segment and radii of its extremities ; but if more than a semicircle, add the area of the triangle to the area of the sector, and the remainder, or sum, is the area of the segment. Thus, suppose the area of the segment A C B e is required, and that the length of the arc A C B equal 9| feet, F A and F B each equal 7 feet, and the chord A B equal 8 feet 4 inches, also the perpendicular e F equal 3| feet. 9-75x7 =3 fr |25 feet ^ the area of the gector vx .' 15-624 feet, area of the triangle. - - And 34-125 15-624 = 18-501 feet, the area of the segment. To fnd the area of the space contained between two concentric circles. Rule. Multiply the sum of the inside and outside diameters by their difference, and by '7854, the product is the area. 4 36 MENSUIIAT10N. 1. Suppose the external circle A B equal 32 niches, and internal circle C D equal 28 inches ; re- quired the area of the space con- tained between them. 32 + 28 = 60, and 32 28 = 4, hence 60 X 4 X -7854=188-496 in., the area. 2. The exterior diameter of the fly-wheel of a steam engine is 20 feet, and the interior diameter 18 feet; required the area of the surface or rim of the wheel. -20+13-5 = 38-5 and 2018-5 =1-5, hence 38-5 X 1-5 x -7854 = 45-35, &c., feet, the area. To find the area of an ellipsis or oval. Rule. Multiply the longest diameter by the short- est, and the product by -7854 ; the result is the area. An oval is 25 inches by 16-5 ; what are its superficial contents ? 25 X 16-5 = 412-5 x '7854 = 323-9775 inches, the area. Note. Multiply half the sum of the two diameters by 3*1416, and the product is the circumference of the oval or ellipsis. To find the area of a parabola, or its segment. Rule. Multiply the base by the perpendicular height, and two thirds of the product is the area. What is the area of a parabola whose base is 20 feet and height 12 ? 240 v 2 20 X 12 = f = 160 feet, the area. o Note. Although the whole of the preceding practical appli- cations or examples are given in measures of feet or inches, these being considered as the most generally familiar, yet the rules are equally applicable to any other unit of measurement whatever, as yards, chains, acres, &c. &c. &c. BIENSURATION. 37 2. MENSURATION OF THE SUPERFICIES, SOLID ITIES, AND CAPACITIES OF BODIES. 7V? find the solidity or capacity of any figure in the vibical form. Rule. Multiply the length of any one side by ita breadth and by the depth or distance to its opposite aide ; the product is the solidity or capacity, in equal terms of measurement. Application of the Rule to practical Purposes. 1. Required the number of cubic inches in a piece of timber 2-{ inches long, 7| inches broad, and 3| inches in thickness. 23-5 X 7-75 x 3-625 = 660-203 cubic inches. 2. A rectangular cistern is in length 8 feet, in breadth 54 feet, and in depth 4 feet; required its ca- pacity in cubic feet, also its capacity in British impe- rial gallons. 8-5 x 5-25 x 4 = 178-5 cubic feet, and 178-5 x 6-232 (see Table of Decimal Approximations, p. 25) = 1112-412 gallons. 3. A rectangular cistern, capable of containing 520 imperial gallons, is to be 7\ feet in length, and 4 feet in width; it is required to ascertain the necessary depth. 520-000 7-25 x 4-5 X 6-232 = 203-318. and = 2-557 feet, or 2 203-318 feet 6| inches nearly. 4. A rectangular piece of cast iron, 20 inches long and 6 inches broad, is to be formed of sufficient dimen- sions to weigh 150 Ibs. ; what will be the depth re- quired ? 20x6x-263 (see Table of Decimal Approximations. Cast 150 Iron, p. 25) == 31-96, and =3 4-69 in., or 4 and 11. in., th* thickness required 38 MENSURATION. To find the convex surface, and solidity or capacity, of a cylinder. Rule 1. Multiply the circumference of the cylinder by its length or height ; the product is the convex sur- face. Rule 2. Multiply the area of the diameter by the length or height, and the product is the cylinder's solid- ity or capacity, as may be required. Application of the Rules. 1. The circumference of a cylinder is 37 inches, and its length 541 inches ; required the convex surface m square feet. 64-75 X 37-5 X -007 (see Table of Approximations) = 14-371 square feet. 2. A cylindrical piece of timber is 9 inches diameter, and 3 feet 4 inches in length; required its solidity in cubic inches, and also in cubic feet 3 feet 4 inches = 40 inches, and 9 2 x-7854 X 40 = 2544-696 cubic inches ; then 2544-61)6 x -00058 = 1-4759 cubic feet. . Suppose a well to be 4 feet 9 inches diameter, and 16^ feet from the bottom to the surface of the water- now many imperial gallons are therein contained ? 4-752 x 16-5 x 4-895= 1822-162 gallons. 4. Again, suppose the well's diameter the same, and its entire depth 35 feet ; required the quantity in cubic yards of material excavated in its formation. 4-7.52 x 35 x -02909 = 22-973 cubic yards. 5. I have a cylindrical cistern capable of holding 7(K)8 gallons, and its depth is 10 feet; now I want to replace it with one of an equal depth, but capable of holding 12,500 gallons; what must be its diameter? 1 2.500 4-895 X 10 = 48-95, and -^ = V 255-3 = 15-9687 feet, or 15 feet 11$ inches. 6. A cylindrical piece of lead is required, 7& inche* MENSURATION. 39 diameter, .nd 168 Ibs, in weight; what must be its length in inches? T5* x '3223 = 18, and = 9-3 inches. 18 To find the length of a cylindrical helix, or spiral, wound round a cylinder. Rule. Multiply the circumference of the base by the number of revolutions of the spiral, and to the square of the product add the square of the height ; the square root of the sum is the length of the spiral. Application of the Rule. L Required the length of the thread or screw twist- ing round a cylinder 22 inches in circumference 3 times, and extending along the axis l(j inches. 22 X 3-5 = 772 = 5929, and 16 = 256, then V 5929 + 256 = 78-64- inches. 2. The well of a winding staircase is 5 feet diameter, and height to the top landing 25 feet ; the hand-rail is to make 2^ revolutions ; required its length. 5 feet diameter = 15-7 feet circumference. 15-7 x 2-5 = S9-25 2 = 1540-5625, and 25 2 = 625, then V1540 + 625 = 46-5 feet, the length required. To find the convex surface, solidity, or capacity of a cone or pyramid. Rule 1. Multiply the circumference of the base by the slant height, and half the product is the slant sur- face. Rule 2. Multiply the area of the base by the per- pendicular height, and one third of the product is the solidity or capacity, as may be required. Application of the Rules. 1. Required the area, in square inches, of the slan surface of a cone whose slant height equal 18| inches, and diameter at the base 6 inches. 6*25 X 3-1416 = 19-635 circumference of the base 5 and =184.0*1125 square inches. ' 4* 40 MENSURATION. 2. Required the quantity of lead, in square feet sufficient to cover the slant surface of a hexagonal pyr amid whose slant height is 42 feet, and the breadth of each side at the base 4 feet 9 inches. 4-75 X 42 X 6 sides = 598-5 square feet. 3. What is the solidity of a cone, in cubic inches, the diameter at the base being 15 inches, and perpendiculai height 32 inches ? 152 x -7854 x 32-5 3 - =1914-4125 cubic inches. 4. In a square solid pyramid of stone 67 feet in height, and l(Ji feet at the base, how many cubic feet ? 16-5 x 16-5 x 67 To find the solidity or capacity of any frustum &f a wne or pyramid. Rule. If the base be a circle, add into one sum the two diameters, or, if a regular polygon, the breadth of one side at the top and at the base; then from the square of the sum subtract the product of these di- ameters or breadths ; multiply the remainder by -7854, if a circle, or by the tabular area (see Table of Poly- gons, p. 31) and by one third of the height; and the product is the content in equal terms of unity. Note. Where the whole height of the cone or pyramid can be obtained, of which the given frustum forms a part, the most simple method is, first to find the whole contents, then the contents extending beyond the fmstum ; and, subtracting the less from the greater, leaves the contents of the frustum required. Application of the Rides. 1. The perpendicular height A B of the frustum of a hexagonal pyra- mid C D E, is 7 feet, and the breadth of each side at top and base equal 33 and %& feet; required the solid contents of the frustum in cubic feet MLNSTJ RATION. 41 5-75 + 2-5 = 6-25, and 6-25 x 6-25 = 39-0625, then 3-75 x 2-5 =s 9-375, and 39-0625 9-375 = 29-6875 x 2-598 (tabular area, p 31) = 77-138 x 2-5 or of the height = 192-845 cubic feet. 2. Required the solidity of the frustum of a cone, the top diameter of which is 7 inches, the base diametef 9, and the perpendicular height 12. 7 + 9-52 = 272-25, and 7x9-5 = 66-5, then 272-25 66-5 = 205-75 x -7854 = 161-576 X 4 or | of the height = 646-3 cubic inches. 3. A vessel in the form of an in- D verted cone, as A B C D, is 5 feet in diameter at the top, 4 feet at the bottom, and 6 feet in depth; re- quired its capacity in imperial gal- lons. 92 = 81, and 5x4 = 20, hence 81 20 = 61 X -7854 ; and by 2 or | of the depth = 95-8188 cubic feet, and X 6-232 = 597-1427 gallons. To find the solid contents of a wedge. Rule. To twice the length of the base add tne length of the edge ; multiply the sum by the breadth of the base, and by the perpendicular height from the base, and one sixth of the product is the solid contents. Application of the Rule. Required the solidity of a wedge, in cubic inches, the base A B C D being 9 inches by 3, the edge E F 7 inches, and the perpendicular height G E 15. - + 7x3-5x 15_ = 218-75 cubic inches. v 11 To find the convex surface^ the solidity, or the capacity, a/" a sphere or globe. Rule 1. Multiply tho square of the diameter by 3'1416 ; the product is the convex surface. Rule 2. Multiply the cube of the diameter bj 5236 ; the product is the solid contents. 42 MENSURATION. Rdt 3. Multiply the cube of the diametei *n feet by 3-263, or in inches by -001888 ; the produce is thp capacity in imperial gallons.. Application of the Rules. 1. Required the convex surface, the solidity, and the weight in cast iron of a sphere or ball 10 inches in diameter. 10-5 2 x 3-1416 = 346-3t>14 square inches. 10-5 3 X '5236 = f>OG- 132. &c., cubic inches; and 606-132 X -263 (see Table of Approximations, p. 25) = 1594 Ibs. 2. A hollow or concave copper ball is required, 8 inches diameter, and in weight just sufficient to sink to its centre in common water ; what is the proper thick aess of copper of which it must be made ? Weight of a cubic inch of water = -03617 Ibs. ) g " copper = -3225 " $ 83 x -5236 X -03617 _ 4 . 84S2g cub ifl Qf waler tQ be displaced4 2 4-848 G) 8 And =. 15-0334 cubic inches of copper in the ball. 3225 Then 8 2 x 3-1416 = 201-0624. and = -0747 inches, the 201-0624 thickness of copper required. 0747 x 16 = Y* of an inch full, or 3 Ibs. copper to a square foot. 3. What diameter must 1 make a leaden ball, so ai to weigh 72 Ibs. ? 72 5236 x -4103 .-= -21483308. and = 3 V 340 = 6-97 21453308 inches, diameter. INSTRUMENTAL ARITHMETIC UTILITY OF THE SLIDE RULE. THE slide rule is an instrument by which the greatei portion of operations in arithmetic and mensuration may be advantageously performed, provided the lines of division arid gauge points be made properly correct, and their several values familiarly understood. The lines of division are distinguished by the letters A B C D ; A B and C being each divided alike, and containing what is termed a double radius, or double series of logarithmic numbers, each series being sup- posed to be divided into 1000 equal parts, and distrib- uted along the radius in the following manner : From 1 to 2 contains 301 of those parts, being the log. of 2. 3 " 477 3. 4 " 602 " 4. 5 " 699 " 5. 6 " 778 " 6. 7 " 845 " 7. 8 903 " 8. 9 " 9.54 " 9 1000 being the whole number. The line D, on tbe improved rules, consists of only 9 single radius ; and although of larger radius, the loga rithrnic series is the same, and disposed of along the line in a similar proportion, forming exactly a line of square roots to the numbers on the lines B C. 44 INSTRUMENTAL ARITHMETIC. NUMERATION. Numeration teaches us to estimate or properly value the numbers and divisions on the rule in an arithmeti- cal form. Their values are all entirely governed by the value set upon the first figure, and, being decimally reckoned, advance tenfold from the commencement to the termi- nation of each radius : thus, sup'pose 1 at the joint be one, the I in the middle of the rule is ten, and 1 at the end one hundred : again, suppose 1 at the joint ten, 1 in the middle is 100, and 1 or 10 at the end is 1000, &c., the intermediate divisions on which complete the whole system of its notation. TO MULTIPLY NUMBERS BY THE RULE. Set 1 on B opposite to the multiplier on A; and against the number to be multiplied on B is the prod- uct on A. Multiply 6 by 4. Set I on B to 4 on A ; and against 6 on B is 24 on A. The slide thus set, against 7 on B is 28 on A. 8 " 3 U 2 " 9 " 36 " 10 40 " 12 " 48 15 " 60 " 25 " 100, &c &c. TO DIVIDE NUMBERS UPON THE RULE. Set the divisor on B to 1 on A; and against the number to be divided on B is the quotient on A. Divide 63 by 3. Set 3 on B to 1 on A ; and against 63 on B is 21 on A INSTRUMENTAL ARITHMETIC. 45 PROPORTION, OR RULE OF THREE DIRECT. Rule. Set the first term on B to the second on A and against the third upon B is the fourth upon A. 1. If 4 yards of cloth cost 38 shillings, what will 3c yards cost at the same rate ? Set 4 on B to 38 on A 5 and against 30 on B is 285 shillings on A, 2. Suppose I pay 31s. 6d. for 3 cwt. of iron, at what rate is that per ton ? 1 ton = 20 cwt. Set 3 upon B to 31-5 upon A j and against 20 upon B i upon A. RULE OF THREE INVERSE. Rule. Invert the slide, and the operation is tt** same as direct proportion. 1. I know that six men are capable of performing t certain given portion of work in eight days, but I wai.l the same performed in three ; how many men must there be employed ? Set 6 upon C to 8 upon A ; and against 3 upon C is 16 upon A. 2. The lever of a safety valve is 20 inches in length, and 5 inches between the fixed end and centre of the valve ; what weight must tht? re be placed on the end of the lever to equipoise a force or pressure of 4C Ibs. tending to raise the valve ? Set 5 upon C to 40 upon A ; and against 20 on C is 10 on A. 3. If 8| yards of cloth, \\ yards in width, be a suf ficient quantity, now much will be required of thaj which is only ths in width, to effect the same purpose : Set 1-5 on C to 8-75 on A 5 and against -875 upon C is 15 yardt upon A. 46 INSTRUMENTAL ARITHMETIC. SQUARE ALND CUBE ROOTS OF NUMBERS. On the engineer's rule, when the lines C and are equal at both ends, C is a table of squares, and D a table of roots, as Squares, 1 4 9 16 23 36 49 64 81 on C. Roots, 123 4 5 6 7 8 9onD. To find the geometrical mean proportion between tii'O numbers, Set one of the numbers upon C to the same number upon D ; and against the other number upon C is the mean number or side of an equal square upon L). Required the mean proportion between 20 and 45. Set 20 upon C to 20 upon D ; and against 45 upon C is 30 on D. To cube any number, set the number upon C to 1 or 10 upon D ; and against the same number upon D is the cube number upon C. Required the cube of 4. Set 4 upon C to 1 or 10 upon D ; and against 4 upon D is 64 upon C. To extract the cube root of any number, invert the slide, and set the number upon B to 1 or 10 upon D; and where two numbers of equal value coincide, on the lines B D, is the root of the given number. Required the cube root of 64. Set 64 upon B to 1 or 10 upon D ; and against * upon B is \ upon D, or root of the given number. On the common rule, when 1 in the middle of the line C is set opposite to 10 on D, then C is a table of squares, and D a table of roots. To cube any number by this rule, set the number upon C to 10 upon D ; and against the same number upon D is th-3 cube upon C. INSTRUMENTAL MENSURATION. 47 MENSURATION OF SURFACE. 1. Squares, Rectangles ', fyc. Ride. When the length is given in feet and the Dreadth in inches, set the breadth on B to 12 on A ; and against the length on A is the content in square feet on B. If the dimensions are all inches, set the breadth on B to 144 upon A ; and against the length upon A ia the number of square feet on B. Required the content of a board 15 inches broad and 14 feet long. Set 15 upon B to 12 upon A j arid against 14 upon A is 17-i square feet on B. 2. Circles, Polygons, Sfc. Rule. Set -7854 upon C to 1 or 10 upon D ; then will the lines C and D be a table of areas and diameters. Areas, 3-14 7-06 12-56 19-63 28-27 33-48 50-26 63-61 upon C. Diam., 234567 8 9 upon D In the common rule, set -7854 on C to 10 on D ; then C is a line or table of areas, and D of diameters, as be fore. Set 7 upon B to 22 upon A ; then B and A form or become a table of diameters and circumferences of cir- cles. Cir., 3-14 6-28 9-42 12-56 15-7 18-85 22 25-13 28-27 upon A Dia., 123 4 56 78 9 upon B Polygons from 3 to 12 sides. Set the gauge-poin upon C to 1 or 10 upon D ; and against the length o* one side upon D is the area upon C. Sides, 356789 10 11 12. Gauge-points, -433 1-7 2-6 3-63 4-82 6-18 7-69 9-37 11-17 Required the area of an equilateral triangle, each side 12 inches in length. Set -433 upon C to 1 upon D j and against 12 upon D are 62-5 square inches upon C, 5 48 INSTRUMENTAL MENSURATION. TABLE OF GAUGE-POINTS FOR THE ENGINEER'S RULE. Names. P, F,P. PI i, i. i,M. r.i. i, i. p. i. ' Cubic inches Cubic feet Imp. gallons Water in Ibs. 578 1 163 16 83 144 231 23 1728 277 276 106 1833 294 293 1273 22 353 352 105 121 306 305 121 33 529 528 Gold " 814 1175 141 149 178 155 269 Silver " Mercury " Brass Copper " 15 118 193 18 216 169 177 26 261 203 333 319 276 216 354 331 334 258 424 397 286 225 369 345 5 389 637 596 Lead " Wro'tiron " Cast iron " 141 207 222 203 297 32 243 357 384 258 338 407 31 453 489 27 394 424 465 682 733 Tin 219 315 378 401 481 419 728 Steel " 202 292 352 372 448 385 671 Coal " Marble " Freestone " 127 591 632 183 85 915 22 102 11 33 116 1162 28 13 14 242 113 141 42 195 21 FOR THq COMMON SLIDE RULE. Namea. P, P,P P, i, i. I, i, i. P, i. I, i. F. I. Cubic inches Cubic feet Water in Ibs. 36 625 10 518 9 144 624 108 174 6e>o 114 184 799 138 22 625 119 191 113 206 329 Gold Silver " Mercury " Brass " Copper " 507 938 738 12 112 735 136 122 174 163 88 157 127 207 196 96 173 132 221 207 118 2(18 162 263 247 939 173 141 23 214 180 354 242 397 371 Lead " Wro't [ron " Cast iron " 880 129 139 126 186 2 152 222 241 162 2:35 254 194 283 304 lfi<) 247 265 289 423 458 Tin " 137 135 235 25 300 261 454 Steel " 136 183 22 tf33 278 239 418 Coal " Marble " Freestone " 795 370 394 114 53 57 138 637 69 146 725 728 116 81 873 151 72 755 262 121 132 INSTRUMENTAL MENSURATION. 49 MENSURATION OF SOLIDITY AND CAPACITY. General rule. Set the length upon B to the gauge- fv nt upon A ; and against the side of the square, or a nneter on D, are the cubic contents, or weight in Ibs. o' C. 1. Required the cubic contents of a tree 30 feet in length, and 10 inches quarter girt. Set 20 upon B to 144 (the gauge-point) upon A j and against 10 upon D is 20-75 feet upon C. 2. In a cylinder 9 inches in length and 7 inches diameter, now many cubic inches ? Set 9 upon B to 1273 (the gauge-point) upon A; and against 7 on D is 346 inches on C. 3. What is the weight of a bar of cast iron 3 inches square, and 6 feet long ? Set 6' upon B to 32 (the gauge-point) upon Aj and against 3 upon D is 168 Ibs. upon C. By the common rule. 4. Required the weight of a cylinder of wrought iron 10 inches long, and 5 diameter. Set 10 upon B to 283 (G. Ft.) upon A; and against 5 upon D is 66-65 Ibs. on C. 5. What is the weight of a dry rope 25 yards long, and 4 inches circumference ? Set 25 upon B to 47 (G. Ft.) upon A 5 and against 4 on D is 63-16 Ibs. on C. 6. What is the weight of a short-linked chain 3C f ards in length, and T \ths of an inch in diameter ? Set 30 upon B to 52 (G. Ft.) upon A j and against 6 on D is ,29 5 Ibs. on C. 50 INSTRUMENTAL RULES. LAND SURVEYING. If the dimensions taken are in chains, the gauge* point is 1 or 10 ; if in perches, 160 ; and if in yards, 4840. R u l e , _ Set the length upon B to the gauge-point on A ; and against the breadth upon A is the content in acres upon B. 1. Required the number of acres or contents of a field 20 chains 50 links in length, and 4 chains 40 links in breadth. Set 20-5 on B to 1 on A ; and against 4-4 on A is 9 acres on B. 2. In a piece of ground 440 yards long, and 44 broad, now many acres ? Set 440 upon B to 4840 on A ; r.nd against 44 on A is 4 acres on B. POWER OF STEAM-ENGINES. Condensing Engines. Rule. Set 3-5 on C to 10 on D ; then D is a line of diameters for cylinders, and C the corresponding number of horses' power ; thus, H Pr 3A 456 8 10 12 16 20 25 30 40 60 on C. C.D. Join. 101 I* 13$ 154 17 181 U 21 24 26| 29$ 33| 37| on D. The same is effected on the common rule by setting 5 on C to 12 on I). Non-condensing Engines. Rule. Set the pressure of steam in Ibs. per square inch on B to 4 upon A ; and against the cylinder's diameter on D is the number of horses' power upon C. Required the power of an engine, when the cylinder is 20 inches diameter and steam 30 Ibs. per square inch. Set 30 on B to 4 on A 5 and against 20 on D is 30 horses' oower on C. The same is effected on the common rule oy setting the force of the steam on B to 250 on A. STRENGTH OF MATERIALS. 51 OF ENGINE BOILERS. How many superficial feet are contained in a boiler } feet in length and 5 in width ? Set 1 upon B to 23 upon A ; and against 5-5 upon B is 126-5 square feet upon A. If 5 square feet of boiler surface be sufficient for each horse-power, how many horses' power of engine is the boiler equal to ? Set 5 upon B to 126-5 upon A 5 and against 1 upon B is 25'5 upon A. STRENGTH OF MATERIALS. MATERIALS of construction are liable to four different kinds of strain ; viz., stretching, crushing, transverse action, and torsion or twisting : the first of which de- pends upon the body's tenacity alone ; the second, on its resistance to compression ; the third, on its tenacity and compression combined ; and the fourth, on that property by which it opposes any acting force tending to change from a straight line, to that of a spiral direc- tion, the fibres of which the body is composed. In bodies, the power of tenacity and resistance to compression, in the direction of their length, is as the cross section of their area multiplied by the results ol experiments on s-milar bodies, as exhibited in the fol- lowing table. 5* 52 STRENGTH OF MATERIALS. Table shouring the Tenacities, Resistances to Compres- sion^ and other Properties of tfie common Materials oj Construction. Absolute Compared with Cast Iron Names of Bodies. Tenacity in Ibs. Resistance to compres- Its Its exten- Its stiff- persq. sion iu 11.8. strength sibility a ness is inch. per *q. in. Ash . 14130 0-23 2-6 0-089 Beech 12225 8548 0-15 2-1 0-073 Brass 17968 10304 0-435 0-9 0-49 Brick 275 562 Cast iron . 13434 86397 1-000 1-0 1-000 I Copper (wrought) . Elm .... 33000 9720 1033 0-21 2-9 0-073 Fir, or Pine, white . " " red 12346 11800 2028 5375 0-23 0-3 2-4 2-4 0-1 0-1 yellow . 11835 5445 0-25 2-9 0-087 Granite (Aberdeen) 10910 Gun-metal (copper 8, and tin 1 ) 35838 __ 0-65 1-25 0-535 Malleable iron . 56000 1-12 0-86 1-3 Larch . . <., 12240 5568 0-136 2-3 0053 Lead 1824 _ 0-096 2-5 0-0385 Mahogany, Honduras 11475 8000 0-24 2-9 0-487 Marble 551 6060 _ Oak . 11880 9504 0-25 2-8 0-093 Rope (1 in. in circum.) 200 Steel 128000 _ __ _ Stone, Bath 478 _ " Craigleith Dundee . 772 2661 5490 6630 ! " Portland 857 3729 __ _ Tin (cast) . 4736 0182 0-75 0-25 Zinc (sheet) 9120 0-365 0-5 0-7,; STRENGTH OF MATERIALS. CO GO 00 ^1 Ci O"* C T CO I Circum. of rope 1 in inches. i CO C* N- CO ^ .91 ^ fSS^in^. Diameter of chain in inches. IO iO i-* t-^ ) ' iO tO Weight per fathom in Ibs. CO Oi ^ Oi CK Circum. of rope in inches. Weight per fathom inTbs. Diameter of chain in inches. Weight per fathom in Ibs. t3 W 10 I 5?! r 5* Note. It must be understood and also borne in mind that, in estimating the amount of tensile strain to which a body is subjected, the weight of the body itself must also be taken into account ; for according to its position so may it approximate to its whole weight, in tending to produce extension within itself 3 as in the almost constant application of ropes and chains to great depths, considerable heights, &c. STRENGTH OF MATEKLALS. Moys that are of greater Tenacity than the Sum of their Constituents, as determined by the Experiments of Muschenbroek. Swedish copper 6 pts., Malacca tin 1 ; tenacity per sq. inch 64,000 Ibs. Chili copper G parts, Malacca tin 1 ; Japan copper 5 parts, Banca tin 1 ; Anjilesea copper ft parts, Cornish tin 1 ; Common block-tin 4, lead 1, zinc 1; Malacca tin 4, regulus of antimony 1 ; Block tin 3, lead 1 ; Block tin 8, zinc Ij Lead 1, zinc 1 ; (10,000 57,000 4 1 ,000 13,000 j 2,000 10,200 10,000 4,500 RESISTANCE TO LATERAL PRESSURE, OR TRANS- VERSE ACTION. The strength of a square or rectangular beam to re- sist lateral pressure, acting in a perpendicular direction to its length, is as the breadth and square of the depth, and inversely as the length ; thus, a beam twice the breadth of another, all other circumstances being alike, equal twice the strength of the other; or twice the depth, equal four times the strength, and twice the length, equal only half the strength, &c., according to the rule. Table o, le of Data, containing the Results of Experiments t the Elasticity and Strength of various Species oj Timber, by Mr. Barlow. Species ol Timber. Value of E. Va!ue ofS. Species of Timber. Value ofE. Value ofS. Teak . . . 174-7 2462 Kim .... 50-64 1013 Poona . . . 122-26 2221 Pitch pine . . 88-68 1632 English Oak . 105 1672 Red pine . . . 133 1341 Canadian do. 1555 1766 JMew England fir 158-5 1102 Dantzic do. 86-2 1457 Riga fir ... 90 1100 Adriatic do. 70-5 1383 Mar Forest do. 63 1200 Ash ... 119 2026 Larch .... 76 900 Bech . . . 98 1556 Norway spruce . 105-47 1474 STRENGTH OF MATERIALS. 55 To find the dimensions of a beam capable of sustain" ing a given weight, with a given degree of deflection, when supported at both ends. Rule. Multiply the weight to be supported in Ibs. by the cube of the length in feet ; divide the product by 32 times the tabular value of E, multiplied into the given deflection in inches ; and the quotient is the breadth multiplied by the cube of the depth in inches. Note 1. When the beam is intended to be square, then the fourth root of the quotient is the breadth and depth required. Note 2. If the beam is to be cylindrical, multiply the quotient by 1-7, and the fourth root of the product is the di ameter. Ex. The distance between the supports of a beam ot Riga fir is 16 feet, and the weight it must be capable of sustaining in the middle of its length is 8000 lbs. ; with a deflection of not more than f of an inch ; what must be the depth of the beam, supposing the breadth 8 inches ? To determine the absolute strength, of a rectangular beam of timber, when supported at both ends, and loaded in the middle of its length, as beams in general ought to be :alculated to, so that they may be rendered capable oj withstanding all accidental cases of emergency. Rule. Multiply the tabular value of S by four times the depth of the beam in inches, and by the area of the cross section in inches ; divide the product by the distance between the supports in inches, and the quotient will be the absolute strength of the beam in Ibs. ./Vote I. If the beam be not laid horizontally, the distance between the supports, tor calculation, must be the horizontal 2. One fourth of the weight obtained by the rule, is the greatest weight that ought to be applied in practice as per* teanent load. 06 STRENGTH OF MATERIALS. Note 3. If the load is to be applied at any other point than the middle, then the strength will be as the product ol the two distances is to the square of half the length of the beam between the supports ; or, twice the distance from one end, multiplied by twice from the oilier, and divided by the whole length, equal the effective length of the beam. Ex. In a building 18 feet in width, an engine boiler of 5i tons is to be fixed, the centre of which to be 7 feet from the wall ; and having two pieces of red pine, 10 inches by (>, which 1 can lay across the two walls for the purpose of slinking it at each end, may 1 with sufficient confidence ^apply them, so as to effect this object ? 2240 x 5-5 __ g to carry at eac h en( j. And 18 feet 7 = 11, double each, or 14 and 22, then 14 * u ~ l - n feet, or "204 inches, effective length of beam. 18 Tabular value of S,red pine. = '" X \^^= W"- the absolute strength of each piece of timber at that point. To determine the dimensions of a rectangular beam capable of supporting a required weight, with a given degree of defection, when jixed at one end. R u l e% _ Divide the weight to be supported, in Ibs., by the tabular value of K, multiplied by the breadth and deflection, both in inches ; and tfie cube root of the quotient, multiplied by the length in feet, equal the depth required in inches. Ex. A beam of ash is intended to bear a load of 700 Ibs. at its extremity ; its length being 5 feet, its breadth 4 inches, and the deflection not to exceed of an men, Tabular value ofE = 1 19 X 4 X -5 = 238 the divisor ; then 700-i- 238 3 y^-94 x 5 = 7-25 inches, depth of the beam STRENGTH OF MATERIALS. 5? To find the absolute strength of a rectangular learn, when fixed at one end, and loaded at the other. Rule. Multiply the value of S by the depth of the beam, and by tne area of its section, both in inches ; divide the product by the leverage in inches, and the quotient equal the absolute strength of the beam in Ibs. Ex. A beam of Riga fir, 12 inches by 4, and pro- jecting G.i feet from the wall ; what is the greatest weight it will support at the extremity of its length ? Tabular value of S = 1 100 12 x 4-5 = 54 sectional area, Then, 110 x 12 >< 54 = 9133.4 Ibs. When fracture of a beam is produced by vertical pressure, the fibres of the lower section of fracture are separated by extension, whilst at the same time those of the upper portion are destroyed by compression hence exists a point in section where neither the one nor the other takes place, and which is distinguished as the point of neutral axis. Therefore, by the law of fracture thus established, and proper data of tenacity and compression given, as in the table, (p. 52) we are enabled to form metal beams of strongest section with the least possible material. Thus, in cast iron, the resis- tance to compression is nearly as fi to 1 of tenacity ; consequently a beam of cast iron, to be of strongest j-^-3 section, must be of the following form, and a parabola in the direction of its length, the quantity of material in the | v \ bottom flange be ng about 6^ times that of the upper. But such is not the case with beams oi timber ; for although the tenacity of timber be on an average twice that of its resistance to compression, its flexibility is so great, that any considerable length of beam, where coiumns cannot be situated to its support, 58 STRENGTH OF MATERIALS. requires to be strengthened or trussed by iron rods, a* in the following manner. And these applications of principle not only tend to diminish deflection, but the required purpose is also i/iore effectively attained, and that by lighter pieces oi timber. To ascertain the absolute strength of a cast iron beam of the preceding J brm, or that of strongest section. Rule. Multiply the sectional area of the bottom flange in inches by the depth^ of the beam in inches, and divide the product by the distance between the supports, also in inches ; and 514 times the quotient equal the absolute strength of the beam in cwts. The strongest form in which any given quantity of matter can be disposed is that of a hollow cylinder ; and it has been demonstrated that the maximum of strength is obtained in cast iron, when the thickness of the an- nulus, or ring, amounts to ith of the cylinder's external diamete~ ; the relative strength of a solid to that of a hollow cylinder being as the diameters of their sec- tions. STRENGTH OF MATERIALS. 59 # Table showing the Weight or Pressure a Beam of Cast Iron, ] inch in breadth, ivill sustain, without de- stroying its elastic force, when it is supported at each end, and loaded in the middle of its length, and also tht defection in the middle which that weight will produce By Mr. Hodgkinson, Manchester. Length. 6 feet. 7 feet. 8 feet. 9 feet. 10 feet. Depth Wt. in Defl. Wt.in De8. Wt.in Defl. Wt. Defl. Wt. in Defl. in in. Ibs. in in. Ibs. in in. Iba. in m. in Ibs. in in. Ibs. 3 4~ 1278 1739 2272 24 205 18 1089 1482 1936 33 28 45 954 1298 1700 426 365 32 855 -54 1164) '46 15201 -405 765 1041 1360 66 :f 44 2875 16 2450 217 2146 284 19241-36 1721 443 5 ' 3560 144 3050 196 2650 256 2375 -32 2125 4 6 5112 12 4356 163 3816 213 3420! -27 30601 -33 7 6958 103 5929 14 5194J -183 4655 -23 41651 -29 8 9088 09 7744 123 6784 16 6080 203 5440! -25 9 ' 9801 109 8586 142 7695 18 6885 -22 10 12100 098 10600 -128 9500 162 8500 2 11 12826 -117 11495 15 110285 182 12 15264 -107 13C80 135 12240 17 13 16100 125 14400 154 14 18600 -115 16700 143 12 feet. 14 feet. 16 feet. 18 fret. 20 fert. 6 2548, -48 2184 65 1912 85 1699 1-08 1530 1-34 7 34711 -41 2975 58 2603 73 2314 -93 2D82 1-14 8 4532! -36 3884 49 3396 64 302) *81 2720 H)0 9 5733 -32 4914 44 4302 57 3825 72 34381 -89 10 7083 ; -28 6071 39 53121 -51 4722 64 4250J -8 11 8570 -26 7346 36 64281 -47 5714 59 5142J -73 12 10192 -24 8736 a3 7648! -43 6796 54 6120 ! -67 13 11971-22 10260 31 8978 -39 7980 49 7182 -61 14 13883! -21 11900 28 10412 36 9255 46 8330 57 15 15937 -19 13660 26 11952 34 10624 43 9562 53 16 18128 -18 ; 15536 24 13584 32 12080 40 10880J -5 17 20500: -17 i 17500 23 15353 -3 1 13647 38 12282 47 18 229321 -16 19656 21 ! 17208! -28 15700 36 13752 -44 Note. This Table shows the greatest weight that eve* ought to be laid upon a beam for permanent load ; and, if therfl be any liability to jerks, &c., ample allowance must be made ulso, the weight of the beam itself must be included 6 CO STEENtTH OF MATERIALS. To find the weight of a cast iron beam of given dinien- 9ions. Rule. Multiply the sectional area in inches by the length in feet, and by 3-^, the product equal the weight in Ibs. Ex. Required the weight of a uniform rectangular beam of cast iron, 1<> feet in length, 11 inches in breadth, and 1 inch in thickness. 11 X 1-5 X 16 X 3-2 = 844-8 Ibs. Resistance of Bodies to Flexure by vertical Pressure. When a piece of timber is employed as a column or support, its tendency to yielding by compression is dif- ferent according to the proportion between its length and area of its cross section ; and supposing the form that of a cylinder whose length is less than seven or eight times its diameter, it is impossible to bend it by any force applied longitudinally, as it will be destroyed by splitting before that bending can take place; but when the length exceeds this, the column will bend under a certain load, and be ultimately destroyed by a similar kind of action to that which has place in the transverse strain. Columns of cast iron and of other bodies are also similarly circumstanced, this law having recently been fully developed by the experiments of Sir. Hodgkinson on columns of different diameters, and of different lengths. When the length of a cast iron column with flat ends equals about thirty times its diameter, fracture will be produced wholly by bending of the material. When of less length, fracture takes place partly by crushing and partly by bending. But, when the column is enlarged in the middle of its length from one and a half to twice its diameter at the ends, by being cast hol- low, the strength is greater by ith than in a solid columi Containing the same quantity of material. STRENGTH OF MATERIALS. 61 To determine the dimtiisions of a support or column to Jew, without sensible curvature, a given pressure in tht direction of its axis. Rule. Multiply the pressure to be supported in Ibs. by the square of the column's length in feet, and divide the product by twenty times the tabular value of E ; and the quotient will be equal to the breadth multiplied by the cube of the least thickness, both being expressed in inches. Note 1. When the pillar or support is a square, its side will be the fourth root of the quotient. 2. If the pillar or column be a cylinder, multiply the tabular value of E by 12, and the fourth root of the quotient equal the diameter. Ex. 1. What should be the least dimensions of an oak support, to bear a weight of 2240 Ibs. without sensi- ble flexure, its breadth being 3 inches, and its length 5 feet? Tabular value of E = 105, ><24o v 5 2 and = 3 V 8 = 2-05 inche,. Ex. 2. Required the side of a square piece of Riga fir, 9 feet in length, to bear a permanent weight of 6000 Ibs. Tabular value of E = 96, 'iflflO V ( ) 2 and t - ^ = 4 V 25 3 = 4 inches nearly. ^.0 X Jo STRENGTH OF MATERIALS. 51 Si | CO 3* sC "f r* OQ i 1-1 s* *o Oi "* o : Ci ^ "O Tf 00 Z) 2SI2SI%i822ga --Sm^-ooog^j-^g STRENGTH OF MATERIALS. 63 Practical Utility of the preceding Table. Ex. Wanting to support the front of a building with cast iron columns 18 feet in length, 8 inches in diam- eter, and the metal 1 inch in thickness ; what weight may F confidently expect each column capable of sup- porting without tendency to deflection? Opposite 8 inches diameter and under 18 feet = 1097 Also opposite 6 in. diameter and under 18 feet= 440 = 657 cwt. Note. The strength of cast iron as a column being 1-0000 steel " =2-518 " wrought iron " = 1-745 " (oak) Dantzic = -1088 red deal = -0785 Elasticity of Torsion, or Resistance of Bodies to Twisting. The angle of flexure by torsion is as the length and extensibility of the body directly and inversely as the diameter; hetice, the length of a bar or shaft being given, the power, and the leverage the power acts with, being known, and also the number of degrees of torsion that will not affect the action of the machine, to deter- mine the diameter in cast iron with a given angle of flexure. Rule. Multiply the power in Ibs. by the length of the shaft in feet, and by the leverage in feet ; divide the product by fifty-five times the number of degrees in the angle of torsion ; and the fourth root of the quotient equal the shaft's diameter in inches. Ex. Required the diameters for a series of shafts 35 feet in length, and to transmit a power equal to VM5 *bs, acting at the circumference of a wheel 2 feet 6* 64 MECHANICS. radius, so that the twist of the shafts on the application of the power may not exceed one degree. 1245 X 35 X 2-5 53x I = 4y 1931 =6-67 inches in diameter. Relative Strength of Metals to resist Torsion. st iron ...==! PP< yellow Brass . = -511 Gun metal . . = -55 Swedish bar iron . = 1'05 English do. , . =1-12 Sheer steel . . =1-96 Cast do. . . = 2-1 MECHANICS. PRELIMINARY REMARKS. MECHANICS, regarded as a science, comprehends the sum of our knowledge relative to the sensible motions of bodies either actually existing or expressed by the opposition of forces tending to produce motion. The science is thus resolvable into a code of discovered laws, applying to the causes which occasion and modify the direction and the velocities of motion, and is therefore distinct from those branches of science in which, al- though presenting phenomena of motion in sensible portions of matter^ we do not consider the circumstances and laws of these motions, but only the effects pro- duced. When motion itself is considered, the reasoning be- longs to mechanics, and it is probable that as our knowl- edge of th* laws which govern the phenomena that are MECHANICS. 65 evolved under the hand of the experimental philosopher becomes more extended, a wider meaning will- be given to the science of motion. The definition which is here given of mechanics is not coeval with the name. The science, like most other sciences, has gradually ex- panded to its present extent. It was originally the sci- ence of machines these being the first subjects of its speculation ; and, as everv material combination em- ployed for producing or preventing motion may be regarded as a machine, and may be resolved into the same elementary principles as those employed in ma- chines, the mechanical powers, the name " mechan- ics " became to be applied to motion, the tendency to motion of any bodies whatever. Mechanics still con- tinues to be defined by some the science of force, and there does not appear to be any valid objection to che definition. Force is the cause of motion, and its laws are identical with the laws of motion : and, consequently, the science of force coincides, in all its parts, with the science of motion, which is mechanics. ELEMENTS OF MACHINERY. THE LEVER. To produce mechanical effects, it is rarely conve- nient to apply directly our available force, mean- ing by mechanical effect moving a body of a certain weight through a certain space, the assistance of ma- chinery is required. In fact, the essential idea of ma- chinery is, that it renders force available for effecting certain practical ends. Machines prepare, as it were, the raw material of force supplied to us from natural sources. It is transmitted and modified by certain combinations of the elements of machinery, and is given off, at last, in a condition suitable for producing the 66 MECHANICS. desired mechanical effect. We do not create force the end of machinery is just to transmit it. and diffuse 01 concentrate it m one or more points of action. The various diffused or concentrated forces, then, being added together, will just amount to the original avail able force. All machinery, when analyzed, will be found to con- sist of a combination of six simple machines, or ele- ments, commonly called mechnnicitl powers. This term is not correctly applied to these elements. They are not powers, or, in other words, sources of power or fo^e they simply transmit and diffuse or concentrate forces. These six elements are, the lever, the pulley, the ivheel and axle, the inclined plane, the wedge, and the screw. To understand, therefore, the nature of any machine, t correct idea of these elements is requisite. A lever is an inflexible rod, by the application of which one force may balance or overcome another. These forces are termed, respectively, the power and the resistance or weight, not from any difference in the action of the forces, but with reference merely to the intention with which the machine is used ; and indeed the same terms are used about all the other mechanical elements. In applying the rod to operate upon any resistance, it must rest upon a centre prop, or fulcrum, somewhere along its length, upon which it turns in the performance of its work. Thus, there are three points in every lever, to be regarded in examining its action, namely, the two points of application of the power and the weight, and the point resting on the fulcrum. There is a certain rela- tion to be observed between the magnitudes of the op- posing force, and their distances from the fulcrum, namely, that, in every case, the power, multiplied by its distance from the fulcrum, is equal to the weight, multiplied by its distance from the same point. From this, simple rules may be deduced for calculation. To know the power to be applied, at a certain dis- tance from the fulcrum, to overcome a resistance acting also at a certain distance, multiply the resistance by its MECHANICS, 67 distance from the fulcrum, which gives its moment, and divide the product by the distance given. Quotient will be the power, it being observed that the distance and the force be each expressed in the same unit of measure. For example, a weight, 1120 Ibs., at -3 inches from the fulcrum, is to be balanced by a force at the distance of 10 feet Now 10 feet are equal to 120 inches ; and the moment of 1120 Ibs. is 1 120 X 3 = 3300. Divide this by 120, we have 28 Ibs. for the power required. Again ; to know the distance at which a given force ought to be applied to balance a given weight at a certain distance, we must, in like manner, multiply the weighc by its distance, as before, and divide by the given power. 1120 Ibs., for example, at 3 inches distance, are to be balanced by a force of 28 Ibs. To find the distance of this weight, 1120 Ibs. multiplied by 3, give 3360, which, divided by 28, give 120 inches, or 10 feet THE WHEEL AND AXLE, OR CRANE. The mechanical advantage of the wheel and axle, or crane, is as the velocity of the weight to the velocity of the power ; and, being only a modification of the first kind of lever, it of course partakes of the same principles. To determine, the amount of effective power produced from a given power, by means of a crane with known peculiarities. Rule,. Multiply together the diameter of the circle described by the handle and the number of revolutions of the pinion to one of the wheel ; divide the product by the barrel's diameter in equal terms of dimensions ; and the quotient is the effective power to 1 of exertive force. Ex. Let there be a crane, the handle of which de- scribes a circle of 30 inches in diameter; the pinion makes 8 revolutions for 1 of the wheel, and the barrel 68 MECHANICS is 11 inches in diameter; required the effective power in principle, also the weight that 36 Ibs. would raise, friction not taken into account 30X 8 = 21-9 to 1 of exertive force, and 21-9 X 36 = 785-5 Ibs. 11 Given any two parts of a crane, to find the third that sltall produce any required proportion of mechanical effect. Rule. Multiply the two given parts together, and the quotient is the dimensions of the other parts in equal terms of unity. Ex. Suppose that a crane is required, the ratio of power to effect being as 40 to 1, and that a wheel and pinion J 1 to 1 is unavoidably compelled to oe employed; also the throw of each handle to be 16 inches; what must be the barrel's diameter, on which the rope or chain must coil ? 16x2 = 32 inches diameter described by the handle. And 32 x 11 = 8-8 inches, the barrel's "diameter. 40 THE PULLEY. The principle of the pulley, or more practically the block and tackle, is the distribution of weight on vari- ous points of support; the mechanical advantage derived depending entirely upon the flexibility and tension of the rope, and the number of pulleys or shelves in the lower or rising block. Hence, by blocks and tackle of the usual kind, the power is to the weight as the num- ber of cords attached to the lower block ; whence the following rules : 1. Divide the weight to be raised by the number of cords leading to, from, or attached to the lower block ; and the quotient is the power required to produce ac equilibrium, provided friction did not exist 2. Divide the wejgnt to be raised oy tne power to be MECHANICS. 09 applied : the quotient is the number of shelves in, or cords attached to, the rising block. Ex. Required the power necessary to raise a weight of 3000 Ibs. by a four and five shelved block and tackle, the four being the movable or rising block. Necessarily, there are nine cords leading to and from the rising block ; 3000 Consequently, = 333 lbs v the power required. i'l. 2. I require to raise a weight 4256 Ibs.; the amount of my power to effect this object being 50Q Ibs. What kind of block and tackle must 1, of necessity, em- ploy ? 425< = 8-51 cords of necessity, there must be 4 shelves, 600 or 9 cords, in the rising block. As the effective power of the crane may, by addi- tional wheels and pinions, be increased to any required amount, so may the pulley and tackle be similarly aug- mented by purchase upon purchase. Two of the most useful are known by the term runner and tackle, and the second by that of Spanish burton. 70 THE INCLINED PLANE. T-< C: *> 'O lO "s^ CO Ctt - i-ii-iOOOGOOOO 00000000 oooooooo OOOOO OOO C> S* C: ift C 00 13 G 03 en i- x x no t^ t>- i^ to r? ^ ^? 7J 7i 7J (>? ?J O? oooooooooo oooooooooo "^ O l> 13 70 -H O 00 t COC L.O ^D O 7J CiXll>sOsCiOOLO r-tOOOOOOOOO oooooooooo > lOCOOIdr-ir-( bo 2^ *v _^ e __. .Js ""S .c 11 .Is js Id ^ S _= !j >c ~"S "r ^ .. 3 - 51 ,31 11 31 f 'i a II 31 ^1 II il 1 80 40 84 40 55 20 60 19 50 95 20, 100 u 80 50 84 90 85 20 90 194 80 120 20 130 14 80 60 84 60 70 20 75 20 60 100 20 120 11 80 70 i 90 90 20 95 20* 40 90 20 90 9 80 90 40 60 20 65 21 80 120 20 140 24 so 90 10 60 75 20 80 22 60 110 20 120 24 80 100 104 50 70 20 75 22* 80 120 20 150 2| 80 110 11 60 55 20 120 80 130 20 140 3 80 120 12 90 90 20 120 23| 40 95 20 100 34 80 130 60 85 20 90 24 65 120 20 130 34 80 140 13 90 90 20 130 25 60 100 20 150 31 80 150 60 90 20 90 25J 30 85 20 90 4 40 80 131 80 100 20 110 26 70 130 20 140 44 40 85 14 90 90 20 140 27 40 90 20 120 44 40 90 144 60 90 20 95 k ^^i 40 100 20 110 41 40 95 15 90 90 20 150 28 75 140 20 150 40 100 16 60 80 20 120 28^ 30 90 20 95 54 6 40 40 110 120 lit 80 80 100 110 20 20 130 120 30 32 70 30 140 80 20 20 150 120 $h 40 130 17 45 85 20 90 33 40 110 20 120 40 140 174 80 100 20 ]4( 34 30 85 20 120 ? 40 30 150 120 18 40 80 60 1 20 J120 100120 1150 35 36 60 J140 301 90 20 20 150 120 CONTINUOUS CIRCULAR MOTION. OA Table by which to determine the Number of Teeth, o? Pitch of Small Whtds, by what is commonly called the Manchester Principle. Diametral Circular Diametral Circular pitch. pitch. pitch. pitch. 3 1-047 9 349 4 785 10 314 5 648 12 262 6 524 14 224 7 449 16 196 8 393 20 157 jKr. 1. Required the number of teeth that a whee* of 16 inches diameter will contain of a 10 pitch. 16 X 10= 160 teeth, and the circular pitch =-314 inch. Ex. 2. What must be the diameter of a wheel for a 9 pitch of 126 teeth ? 126 = 14 inches diameter, circular pitch -349 inch. Note. The pitch is reckoned on the diameter of the wheel instead of the circumference, and designated wheels of 8 pitch. 12 pitch, &c. Strength of the Teeth of Cast Iron Wheels at a given Felociti/. Pitch of teeth in inches Thicknew of teeth in inches. Breadth of teeth in inches. Strength of teeth in horse-pcnver at 3 feet per 4 feet per 6 feet per second. 8 feet p-F second. 3-99 1-9 7-6 20-57 27-43 41-14 54-85 3-78 1-8 7-2 17-49 23-32 34-98 46-64 3-57 1-7 6-8 14-73 19-65 29-46 39-28 3-36 1-6 6-4 12-28 16-38 24-55 32-74 3-15 1-5 6 10-12 13-50 20-24 26-98 2-94 1-4 5-6 8-29 10-97 16-44 * 21-92 2-73 1-3 5'2 6-58 8-78 13-16 17-54 2-52 1-2 4'8 5-18 6-91 10-36 13-81 2-31 1-1 4'4 3-99 5-32 7-98 10-64 2-1 1-0 4 3-00 4-00 6-00 8-00 1-89 9 3-6 2-18 2-91 4-36 5-81 168 8 3-2 1-53 2-04 3-06 3-08 1-47 7 2-8 1-027 1-37 2-04 2-72 1-26 6 2-4 64 86 1-38 1-84 1-05 5 2 375 50 75 1-00 82 ritAcj (,AL PROPERTIES OF WATER. PRACTICAL PROPERTIES OF WATER BY analysis it is ascertained, that water is composed of the gases oxygen and hydrogen in a state of chemical anion ; its distinguishing properties, like that of othei liquids, being nearly incompressible gravity, capability of flowing, and constant tendency to press outwards in every direction ; also that of being easily changed by the absorption of caloric to an aeriform state of any re- quired density or degree of elastic force: hence the principle of the hydraulic press, the water-wheel, the steam engine., &c Effects produced by Water in Us natural State. Because of liquids possessing the properties of gravity and capability of flowing freely in every direction, sides of vessels, flood-gates, sluices, &c.. sustain a pressure equal to the product of the area multiplied by half the depth of the fluid, and by its gravity in equal terms of unity. But when a sluice or opening through which a liquid *nay issue is under any given continued head, the pres- sure is equal the product of the area multiplied into the height, from the centre of the opening to the surface of the fluid. Ex. 1. Required the pressure of water on the sides of a cistern 18 feet in length, 13 in width and 9 in dapth. The terms of measurement or unity are in feet, 1 cubic foot ot water .-= (i-2-5 Ibs. ; hence 18 x 9 X 2 + 13 X 9 X 2 558 X 4-5 x 62- 5 = 156937-5 Ibs. weight of water on bottom = 18 X 13x9x62-5 =131625 Ibs. Ex. 2. Required the pressure on a sluice 3 feet square, and its centre 30 feet from the surface of the water 3 x 3 x 30 x 62-5 = 16875 Ibs. pressure. PRACTICAL PROPERTIES OF WATER. 83 The weight of water or other fluid is as the quantity but the pressure exerted is as the vertical height. Hence, as fluids press equally in every direction, any vessel containing a fluid sustains a pressure equal to as many times the weight of the column of greatest height of that fluid, as trie area of the vessel is to the sectional area of the column. JEr. Let a cubical vessel, whose sides are each 4 square feet, have a tube inserted 1 inch in diameter, and 6 feet in height, and let both vessel and tube be filled with water; required the whole weight of the water therein contained, and also the whole pressure exerted intending to burst the vessel. Cubic contents of the vessel = 8 feet, and each foot = 62-5 Ibs. ; then 62-5 X 8 = 500 area of pipe's section = -7854 inches, and height 72 inches, also a cubic inch of water = -03617 Ibs.j hence,-7854 X 72 x '03617 = 2 Ibs. + 500 = 602 Ibs., total weight of the water. Again ; the whole height of the column = 96 inches ; then -7854 X 96 X -036 17 = 2-33 Ibs., pressure of column on an equal 14* x 4 X 6 side3 area. 144 square inches = 1 square foot, and 7854 = 4400*4 times the area of the pipe's diameter in the whole surfnce ; therefore, 4400-4 X 2-33 = 10253 lbs. ; or total amount of pressure exerted. To find the velocity of water issuing a circular orifice ai any given depth from the surface. Rule. - Multiply the square root of the height or depth to the centre of the orilice by 8-1 ; and the product is the velocity of the issuing fluid in feet per second. JE.r. Required the velocity of water issuing through an orifice under a head of 11 feet from the surface. V 11 = 3-3166 X 8-1 = 26-864 feet, velocity per second. In the discharge of water by a rectangular aperture in the side of a reservoir, and extending to the surface, the velocity varies nearly as the square root of the height, ana the quantity discharged per second equal |rds of the velocity due to the mean height, allowing for the 8 84 PRACTICAL PROPERTIES OF WATER. contraction of the fluid according to the form of tfi opening, which renders the coefficient in this case equal to 5-1 ; whence the following general rules. 1. When the aperture extends to the surface of the fluid. Multiply the area of the opening in feet by the square root of its depth also in feet and that product by 5'1 : then will :;rdsof the last product equal the quantity discharged, in cubic feet, per second. 2. When the aperture is under a given head. Mul- tiply the area of the aperture, in feet, by the square root of the depth, also in feet, and by 5-1 ; the product is the quantity discharged, in cubic feet, per second. Ex. 1. Required the quantity of water in cubic feet per second, discharged through an opening in the side of a dam or weir, the width .or length of the opening being G feet, and depth 1) inches, or *75 of a foot. Square root of -75 = -866. cubic feet Ex. 2. What would be the quantity discharged through the above opening, if under a head of water 4 feet in height ? Square root of 4 = 2, and 2x5-1 = 10-2 feet, velocity of the water per second. And 6-5 X -75 x 2 x 5 1 == 49-725 cubic feet discharged in the same time. The combined properties of gravity and fluidity which water possesses, renders it so available as a source of motive power; gravity being the property ,by which the power is produced, and fluidity that by which it is so commodiously qualified to the various modifications in which it is employed. Water, it is ascertained, is subject to the same laws of gravity as those of solid bodies, and thereby accumu- lates velocity or effect in an equal ratio when filling through an equal space, or descending from an equal height. Hence, the velocity attained is as the square root of the height of its fall ; and it is now quite satis- PRACTICAL PROPERTIES OF WATER. 85 factorily decided, that, because of the non-elastic prop- erty of water, its greatest is obtained when acting by gravity throughout its whole height, whether it be ap- plied on a water-wheel, turbine, or other machine through which circular motion is to be the immediate result. In regard to water-wheels, and other machines through which motion is produced by the effort ot water, much discrepancy of opinion has, until lately, existed, both as to form and velocity, besides other essential points requisite in gaining a maximum of effect with the least possible strain ; but these doubts are now in a great measure removed through experi- ments by the Franklin Institute in this country, added to ti ose in France by Morin, and the results of a pa tentc d machine by Whitelaw and Stirrat, Scotland, combined with pertinent observations and remarks by interested parties in this as well as other countries. Hence have been deduced the following demonstrative conclusions : 1. That, to gain a maximum of effect by a horizontal water-wheel, the water must be laid upon the wheel on the stream side, and the diameter of the wheel so pro- portioned to the height of the fall, that the water may may be laid on about 52$ degrees distant from the summit uf the wheel, or the height of the fall, being 1 the height or diameter of the wheel equal 1-108. 2. That the periphery of a water-wheel ought to move ai. a velocity equal to about twice the square root of the fall of the water in feet per second, and the number of buckets equal SM times the wheel's diameter in feet ; also, that precautionary means be adopted for the escape of the air out of the buckets, either by making the stream of water a few inches narrower than the wheel, or otherwise. 3. That, because of water producing a less efficient power by impulse than gravity, turbines, or machines through which the motion is obtained by reaction, are greatly preferable to undershot, or low-breast wheels. 66 PRACTICAL PROPERTIES OF WATER. 4. That a head of water is required sufficient to cause the velocity of its flowing to be as 3 to 2 of the wheel ; i of the wheel's diameter being an approximate height, near enough for practical purposes. 5. That the effective power of a wheel constructed according to these restrictions, is equal to the product of the number of cubic feet and velocity in feet per minute, multiplied into -001325. Example for general Rluslration. Suppose a fall of water 25 feet in height, over which is delivered 112 cubic feet per minute; required the various peculiar requisites for a wheel *o be in accord- ance with the preceding rules. 1st. 25 X 1-08 = 27 feet, the wheel's diameter. 2d. V tb x 2 = 10 feet, velocity of the wheel in feet per second. Also : 27 X 2-1 = 5fr7, say 57 buckets, 3d. 27 9 = 3 feet, head of water required. 4th. lit x 10 X 60 X -001325 = 89 horses' power. The turbine of Fourneyron, in France, and the patented water-mill of Whitelaw and Stirrat, Scotland, have, of late years, attracted a considerable share of public attention ; their simplicity of construction and asserted effects in like situations, being equal to those of the best applied water-wheels. In their manner of construction they differ, but in principle they are the same ; the action of each being created by a centrifugal and tangential force, caused by the weight or impulsion of a column of water whose height or altitude is equal to twice the height of the fall due to the water's velo- city ; and in order to produce a maximum of effect in father the one or the other by the pressure and centrif- ugal force of the effluent water, it is necessary that the emitting tubes or helical channels of the machine be so curved that the apertures shall be in a right line with the radius of the wheel. STEAM POWER. 87 1. That turbines are equally adapted to great as to small waterfalls. 2. That they are capable of transmitting a useful effect to from 70 to 78 per cent, of the absolute power. 3. That their velocities may vary considerably from the maximum effect, without differing sensibly from it. 4. That they will work nearly as effectually when drowned to the depth of 6 feet as when free, and, consequently, they will make use of the whole of the fall when placed below the level of extreme low water. 5. That they receive variable quantities of water, without altering the ratio of the power to the effect. STEAM POWER. THERE is no application of science to the arts of more importance, and more extensive in its effects, than that of the employment of steam for driving all kinds of machinery. It is not my intention to enter into the details of the power of steam or the steam-engine, but to give some practical rules, the utility of which have been tested. Steam is of great utility as a productive source of motive power; in this respect, its properties are, elastic force, expansive force, and reduction by condensation. Elastic signifies the whole urgency or power the steam is capable of exerting with undiminished effect. By expansive force is generally understood the amount of diminishing effect of the steam on the piston of a steam-engine, reckoning from that point of the stroke where the steam of uniform elastic force is cut off; but it is more properly the force which steam is capable of exerting, when expanded to a known number of times its original bulk. And condensation, here understood, 88 STEAM POWER is tho abstraction or reduction of heat by another body and conrequently not properly a contained property of the steam, but an effect produced by combined ao-ency in which stearn is the principal ; because any colder body will extract the heat and produce condensation, but steam cannot be so beneficially replaced by any other fluid capable of maintaining equal results. The rules formed by experimenters, as corresponding with the results of the;r experiments on the elastic force of steam at given temperatures, vary, but ap- proximate so closely, that the following rule, because of being simple, may, in practice, be taken in preference to any other. Rule. To the temperature of the steam, in degrees of Fahrenheit, add 100; divide the sum by 177 ; and the 6th power of the quotient equal the force in inches of mercury. Ex. Required the force of steam corresponding to a temperature of 312. 312 4- 100 177 = 2-S277 6 = 159 inches of mercury. To estimate the amount of advantage gained by using steam expansively in a steam-engine. When steam of a uniform elastic force is employed throughout the whole ascent or descent of the piston, the amount of effect produced is as the quantity of steam expended. But let the steam be shut off at any portion of the stroke, say, for instance, at one-half, it expands by degrees until the termination of the stroke, and then exerts half its original force ; hence an accumulation of effect in proportion to the quantity of steam. Ru!e. Divide the length of the stroke by the dis- tance or space into which the dense steam is admitted, and find the hyperbolic logarithm ot the quotient, to which add 1 ; and the sum is the ratio of the gain. STEAM POWER. 89 Ex. Suppose an engine with a stroke of 6 feet, and uie steam cut off' when the piston has moved through ; required the ratio of gain by Uniform and expansive force. G-f-2 = 3 ; hyperbolic logarithm of 3 = 1-0986 -f 1 = 2-0986, ratio of effect; that is, supposing the whole effect of the steam to be 3, the effect by the steam being cut off at I = 2-0986. Again ; let the greatest elastic force of steam in the cylinder of an engine equal 48 Ibs. per square inch, and let it be cut off from entering the cylinder when Jie piston has moved 4-i inches, the whole stroke being 18 ; required an equivalent force of the steam through- out the whole stroke. 18 4-5 = 4, and 48 4 = 12. Logarithm of 4-f 1 =2-38629. Then 9-38629 X 12 = 28-635 Ibs. per square inch. In regard to the other case of expansion, when the temperature is constant, the bulk is inversely as the pressure; thus, suppose steam, at 30 Ibs. per square inch, required its bulk to that of original bulk, when expanded so as to retain a pressure equal to that of the atmosphere, or 15 Ibs. 15 + 30 15 = 3 times its original bulk. It is because of the latent heat in steam, or water in an aeriform state, that it becomes of such essential service in heating, boiling, drying, &c. In the heating of buildings, its economy, efficiency, and simplicity of application, are alike acknowledged ; the steam, being simply conducted through all the departments by pipes, by extent of circulation condenses, the latent heat being thus given to the pipes, and diffused by radiation. In boiling, its efficiency is considerably increased, if advantage be taken of sufficiently enclosing the fluid, and reducing the pressure on its surface, by means of 90 PRODUCTION OF STEAM. an air-pump. Tins water in a vacuum boils at about a temperature of .to- ; and in sugar-refining, where such means are employed, the sirup is boiled at 150 : Effects produced by Water in an Aeriform State. When water in a vessel is subjected to the action of fire, it readily imbibes the heat, or fluid principle of which the fire is the immediate cause, and, sooner or later, according to the intensity of the heat, attains a temperature of 212 Fahrenheit. If, at this point of temperature, the water be not enclosed, but exposed to atmospheric pressure, ebullition will take place, and steam or vapor will ascend through the water, carrying with it the superabundant heat, or that which the water cannot, under such circumstances of pressure, absorb, to be retained, and to indicate a higher temperature. Water, in attaining the aeriform sbite, is thus uni- formly confined to the same laws, under every degree of pressure ; but, as the pressure is augmented, so is the indicated temperature proportionately elevated. Hence the various densities of steam, and correspond- ing degrees of elastic force. PROPERTIES OF STEAM. 91 Table of the Elastic Force of Slectm, and corresponding Temperature of the Water with which it is in Contact. I'ressure per square inch, atmospheric pressure included. Elastic Force in Temperature in Degrees of Volume ol Steam compared with Vol. of Water. Inches of 1 Mercury. Ms ires of Mercury. Fahr. Reaum. Cent. Ibs. kilog. 14-7 6-668 30-00 -762 212-0 80-0 100-0 1711 15 6-80 30-60 778 212-8 80-4 100-4 1670 16 7-26 32-64 829 216-3 81-9 102-4 1573 17 7-71 34-68 880 219-6 83-3 104-2 1488 18 8-16 36-72 932 222-7 84-7 105-9 1411 19 8-62 38-76 984 225-6 86-0 107-6 1343,., 20 9-07 40-80 1-037 228-5 87-3 109-2 1281 21 9-52 42-84 089 231-2 88-5 110-7 1225 22 9-98 44-88 140 233-8 89-7 112-1 1174 23 10-43 46-92 192 236-3 908 113-5 1127 24 10-88 48-96 244 238-7 91-9 114-8 1084 25 11-34 51-00 296 241-0 93-0 116-1 1044 26 11-79 53.04 3-18 243-3 93-9 117-4 1007 27 12-25 55-08 1400 245-5 94-9 118-6 973 28 12-70 57-12 1-452 247-6 95-8 119-8 941 29 13-15 59-16 1-503 249-6 96-7 120-9 911 30 13-61 61-21 1-555 251-6 97-6 122-0 883 31 14-06 63-24 1-607 253-6 98-5 123-1 857 z 14-51 65-28 1-659 255-5 99-3 124-2 833 33 14-97 67-32 1-711 257-3 100-1 125-2 810 34 15-42 69-36 1-763 259-1 100-9 126-2 788 35 15-87 71-40 1-814 260-9 101-7 127-2 767 36 16-33 73-44 1-866 262-6 102-5 128-1 748 37 16-78 75-48 1-918 264-3 103-2 129-1 729 38 17-23 77-52 1-970 265-9 104-0 129-9 712 39 17-69 79-56 2-022 267-5 104-7 130-8 695 40 18-14 81-60 2-074 269-1 105-4 131-7 679 41 18-59 83-64 2-126 270-6 106-0 132-6 664 42 19-05 85-64) 2-178 272-1 106-7 133-4 649 43 19-50 87-72 1-229 273-6 1074 134-2 635 44 19-96 89-76 2-281 275-0 108-0 135-0 622 45 20-41 91-80 2-333 276-4 108-6 135-8 610 46 20-86 93-84 2-385 277-8 109-2 136-6 598 47 21-32 95-88 2-437 279-2 109-9 137-3 586 41 21-77 97 '? 2-489 280-5 110-4 138-1 575 49 22-22 99-y> 2-541 281-9 111-1 138-8 564 50 22-68 102-00 2-592 283-2 11 If 139-6 554 02 PROPERTIES OF STEAM. The preceding table is peculiarly adapter] for esti mating the power of steam engines on the condensing principle, because, in such, the effective force of the Btearn is the difference between the total force and the resisting vapor retained in the condenser. The fol- lowing table is more adapted for estimating the effects of non-condensing engines; as, in such, the atmos- pheric pressure is not" generally taken into account, engines of this principle being supposed to work in a medium: or, the atmospheric pressure on the boilers, to cause a greater density of steam, is equal to the resisting atmosphere which the effluent steam has to contend with, on leaving the cylinder. Steam, independent of the heat indicated by an im- mersed thermometer, also contains heat that cannot be measured by any instrument at present known, and, in consequence of which, is termed latent or concealed heat ; the only positive proof we have of its existence beino- that of incontestable results, or effects produced on various bodies. Thus, if one part, by weight of steam at 212, be mixed with nine parts of water at 62, the result is water at 1/H>; therefore, each of thi> 9 parts of water has received from the steam 1KH> of heat and consequently, the steam has diffused, or given out, 1 HHi X 9 = 104<>4 334 == 1016 of heat, which it must have contained. Ao-ain; it is ascertained, by experiment, that it one 52 220 Sulphate of limp . C 45 20 Sulphate of magnesia . . mini 57-5 30 222 224 Nitrate of soda 8 60 246 Acetate of soda e 60 256 Elastic Force of Steam in Inches of Mercury. Common water ) boiling point, 212 F. ( elastic force, 30 in Sea water . . . $ at 212 ? 23-05 Common water ) boiling point, 216 F. ( elastic force, 32-5 in, Sea water . . . $ at 216 " ^ 24-6 " Common water ) boiling point, 220 F. ( elastic force, 35-1 in Sea water ... 5 at 220 " ? " 26-5 " Hence the propriety of procuring, for steam, water in its purest state. Effects produced by Air in its natural and also in a rarefied State. The weight or pressure of the atmosphere is equal to the weight of a column of water 34 feet in hei"ht, or to a column of mercury 30 inches in height, or to 14-7 Ibs. a,verage per square inch, at a mean temperature. But air, like all other gases, is rendered lighter by the ap- plication of heat ; for then the particles of the mass are repelled from each other, or rarefied, and occupy a greater space. Rarefied air, being specifically lio-htest, mounts above that of common density; hence change of temperature, and the principal cause of winds. 94 PROPERTIES OF AIL. Table of the Expansion of Atmospheric Mr by Heat. Degrees of , Fahrenheit. Bulk. Degrees of Fahrenheit. Bulk. Degrees of Fahrenheit. Bulk, 32 1000 65 1077 100 1152 1 35 1007 70 1089 120 1194 40 1021 75 1099 140 1235 ! 45 1032 80 1110 160 1275 50 1043 85 1121 180 1315 * 55 1055 90 1132 200 1364 j 60 1066 95 1142 212 1376 The pressure or gravity of the atmosphere, being equal to a column of water 34 feet in height, is the means or principle on which rests the utility of the common pump, also of the syphon and all other such hydraulic applications. In a pump, the internal pres- sure on the surface of the liquid is removed by the iction of the bucket; and as by degrees the density becomes lessened, so the water rises by the external pressure to the abovo-nanied height; and at such leight it will remain, urJess, by some derangement of construction taking place, the atmospheric fluid is allowed to enter and displace the liquid column. But observe, if the temperature of the water or other liquid be so elevated that steam 01 vapor arise through it, ehen, according to tLo vapcA accumulation of density, may the action ol the purrp be partially or wholly destroyed; and the oh'vmepns >f evasion in such cases >, to place the working W*k*< beneath the surface of ^ho K;u:u wu:ch s tequ ; rt>j < *>e raised. PTJMPS. 95 Table slmving the Quantity of Water per Lineal Foot in Pumps, or Vertical Pipes of different Diameters. Diameter of pump in inches. Number of gallons per lineal ft. Number of cubic feet per lin. ft. Diameter of pump in inches. Number of gallons per lineal ft. Number of cubic feet per lin ft. 2 136 0218 8 2 176 3490 2* 172 0276 8 2314 3712 2 212 0340 8| 2-456 31140 21 257 0412 8| 2-603 4175 3 306 0490 9 2754 4417 3| 359 0576 9i 2-909 4666 34 416 0668 9^ 3-068 41*23 31 478 0766 91 3-232 5184 4 544 0872 10 3-400 5454 ii 614 688 0985 1104 104 3-572 3-748 5730 6013 41 767 1230 10| 3-929 6302 5 850 1363 11 4-114 6599 5| 937 1503 111 4-303 6902 5^ 1-028 1649 Hi 4-496 7212 5| 1-124 1803 llf 4-694 7529 6 1-224 1963 12 4-896 7853 DT 1-328 2130 I2i 5-312 8521 el 1-436 2304 13 5746 9217 1-549 2489 13 6196 9939 7 1-666 2672 14 6664 1-0689 74 1-787 2866 15 7-650 12271 g 1-912 3067 16 8-704 1-3962 1 2-042 3275 18 11-016 17670 Examples illustrative of the Utility of the Table. 1. Required the quantity of water lifted by each Btroke of the bucket of a 9 -inch pump, the length of the stroke being 2| feet 3-068 X 2-25 = 6-903 gallons, each stroke. 2. What length of stroke with a 6-inch pump will De necessary, to discharge 44 gallons of water per 9 B6 PROPERTIES OF AIR. minute, the number of strokes being 18 in the given time? 44 = 2 feet, the length of stroke. 1-224 X 18 3. What must be the diameter capable of raising 25 cubic feet of water per minute, the length of the stroke being 2 feet, and making 16 effective strokes per minute ? 25 == -625, or 105 inches, nearly. 2-5 x 16 It is by the oxygen of the atmosphere that com- bustion is supported. The common combustibles of nature are chiefly compounds of carbon and hydrogen, which, during combustion, combine with the oxygen of the atmosphere, and are converted into carbonic acid and watery vapor, different species of fuel re- quiring different quantities of oxygen. The quantity required for the combustion of a pound of coal varies from 2 to 3 Ibs., according to the quality of the coal. 60 cubic feet of atmospheric air is necessary, to pro- duce 1 Ib. of oxygen. The pressure or fluid properties of the atmosphere oppose bodies in passing through it, the opposing re- sistance increasing as the square of the velocity of the body, and the resistance per square foot in Ibs. as its velocity in feet per second, multiplied into -002288. Thus, suppose a locomotive engine in a still atmosphere, at a velocity of 25 miles per hour, presents a resisting frontage of 20 feet ; required the amount of opposing resistance at that velocity. 25 miles per hour equal 3fr67 feet per second. Then 36-672 x -002288 x 20 = 61-5 Ibs., constant opposing force WINDS. 97 Table of the Force and common Appellations given /o Winds at different Velocities. Velocity of the Wind in Force in Ihs. avoirdupois per square foot. Common Appellations given to the Wind. Miles per hour. Feet per second. 1 1 47 005 Hardly perceptible. 2 3 2-! 13 440 020 044 Just perceptible. 4 5 5 87 7-33 079 123 Gentle, pleasant wind. 10 15 1467 22-00 492 1 107 > Pleasant, brisk gale. 20 25 2! 134 3H67 1 968 3075 > Very brisk. 30 35 4401 51 34 4-42!) 6(i27 > High winds. 40 45 58-68 6601 7873 9-963 > Very high. 50 73 35 12-300 A storm or tempest. 60 8802 17715 A oreat storm. 80 117-36 31 490 A hurricane. Ill order to gain the greatest amount of the wind's impulsive effect, to produce rotary or circular motion by the sails of a wind- mill, the total surface of the sails presented to the wind ought to be about seven-eighths of ihe circle's surface which is formed by their motion, and each sail angled to the plane of motion as follows, the whip or back being divided into six equal parts: Distance from centre of motion, 1 2345 6 ) Smeaton'i >.ngle with plane of motion, 18 19 18 16 l2 7 $ rule. % G. Forrester, Liverpool, 24 21 18 14 9 3 FRICTION. FRICTION. FRICTION is an effect produced by bodies rubbing one upon another, which acts as a retarding influence in the motion of all mechanical contrivances, hut might not unfrequently be considerably diminished by a due regard to its laws, and a proper attention to the selection of those materials on which a uniform smooth surface may he attained, and which, according to experiments, are least liable to tear or become hot, and cause a roughness to arise when in working contact Several doubts existed, until lately, respecting the laws of friction ; but those are now entirely removed, through the experiments of Mr. G. Rennie, on his own account, and those of M. Morin, acting for, and under the sanction of, the French government, from or by which the following laws have been fully established : 1. The friction accompanying the motion of two surfaces, between which no unguent is interposed, bears the same proportion to the force by which those surfaces are pressed together, whatever may be the amount of that force. 2. This friction is independent of the extent of the surfaces of contact. 3. Where unguents are interposed, a distinction is to be made between the case in which the surfaces are simply unctuous and in intimate contact with one another, and the case in which the surfaces are wholly separated from one another by an interposed stratum of the unguent. If the pressure upon a surface of contact of given dimensions be increased beyond a certain limit, the latter of these cases passes into the first; the stratum of unguent being pressed out, and the unctuous surfaces, which it separated from one FRICTION. 99 another, being: brought into intimate contact. As long as either of these two states remain, the laws of its friction are not affected by the presence of the unguent : but, in the transition from the one state to the other, an exception is made to the independence of the friction upon the extent of the surface of contact; for, sup- posing the extent of two surfaces of contact, between which a stratum of unguent is interposed, and which sustain a given pressure, to be continually diminished, it is evident, that the portions of this pressure which take effect upon each element of the surfaces of con- tact will be continually increased, and that they may thus be so increased as to press out the interposed stratum of unguent, and cause the state of the surfaces to pass into that which is designated as unctuous, thereby changing the coerficient of friction. That law of friction, then, which is known as the law of : : the independence of the surface, is to be received, in the case where a stratum of unguents is interposed, only within certain limits. It will be understood, from what has been said, that there are three states, in respect to friction, into which the surfaces of bodies in contact may be made suc- cessively to pass : one, a state in which no unguent is present; the second, a state in which the surfaces are unctuous, but intimately in contact; the third, a state in which the surfaces are separated by an entire stratum of the interposed unguent. Throughout each of these states, the coefficient ot friction is the same; but it is essentially different in the different states. 4. It is a law common to the friction of all the states of contact of two surfaces, that their friction, when in motion, is altogether independent of the velocity of the motion. M Morin has verified this law, as well in various st >tes of contact without inter- oosed fluids, as in the cases where water, oils, grease, glutinous liquids, sirups, pitch, were interposed in fc continuous stratum. 9* 100 BOILERS. The variety of the circumstances under which these laws obtain in respect to the friction of motion, and the accuracj? with which the phenomena of motion accord with them, may be judged of from one example, taken from the first set of experiments of M. Morin upon the friction of surfaces of oak, whose fibres were parallel to the direction of their motion upon one another. He caused the surfaces of contact to vary their dimensions in the ratio of 1 to 84, from less than 5 square inches to nearly 3 feet square; the forces which pressed them together he varied from 88 Ibs. to 2205 Ibs., and their velocities from the slow- est possible to 9-8 feet per second, causing them to be at one period accelerated motions, at another uni- form, at a third retarded ; yet, through all this wide range of variation, he in no instance found the co- efficient of friction to deviate from the same fraction of 0-478 by more than ^V of the amount of the fraction. RULES, TABLES, ETC., RELATIVE TO BOILERS AND THE STEAM-ENGINE. THE boiler of a steam-engine may be explained as that portion of the structure in which the vital prin- ciple of the engine is generated; consequently, its construction is of the utmost importance ; for upon the proper efficiency of the boiler depends, in a great measure, the efficiency of the engine. Boilers not unfrequently, because of unavoidable peculiarities, are necessarily constructed of various forms ; but, for land or stationary engine boilers, if no thwarting circumstances intervene,* either the wagon or cylindrical forms are commonly resorted to; the BOILERS. 101 former for those of condensing engines, and the latter for those of the high-pressure principle. In the construction of boilers, much attention ought to be paid in avoiding thin films of water where the action of the fire is great ; because it is neither con- sistent with safety, nor can there be the proper quan- tities of steam generated, according to the surface exposed, unless under some extraordinary degree of pressure. Also, convex surfaces, exposed to the action of the steam, unless properly supported, ought strenu- ously to be avoided. Large water spaces, concave surfaces, or straight plates securely stayed, with ample steam-room, are the chief requisites to l* attended to. 1. To determine the proper quantity of heating sur- face in a boiler for an engine with a cylinder of a given capacity, and steam at any density required. Rule. Multiply 375 times the area of the cylinder in feet by the velocity of the piston in feet per minute, and divide the product by the volume of steam to 1 of water at the density required, (see Table, page 91 ;) and the quotient is the amount of effective heating surface in square feet. Ex. Required the amount of effective heating sur- face in a boiler for an engine whose cylinder is 4 square feet in area, and the piston's velocity !224 feet per minute, the pressure of the steam to eq'ual 5 Ibs. per square inch above the pressure of the atmosphere. 375 x 4-5 X 224 = 295 square feet ; nearly ; the fire-grate be- ing in accordance with the following rule. Multiply the number of square feet of heating sur- face by -12, the product equal the area of fire-grate in square feet, thus : 295 X -12 = 354 square feet of furnace bar. Note. By effective heating surface is meant horizontal sur- faces over fire, flame, or heated air; vertical or side surfaces requiring about If feet to equal in effect 1 of hori/ontal su-fai *. 102 2. To determine the proper dimensions for a loagon- haped boiler, when the amount of effective heating sur- face in square fed is obtained by the preceding ride. 1. The bottom surface equal half the whole surface 2. The length of the boiler equal twice the square root of bottom surface. 3- The width equal one-fourth the length ; and 4. The height equal one-third the length. Ex. Roquired the dimensions for a boiler of the wagon form, that may present an effective heating sui- face of 295 square feet. Bottom surface =295 2, or 147-5 square feet Length . . . = V14r5 x 2, or 24-26 feet. Width . . . = 24-2fi 4, or fi-Ofi foot. Height. . . =24-264-3, or 8-08 feet. Note. The amount of side or vertical surface equal twice the length of the boiler, added to the width, and multiplied \*j 75 to obtain that of effective surface j hence, 147-5 x 1-75 - = 4-7 feet, depth of side flue. 24-26 x 2 + G-06 3. To determine the dimensions for a cylindrical boiler. Ru'e. Extract the square root of 1 34 times the effective heating surface in square feet, and twice the root equal the builer's circumference in feet; also, the circumference equal the length. E.r. Let a cylindrical boiler be required with ai effective heating surface of 8<> square feet; what mus be its length and diameter in feet? y8G X 1-31= 10-71 X 2 = 21-48 foot circumference, or b feet 10 nches diameter, and 21-48 feet in length. Note. When an internal flue is to be insrrtod in a boilei tie external surface of the boiler may be diminished in lengtf< BOILERS. lUft equal to half the exposed surface of the flue. Observe, also, that the height of the contained water in boilers generally ought to be about two-thirds the whole height of the boiler Specified Particulars relative to the Boiler and Engine, Diameter of cylinders, 14 inches. Length of stroke, 18 < T^ap of the valve, 1 inch. Diameter of driving wheels, 5^ feet. Length of internal fire-box, . . . 2 feet llj inches. Width of do., 3 " 5 " Length of cylindrical part of boiler, 8 " 8 " Diameter of do., 3 " 4A " Length of tubes, . 8 " 11 J Number of tubes, ...... 133, of brass. Interior diameter of do., 1^ inches. Diameter of blast-pipe, 4 " About 112 Ibs. of coke, consumed in this boiler evaporate 84 gallons of water ; and from 30 to 25 Ibs of coke are consumed per mile. Heating Powers of Combustible Substances Species of combustible. ' Ibs. of water heated from 32 to 212. Ibs. of boil- ing water evaporated by 1 lb. of fuel. Ibs. of atmospheric air to each lb. of fuel. Wood in its ordinary state Wood charcoal 26 73 4-72 13-37 4-47 11-46 Coal 60 10-90 9-26 Coke 65 11-81 11-46 Turf 30 5-45 4-60 L Tnrf charcoal 64 11-63 9-86 104 STEAM-ENGINES. Table of Dimensions for Steam- Engine Cylinders by celebrated Makers. Sin l OIIKFV Con- deiMiif ,*., y B-iilioii & Wat ' ' f) 8 10 12 14 1(5 18 i 20 24 25 2fi 28 30 3.0 40 50 r.o i! Marine Engine., by iM;ui.Uley, Napier, &c. 10 15 20 25 30 40 50 70 80 90 100 110 120 130 150 200 250 i 84 20 24 27 32 3fJ 40 43 If Hitrh Pressure, or Non-Conilfiisin? Kr.g-inet, by vurioiis makers. FMameters of cylinders, the torce ol (.he team being, per square inch, 25 Ibs. 30 Ibs. 40 1U. 5u ?f 15 The ?m?7 of nominal power for steam-engines, or the usual estimate of dynamical effect per minute of a horse, called, hy engineers, a horse-powrr, is 33,000 Ibs., at a velocity of 1 foot per minute; or, the effect of a load of 2i.O Ibs., raised by a horse, for 8 hours a day, at the rate of '<> miles per hour, or 150 Ibs. at the rate of l&JO feet per minute TROi^KKTlhS OF BODIES. 10.5 ip"!-H qsruo upithu euoj. I |& I ob I S I I 1^ |OQ | g K~ standard of cumparis en, I" *S --rf or 1000. Names. If "1-0 s c '* |l UQ *t Names. l! Acid, sulphuric " nitric . . 1850 1271 18-5 12-7 Hydriodic acid gas Chlorine " " 4340 25fO " muriatic . 1200 12-0 Carbonic " " 1527 1 " fluoric . . 1060 10-6 JVitrous oxide " 1527 " citric . . 1034 10-3 Cvariogen " 1805 | " acetic . . 1062 10-6 Oxygen " nil Water from the Carbonic oxide " 972 Baltic 1015 10-2 Water from the drotren ^" u 972 Dead Sea . . . 1240 12-4 Prussic acid " 937 Water from the Amrnoniacal " 590 Mediterranean 1029 10-3 Steain of water " 623 Water, distilled 1000 IOO Hydrogen ' 69 ; Oils, ex pressed : linseed .... 940 9-4 Weijiht of water at the sweet almond 932 9-3 common temperature : whale .... 923 9-2 1 cubic ln.= -aW/ Ib. ; ' hempseed . . olive . . . 926 915 9-3 9-2 1 ' " ft, (52-5 Ihs. 1 " = 6-2/i imp. galls. , Oils, essential : cinnamon . . lavender . . . tuq>entme . . 1043 894 870 10-4 8-9 8-7 1-8 " " = 1 rwt. 1 cylin. Jn.= -(h>842 Ib. 1 " ft. =4P-I Ibs. 1 " " = 5 imp. galls. 2-282 feet = 1 cwt. i amber .... 8(58 87 11-2 imp. galls. = 1 cwt. 825 8-2 224 =rlton. Kther, nitric . . 908 9-1 Proof spirit . . Vinegar 922 1009 9-2 10-1 10 V PRACTICAL 1ABLES. 109 PRACTICAL TABLES, WEIGHT OF METALS. WROUGHT IRON J SQUARE, ROUND, AND FLAT. Table I. contains the weight of Square Iron in sizes, from 4 inch to six inches square, advancing by inch ; and from 6 to 12 inches square, advancing by | inch ; and in lengths, from 1 foot to 18 feet The sizes are arranged in the first column of each page, and the lengths along the top ; the weight in Ibs. immediately under the lengths, and in a line with the sizes. Table II. contains the weight of Round Iron in sizes from \ inch to 6 inches diameter, advancing by J inch ; and from 6 to 12 inches diameter, advancing by | inch ; and in lengths from 1 foot to 18 feet. The sizes, lengths, and weights are arranged as in Table I. Table III. contains the weight of Flat Iron in widths, from | inch to 6 inches diameter, advancing by | inch ; in thicknesses from inch to 1 inch, advancing by \ inch ; and in lengths, from 1 to 18 feet The widths, lengths, and weights, are arranged as in the preceding tables, and the thicknesses alongside of tha widths, 110 PRACTICAL TABLES. TABLE I SaUARE IRON. size. ( Itt *. 3ft. * 5ft. Gft. 7ft. 8ft 9ft. inch. \s. Ibs. Ibs. Ibs. Ibs. Ibs. His. Ibs. Ibn ^ 0-2 04 0-6 0-8 1-1 13 1-5 1-7 19 I 0-5 10 1 4 1-9 2-4 2-9 3-3 3-8 4-3 i 0-8 17 2-5 3-4 4-2 5-J 5-9 68 7-6 1 1-3 2-6 4-0 5-3 6-6 7-9 9-2 10-6 11-9 1 1-9 3-8 5-7 7-6 9-5 11-4 13-3 15-2 17-1 I 2-6 5-2 7-8 10-4 12-9 15-5 18-1 20-7 23-3 1 3-4 6-8 10-1 13-5 16-9 20-3 23-7 27-0 30-4 1! 4-3 8-6 12*8 17-1 21-4 25-7 29-9 34-2 38-5 14 5-3 10-6 15-8 21-1 26-4 31-7 37-0 42-2 47-5 M 6-4 12-8 19-2 25-6 32-0 38-3 44-7 51-1 57-5 i._i 7-6 15-2 22-8 30-4 38-0 45-6 53-2 6)-8 68-4 ii 8-9 17-9 2(5-8 3>7 44-6 53-6 62-5 71-4 80-3 15 10-4 20-7 31-1 41-4 51-8 62-1 72-5 82-8 93-2 ii 11-9 23-8 35-6 47-5 59-4 71-3 83-2 95-1 10G-9 2 13-5 27-0 40-6 54-1 67-6 81-1 94-6 108-2 121-7 2 15-3 30-5 45-8 61-1 76-3 91-6 106-8 122-1 137-4 24 17 1 ! 34-2 51-3 68-4 85-6 102-7 119-8 136-9 154-0 21 19-1 38-1 57-2 76-3 95-3 114-4 133-5 15Q-5 171-6 2 21-1 42-2 63-4 84-5 105-6 126-7 147-8 169-0 190-1 2 1 23-:< 4(;-6 69-9 93-2 116-5 139-8 163-0 186-3 209-6 2^ 25-6 51-1 767 102-2 127-8 153-4 178-9 204-5 230-0 28 27-9 55-9 83-8 111-8 139-7 1676 195-7 223-5 251-5 3 30-4 60-8 91-2 121-7 152-1 182-5 212-9 243-3 273-7 3$ 33-0 66-0 99-0 132-0 165-1 198-1 231-1 264-1 297-1 34 35-7 71-4 107-1 142-8 178-5 214-2 249-9 285-6 321-3 Jj| 38-5 77-0 115-5 154-0 192-5 231-0 2C9-5 308-0 346-5 3* 41-4 82-8 124-2; 165-6 207-0 248-4 289-8 331-3 372-7 3| 44-4 88-8 133-3 17" -7 222-1 266-5 310-9 355-3 ,399-8 33 47-5 95-1 142-6 190-1 2377 285-2 3327 380-3 427-8 31 5-8 10J-5 '152-3 203-0 253-8 304-5 355-3 406-0 456-8 fj PRACTICAL TABLES. Ill TABLE I. SQUARE IRON. size 10ft lift 12ft 13ft 14ft. 15ft. 16ft. 17ft. 18ft J inch. ibs. Ibs. Ibs. Ibs. Ibs. Ibs. Ibs. Ibs. Ibs. i 2-1 2-3 2-5 2- 3- 3-2 3- 3-6 3-8 I 4'8 5-2 5-7 6-2 6-7 7-1 7- 8-1 8-6 i 8-5 9-3 10-1 11-0 11-8 12-0 13- 14-4 15-2 I 13-2 14-5 15-8 17-2 18-5 19-8 2J- 22-4 23-8 1 19-0 20-9 22-8 24-7 26-6 28-5 30-4 32-3 34-2 25-9 28-5 31-1 33-6 36-2 38-8 41-4 44-0 46-6 i 33-8 37-2 40-6 43-9 47-3 50-7 54-1 57-5 60-8 i* 42-8 47-1 51-3 55-6 59-9 64-2 68-4 72-7 77-0 i* 52-8 58-1 63-4 68-6 73-9 79-2 84-5 89-8 95-0 if 63-9 70-3 76-7 83-1 89-5 95-9 102-2 108-6 115-0 u 76-0 83-6 91-2 98-9 106-5 114-1 121-7 129-3 136-9 It 89-3 98-2 107-1 116-0 125-0 133-9 142-8 151-7 160-7 11 103-5 133-9 124-2 134-6 144-9 155-3 165-6 176-0 186-3 is 118-8 130-7 142-6 154-5 166-4 178-2 190-1 202-0 213-iJ 2 135-2 148-7 162-2 175-8 189-3 202-8 216-3 229-8 243-4 < 2 152-6 167-9 183-2 198-4 213-7 2289 244-2 259-5 274-7 2i 171-1 188-2 205-3 222-5 239-6 2567 273-8 290-9 308-o) 2| 190-7 209-7 228-8 247-9 266-9 286-0 305-1 324-1 343-2 24 211-2 232-3 253-4 274-6 295-7 316-8 337-9 359-0 380-2 21 232-9 256-2 279-5 302-8 326-1 349-4 372-7 396-0 419-3 21 255-6 281-2 306-7 332-3 357-8 383-4 409-0 434-5 460-1 2$ 279-4 307-3 335-3 363-2 391-1 419-1 447-0 475-0 5029 3 304-2 334-6 365-0 395-4 425-8 456-2 486-7 517-1 547-5 3J 330-1 363-1 396-1 429-1 462-1 495-2 528-2 561-2 594-2 3| 357-0 392-7 428-4 464-2 499-9 535-6 571-3 607-0 642-7 3| 385-0 423-5 462-0 500-5 539-0 577-5 616-0 654-6 693-1 3 414-1 455-5 496-9 538-3 579-7 621-1 662-5 703-9 745-3 3| 444-2 488-6 533-0 577-4 621-9 666-3 710-7 755-1 799-5 31 475-3 522-9 570-4 617-9 665-5 713-0 760-5 808-1 855-6 3} 507-6 558-3 609-1 659-8 710-6 761-3 812-1 862-9 913-6 10* B PRACTICAL TABLES. TABLE I. SQUARE IRON. size. 1ft. aft. |m 4ft. 5ft. Gft. 7ft 8ft 9ft inch Ibs. Ibs. Ibs. !bs. Ibs. 11.9. Ibs. 11)9. Ibs. 4 54-1 108-2 162-3 216-3 270-4 324-5 378-6 432-7 486-8 4& 57-5 1 15-0 172-6 230-1 287-6 345- 1 41)2-6 460-1 517-7 4 102-2 204-5 306-7 409-0 511-2 613-4 715-7 817-9 920-2 5| 107-0 213-5 320-9 427-8 534-8 641-7 748-7 855-6 962-6 51 111-8 223-5 335-3 447-0 558-8 670-5 782-3 894-0 1005-8 55 116-7 233-3 350-0 466-7 583-4 700-0 816-7 933-4 1050-0 6 121-7 243-3 365-0 486-7 608-3 730-0 841-6 973-3 1095-0 *>4 132-0 264-1 396-1 528-2 660-2 792-2 924-3 1056-3 1188-4 Gd 142-8 285-6 428-4 571-3 714-1 856-9 999-7 1142-5 1285-3 HI 154-0 308-0 462-0 616-0 770-1 J24- 1 1078-1 1232-1 1386-1 7 V 165-6 331-2 496-9 662-5 828-2 993-8 1159-4 1325-1 1490-7 7| 177-7 355-3 533-0 710-7 888-4 K)66-o| 1243-7! 1421-4 1599-0 71 190-1 380-3 570-4 760-5 950-7 1J4H-8', 1331-0 1521 ; 1711-2 71 2J3-0 406-0 609-1 812-1 1015-1 1218-1 1421-2 1621-2 1827-2 8 216-3 432-7 649-0 865-3 1081-7 1298-0 1514-4 1730-7 {U47-0 84 23>1 460-1 :s2 92' 1-3 1150-3 1380-4 1J10-5 1840-5' -2 >70-0 8i 241-2 488-4 732-7 976-9 1221-1 1465-3 1709-5 1953-8 'ai 118-u 81 258-8 517-6 776-4 10:15-2 1294-0 1552-8 1811-6 2070-4 2329-2 9 273-8 | 547-6 1H 1095-2 I3C9-0 1642-8 19U>-5 2190-3 2464-1 PRACTICAL TABLES. TABLE I. SaUARE IRON. size.' 10 ft lift. 12 ft. 1 13 ft 14ft lot 1 . 1<> ft 17ft. 18ft inch. Ibs. Ibs. Ibs. Ibs. Ibs. Ibs. Ibs. Ibs. Ibs. 4 540-8 594-9 649-0 703- 757-2 811-3 8G5-; 919-4 973-5 575-2 632-7 693-2 747-7 805-2 862-8 920-3 977-8 1035-3 44 610-6 671-6 732-7 793-7 854-8 915-8 976-9 1037-9 1099-0 41 646-0 711-7 776-4 841-1 905-8 970-5 1035-2 1099-9 1164-6 41 684-5 752-9 821-4 889-8 958-3 1026-7 1095-2 1163-6 1232-1 41 723-1 795-4 867-7 940-0 1012-3 1084-6 1 156-9 1229-2 1301-5 4:| 762-6 838-9 915-2 991-4 1067-7 ! 1144-0 1220-2 1296-5 1372-8 4j 803-3 883-7 964-0 1044-3 1124-7 1205-0 1285-3 1365-7 1446-0 5 844-8 929-3 1013-8 1098-2 1182-7 1267-2 1351-7 1436-2 1520-6 5k 887-8 976-6 1065-4 1154-2 1243-0 ! 1331-8 1420-5 1509-3 1598-1 54 931-7 1024-8 1118-0 1211-2 1304-4 1397-5 1490-7 1583-9 1677-0 51 976-6 1074-2 1171-9 1269-5 1367-2 1464-9 1562-5 1660-2 1757-8 5 1022-4 1124-6 1226-9 1329-1 1431-4 1533-6 1635-8 1738-1 1840-3 5| J 069-5 '1176-5 1283-4 1390-4 1497-3 1604-3 1711-2 1818-2 1925-2 52 1117-6 1229-3 1341-1 1452-8 1564-6 1676-3 1788-1 1899-9 2011-6 5 1160-0 1283-4 1400-1 1516-7 1633-4 1750-1 1866-7 1983-4 2100-1 6 12296 1338-3 1460-0 1581-6 1703-3 1825-0 1946-6 2068-3 2190-0 (J4 1320-4 1452-4 1584-4 i 1716-5 1848-6 1980-6 2112-6 2244-7 237b-7 (>d 1428-2 1571-0 1713-8 1856-6 1999-4 2142-2 2285-1 2427-9 2570-7 6| 1540-1 1694-1 1848-1 2002-2 2056-2 2310-2 2464-2 2618-2 2772-2 7 1656-3 1822-0 1987-6 2153-2 2318-8 2484-5 2650^1 2815-7 2981-4 74 1776-7! 1954-4 2132 1 2309-7 2487-4; 2665-1 2842-8 3020-4 3198-1 ?<| 1901-4 2091-5 2281-6 2471-8 2661-9 2852-0 3042-2 W32-3 3422-4 71 2030-2 2233-3 2436-3 2839-3 2842-3 3045-4 3248-4 3451-4 3u54-4 8 2163-4 2379-7 2596-0 2812-4 3028-7 3245-0 3461-4 3677-7 3894-0 4 2300-7 2530-7 2760-8 2990-9 3220-9 3451-0 36*1-1 3911-1 4141-2 8 2442-2 2686-4 2930-6 3174-9,3419-1 3663-3 3907-5 4151-7 4396-0 8| 2588-0 2846-8 3105-6 3364-4:3623-2 3882-0 4140-8 4399-6 4658-4 , 2737-9 3011-7 3285-5 1 3559-3 3833-1 4106-9 4380-7 4654-5 4928-3 114 PRACTICAL TABLES TABLE I SaUARE IRON size. 1ft. 2ft. 3ft. 4ft. 5ft. 6ft. 7ft 8ft. 9ft. inch. Ibs. Ibs. Ibs. Ibs. Ibs. Ibs. Ibs. Ibs. Ibs. 94 289-2 578-4 867-7 1156-9 1446-1 1735-3 2024-5 2313-8 2603-0 305-1 610-1 915-2 1220-2; 1525-3 1830-3 2135-4 2440-4 2745-5 9! 321-3 642-7 964-0 1285-3 1606-7 1928-0 2249-3 2570-7 2892-3 10 337-9 675-8 1013-8 1351-7 1689-6 2027-5 2365-4 2703-4 3041-0 104 355-1 710-3 1065-4 1420-5 1775-7 2130-8 2486-0 2841-1 3196-2 372-7 745-3 1118-0 1490-7 1863-4 2236-0 2608-7 2981-4 3354-0 10| 390-6 781-3 1171-9 1562-5 1953-1 2343-8 2734-4 3125-0 3515-7 11 409-0 817-9 1226-9 1635-8 2044-8 2453-8 2862-7 3271-7 3680-6 114 427-8 855-6 1283-4 1711-2 2139-1 2566-9 2994-7 3422-5 3850-3 Hi 447-0 894-0 1341-1 1788-1 2235-1 2682-1 3129-2 3576-2 4023-2 HI 466-7 933-4 1400-1 1866-7 2333-4 2800-1 3266-8 3733-5 4200-2 J2 486-7 973-3 1460-0 1946-6 2433-3 2919-9 3406-6 3893-2 437-t PRACTICAL TABLES. 115 TABLE 1. SQUARE IRON. size. 10 ft. lift. 12ft. 13ft. 14ft. 15ft. 16ft. 17ft. 18ft inch. Ibs. Ibs. ll.s. Ibs. Ibs. Ibs. Ibs. Ihs. Ibs. 94 2892-2 '3181 -4 ! 3470-6 3759-9 4049-1 4338-3 j 4627-5 4916-7 5206-0 94 31)50-6 3355-6 3660-7 3965-7 4270-8 4575-8 ! 4880-9 5186-0 5491-0 9$ 3213-3 3534-7 3856-4 4177-3 44U8-6 4020-0 5141-3 5462-6 5784-0 10 3379-2 3717-1 4055-0 4393-0 4730-9 5068-8 5406-7 5744-6 6082-6 104 3551-4 3906-5 4261-6 4616-8 4971 -9 1 5327-0 5682-2 6037-3 6392-4 104 3726-7 4099-4 4472-1 4844-7 52 17-4 1 5590-1 5962-8 r 6335-4 6708-1 101 3906-3 4297-0 4687-5 5078-2 5468-8 5859-4 6250-0 6644-7 7031-3 11 4089-6 4498-6 4907-5 5316-5 5725-4 6134-4 6543-4 6952-3 7361-3 Ml 4278-1 47 5-9 5133-7 5561-6 5989-4 6417-2 6845-0; 7272-8 7700-6 114 4470-2 4917-3 5364-3 581 1-3 6258-3 6705-4 7 152-4; 7599-4 8046-4 111 4666-8 5133-5 5600-2 6066-9 6533-6 7000-3 7466-9 7933-6 8400-3 ! 12 4S66-6 5353-2 5839-9 6326-5 6?.13~2 7299-8 7786-5 8273-2 8759-8 116 PRACTICAL TABLES. TABLE II ROUND I3LON. size. 1ft 2ft 3ft. 4ft 5ft, 6ft. 7ft 8ft 9ft inch. Ibs. Ibs. Ibs. Ibs. Ibs. Ibs. Ibs. Ibs. Ib3. k 0-2 0-3 0-5 0-7 0-8 1-0 1*2 1*3 1.5 1 0-4 0-7 1-1 1-5 1*9 2-2 2-6 30 3*4 i 0-7 1-3 2*0 2-7 3*3 4-0 4-6 5-3 6-0 i 1-0 2-1 3-1 4-2 5-2 6*3 7*3 8-3 9-4 I 1*5 3-0 4-5 6*0 7-5 9-0 10*5 11*9 13-4 1 2*0 4-1 . 6-1 8-1 10*2 12-2 14*2 16-3 18-3 i 2*7 5-3 8-0 10-6 13*3 15*9 18*6 21*2 23*9 U 3-4 6-7 10-1 13-4 16-8 20-2 23-5 26-9 30-2 H 4-2 8-3 12*5 16-7 20*9 25*0 29*2 33-4 37-5 11 5-0 10-0 15-1 20*1 25-1 30-1 35-1 40*2 45-2 U 6-0 11-9 17-9 23-9 29-9 35-8 41-8 47-8 53-7 11 7-0 14-0 21-0 28*0 35-1 42*1 49-1 56*1 63-1 1| 8*1 16-3 24-4 32-5 40-6 48*8 56-9 65-0 732 9*3 18-7 28-0 37*3 46-7 56*0 65*3 74*7 84-0 2 10-6 21-2 31-8 42*5 53*1 63-7 74-3 84-9 95*5 2J 12-0 24-0 36-0 480 59*9 71*9 83-9 95-9 107*9 2| 13-5 26-9 40-3 53-8 67-2 80*6 94-1 107-5 121*0 2f 15-0 30*0 44-9 60-0 74-9 89-9 104-8 119-8 134-8 16-7 33-4 50-1 66-8 83*4 100*1 116-8 133-5 150-2 21 18-8 36-6 54-9 73-2 91-5 109*8 128*1 146-3 164-6 21 20*1 40-2 60-2 80-3 100-4 120-5 140-5 160*6 180*7 2 21*9 43-9 65*8 87*8 109-7 131-7 153-6 175-6 197-5 3 23*9 47-8 717 95-6 119-4 143-3 167-2 1911 215-0 3& 25-9 51*9 77-8 103-7 129-6 155*6 181-5 207-4 233-3 3i 28-0 56-1 84-1 112-2 140*2 168*2 196-3 224*3 253-4 3| 30-2 60-5 90*7 121-0 151-2 181-4 211-7 241-S 272-2 3 32-5 65-0 97-5 l'0-O 162*6 195-1 227-6 260-1 292-6 3| 34-9 69-8 104-7 139-5 174*4 209-3 244-2 279*1 314*0 31 37-3 74-7 l.'9-O 149*3 186-7 224-0 261-3 298-7 336*0 3& 39-9 79*7 * >j 159-5 199*3 239*2 279*0 318*9 358*8 1 1 PRACTICAL TABLES. TABLE II. RO T TND IRON. 11? size. 10ft lift. 12ft. 13ft. 14 ft 15ft. 16ft. 17ft. 18ft inch. Ibs. Ibs. Ibs. Ibs. Ibs. Ibs. Ibs. Ibs. Ibs. i 1-7 1-8 2-0 2-1 2-3 2-5 2-6 2*8 3-0 3-7 4-] 4-5 4-8 5-2 5-6 6-0 6-3 6-7 h 6-6 7-3 8-0 8-6 9-3 9-9 10-6 11-3 11-9 1 10-4 11-5 12-5 13-6 14-6 15-6 16-7 i7-3 18-8 1 14-9 16-4 17-9 19-4 20-9 22-4 23-9 25-4 26-9 i 20-3 22-4 24-4 26-4 28-4 30-5 32-5 34-5 36-6 1 26-5 29-2 31-8 34-5 37-2 39-8 42-5 45-1 47-8 U 33-6 37-0 40-3 43-7 47-0 50-4 53-8 57-1 60-5 1* 41-7 45-9 50-1 54-2 58-4 62-6 66-8 70-9 75-1 U 50-2 55-2 60-2 65-2 70-3 75-3 80-3 85-3 90-3 U 59-7 65-7 71-7 77-6 83-6 89-6 95-6 101-5 107-5 If 70-1 77-1 84-1 91-1 98-1 105-2 112-2 119-2 126-2 11 81-3 89-4 97-5 105-7 113-8 121-9 130-0 138-2 146-3 H 93-3 102-7 112-0 121-3 130-7 140-0 149-3 158-7 168-0 2 106-9 116-8 127-4 138-0 148-6 159-2 169-9 180-5 192-1 1 2 119-9 131-9 143-9 155-8 167-8 179-8 181-8 193-8 205-8 2i 134-4 147-8 161-3 174-7 188-2 201-6 215-0 228-5 241-9 2 149-8 164-7 179-7 194-7 209-7 224-6 239-6 254-6 269-6 2i 166-9 183-6 200-3 216-9 233-6 250-3 267-0 283-7 300-4 2| 182-9 201-2 219-5 237-8 256-1 274-4 292-7 311-0 329-3 21 iOO-8 220-8 240-9 261-2 281-1 301-1 321-2 341-3 361-4 2 219-4 241-4 263-4 285-3 307-2 329-2 351-1 373-0 395-0 5 JJ38-9 262-8 286-7 310-5 334-4 358-3 382-2 406-1 430-0 31 259-3 285-2 311-1 337-0 363-0 388-9 414-8 440-7 466-7 3* 280-4 308-4 336-5 364-5 392-6 420-6 448-6 476-7 504-7 3! 302-4 332-6 362-9 393-1 423-4 453-6 483-8 514-1 544-3 3i 325-1 357-6 390-1 422-7 455-2 487-7 520-2 552-7 585-2 3| 3489 383-7 418-6 453-5 488-4 523-3 558-2 593-1 627-9 31 3733 410-7 448-0 485-3 522-6 560-0 597-3 634-6 672-0 31 3986 438-5 478-4 518-2 558-1 598-0 637-8 677-7 717-6 ^ 118 PRACTICAL TABLES. TABLE 11 ROUND IRON. size. 1ft 2ft. 3ft. 4ft. 5ft. 6ft. 7ft. 8ft 9ft. inch. Ibs. Ibs. Ibs. Ibs. Ibs. Ibs. Ibs. Ibs. Ibs. 4 42-5 84-9 127-4 169-9 21-2-3 254-8 297-2 339-7 382-2 4j 45-2 ,90-3 135-5 180-7 sSn-9 27 K 316-2 3)1-4 406-6 4i 48-0 95-9 143-9 191-8 239-8 287-7 335-7 383-6 431-6 41 50-8 101-6 152-4 1 203-3 254-1 304-9 355-7 40i-5 457-3 44 53-8 107-5 161-3 215-0 268-8 322-0 37fi-3 43.)- 1 483-8 4| 56-8 113-6 170-4 227-2 283-9 34U-7 397-5 454-3 511- 41 60-0 1 19-8 179-7 239-t 299-5 359-4 419-3; 479-2 539- 4$ 63-1 126-2 189-3 252-4 315-5 378-6 441-7 504-8 567-8 5 66-8 133-5 200-3 267-0 333-8 400-5 467-3 534-0 600-8 5$ 69-7 139-5 209-2 278-9 348-7 418-4 488-1 557-8 627-6 5i 7*2 146-3 2 1 9-5 j 292-7 3(55-9 439-0 51-2-2 585-4 658-5 5* 76-7 153-4 23-9 613-6 6903 54 80-3 160-6 24'HJ 321-2 401-5 481-8 562-1 642-4 722-7 51 84-0 1(58-0 252-0 336-0 420-0 504-0 588-0 1 572-1 75J 91-6 183-3 274-9 366-5 458-2 549-8 641-4 733-1 824-7 tf 95-6 191-1 286-7 382-2 477-8 573-3 668-9 764-4 860-0 6| 103-7 207-4 311-1 414-8 518-5 622-2 725-9 829-6 933-3 64 112-2 224-3 336-5 448-6 560-8 673-0 785-1 897-3 1009-4 61 121-0 241-9 362-9 483-8 604-8 725-8 846-7 967-6 1088-6 7 130-0 260-1 390-1 520-2 650-2 780-3 910-3 1040^4 1170-4 74 139-5 279-1 418-6 558-2 697-7 837-3 976-8 1116-4 1255-9 74 149-3 298-7 448-0 597-3 741-6 896-0 1045-3 1 1194-6 1344-0 71 159-5 318-9 478-4 637-8 797-3 956-7 1116-2 1275-6 1435-1 8 169-9 339-7 509-6 679-4 849-3 1019-1 1189-0 1358-8 1528-7 at 180-7 361-4 542-1 722-8 903-5 1084-2 1264-9 1445-6 1626-3 84 191-8 383-6 595-4 767-2 959-0 1150-8 1342-6 1534-5 172(5-3 81 203-3 406-5 609-8 813-0 1016-3 1219-6 422-8 1626-1 1829-3 9 215-0 430-1 645-1 860-2 1075-2 1290-2 505-3 1720-3 1935-4 PRACTICAL TABLES. 119 TABLE II. ROUND IRON. r - size 10ft lift. 12ft tan 14ft. 15ft. ! l(jft 17ft. 18ft inch. Ibs. Ibs. Ibs. Ibs. Ibs. Ibs. Ibs. Ibs. Ibs. 4 424-6 467-1 509-( 552M 594-5 637-0 676-4 721-9 7(i4-4 4| 451-7 496-9 54-2-1 587-q 632-4 677-6 722-8 761-0 313-1 44 479-5 527-5 575-4 623-4 671-3 719-3 767-2 815-2 603-1 4| 508-2 559-0 609-8 660- 6 i 711-4 762-2 813-0 8(53-9 914-7 4i 537-b 591-4 645-1 698-9 752-6 806-4 860-2 913-9 9J!7-7 41 567-9 624-7 681-5 738-2 795-0 851-8 908-r 9;>5-4 1022-2 41 599-0 658-9 718-8 778-7 838-6 898-5 958-4 1018-3 1078-2 4i 630-9 694-0 757-1 820-2 883-3 946-4 1009-5 ! 1072-6 1135-7 5 667-5 734-3 801-0 867-8 934-5 1001-3 ' 1068-0 1 134-8 1201-5 5 697-3 767-0 830-8 906-5 976-2 1046-0 HI5-7JliaV4 1255-2 54 731-7 804-9 878-1 951-2 1024-4 K)97-() 1 1 70-8 i 1243-9 1317-1 767-0 813-7 920-4 997-1 1073-8 1150-5 1227-2 1383-9 1380-6 5d 803-0 883-3 9fi3-6 1044-1 1124-3 1204-6 1284-9 1365-2 1445-5 5| 840-0 924-0 1008-0 1092-0 1176-0 1260-0 1344-0 1428-0 1512-0 51 877-8 965-5 1053-3 1141- 1228-9 j 131 6-6 1404-4 1492-2 1580-0 5| 916-3 1008-0 1099-6 1191-2 1282-9 1374-5 1466-1 1557-8 1649-4 6 955-5 1051-1 1146-6 1242-2 1337-7 1433-3 1528-8 1624-4 1719-9 04 1037-0 1140-7 1244-4 1348-2 1451-9 1555-6 1659-3 1763-0 1866-7 0* 1121-6 1233-8 1345-9 1458-1 1570-2 1682-4 1794-6 1906-7 '2018-9 01 1209-6 1330-6 1451-5 1572-5 1693-4 1814-4 1935-4 2056-3 2177-3 7 1300-5 1430-5 1560-6 1690-6 1820-7 1950-7 2088-8 2210-8 2340-9 74 1395-4 1535-0 1674-5 1814-1 1953-6 2093-2 2232-7 2372-2 2511-8 74 1493-3 1642-6 1791-9 1941-3 2090-6 2339-9 2389-2 2538-6 2687-9 71 1594-6 1754-0 1913-5 2072-9 2232-4 2391-8 2551-3 2710-8 2870-2 8 1698-6 1868-4 2038-3 2208-1 2378-0 547-8 2717-7 2887-6 3057-4 84 18 f9-0 1987-7 2168-4 2349-0 2529-7 2740-4 2891-1 3071-813252-5 84 1918-1 2109-9 2301-7 2493-5 2685-3 2879-1 30(58-9 3260-7 ! 3452-5 81 2032-6 2235-9 2439-1 2642-4 2845-6 3048-9 3252-2 3455-4 3658-7 9 2150-4 2365-4 2580-5 2795-5 30106 3225-6 3440-6 3655-7 , J870-7 11 1 \ J20 PRACTICAL TABLES. TABLE II. ROUND IRON. size. 1ft. 2ft. 3ft. 4ft. 5ft. 6ft. 7ft. 8ft. 9ft. inch. Ibs. Ibs. Ibs. Ibs. Ibs. Ibs. Ibs. Ibs. Ibs. Q| 227-2 454-3 681-5 908-6 1135-8 1362-9 1590-1 1817-2 2044-4 CU 239-6 479-2 718-8 958-4 1198-0 1437-6 1677-2 1916-8 2156-4 ! 9| 252-4 505-8 757-1 1009-5 1261-9 1514-3 1766-6 2019-0 2291-4 10 266-3 532-6 798-9 1065-2 1331-4 1597-7 1864-0 2130-3 2396-6 lOi 278-9 557-8 836-8 lllf-7 1394-6 1673-5 1952-5 2231-4 2510-3 10 292-7 585-4 878-1 1170-8 1463-4 1756-1 2048-8 2341-5 2(534-2 101 306-8 603-6 920-4 1227-2 1534-0 1840-8 2147-6 2454-4 2761-2 11 321-2 642-4 963-6 1284-9 1606-1 1927-3 2248-5 2569-7 2890-9 Hi 336-0 672-0 1008-0 1344-0 1680-0 2016-0 2352-0 2688-0 3024-0 in 351-1 702-2 1053-3 1404-4 1755-5 2106-6 2457-7 2808-8 3159-9 in 366-5 733-1 1099-6 14-36-1 1832-7 2199-2 '2565-8 2932-3 3298-8 12 382-2 764-4 1146-6 1528-8 1911-0 2293-2 2675-5 3057-7 3439-9 ... PRACTICAL TABLES. 121 TABLE II. ROUND IRON. size. 10 ft. lift. 12ft. 13ft. 14ft. 15ft. 16ft. 17ft. 18ft. inch. Ibs. Ibs. Ibs. Ibs. Ibs. Ibs. Ibs. Ibs. Ibs. 9i 2271-5 2396-0 2498-7 2635-6 2725-8 2875-2 2953-0 3114-8 3180-1 3354-4 3407-3 3594-0 3634-4 3833-6 3861-6 4073-2 4088-7 4312-8 91 2523-8 2776-1 3028-5 3280-9 3533-3 3785-6 4038-0 4290-4 4542-8 10 2662-9 2929-2 3195-5 3461-7 3728-0 3994-3 4260-6 4526-9 4793-2 10| 2789-2 3068-2 3347-1 3626-0 3904-9 4183-9 4462-8 4741-7 5020-6 10 2926-9 3219-6 3512-3 3804-9 4097-6 4390-3 4683-0 4975-7 5268-4 101 3068-0 3374-8 3681-6 3988-4 4295-2 4602-0 4908-8 5215-6 5522-4 11 3212-2 3533-4 3854-6 4175-8 4497-0 4818-2 5139-5 5460-7 5781-9 m iu 3360-0 3511-0 3696-0 3862-1 4032-0 4213-2 4368-1 4564-4 4704-1 4915-5 5040-1 5266-6 5376-1 5619-7 5712-1 5968-8 6048-1 6319-9 111 3665-4 4031-9 4398-4 4765-0 5131-5 5498-0 5864-6 6231-1 6597-6 12 3822-1 4204-3 4586-5 4968-7 5350-9 5733-1 6115-3 6497-5 6879-7 22 PRACTICAL TABLES. TABLE III. FLAT IRON. Th'k. Wid. 1 ft 2ft :jftj 4ft 511 <>ft 7ft 8ft|9ft inzh. ir.ch. Ihs. Ihs. ll.s. n.s. Ibs. U.s. Ihs. lt>3. Ibs. 4 1 0-8 1-7 2-5 3-4 4-2 5-1 5-9 6-8 76 4 14 1-1 2-1 3-2 4-2 5-3 6-3 7-4 8-4 9-5 4 u 1-3 2-5 3-8 5-1 6-3 7-6 8-9 KM 114 ~ 4 u 1*5 3-0 4-4 5-9 7-4 8-9 10-4 11*6 13-3 i 2 1-7 3-4 Sri 6-8 8-5 10-1 11 '8 13-5 15-2 4 24 1-9 3-8 5-7 7-6 9-5 11-4 13-3 15-2 17-1 4 2d 2-1 4-2 H-3 8-4 10-fi 12-7 14-8 16'9 190 4 25 2-3 4-ti 7-0 9-3 11-6 13-9 16-3 18-6 209 4 3 2-5 5-1 7-fi 1 0-1 12-7 15-2 17-7 20-3 228 4 si 2-7 5-. r > 8-2 II -ii 13-7 16-5 19-2 2-2-0 24-7 4 34 3-0 5-9 8-9 ll-H 14-8 17-7 20-7 23-7 2G-G 4 31 3-2 6-3 9-5 12-7 15-8 19-0 32-J 25-4 28-5 4 4 3-4 6-8 in-i 13-5 KV9 20-3 23-7 27-0 30-4 4 44 3-H 7-2 1 08 14-4 18-0 21-5 25-1 28-7 32-3 4 4i 3-8 7- 39-9 4 M 4-6 9-3 13-9 18-6 23-2 27-9 3 r >-5 37-2 41-8 4 51 4-9 9-7 146 19-4 24-3 29-2 34-0 38-9 43-7 4 G 5-1 10-1 15-2 20-3 25-3 30-4 35-5 40-6 45-6 1 1 1-3 2-5 3-8 5-1 6-3 7-6 8-9 10-1 11-4 8 1-6 3-2 4-8 6-3 7-9 9-5 11-1 12-7 14-3 li 1-9 3-8 5-7 7-b 9-5 IM 13-3 15-2 17-1 1 U 2-2 4.4 6-7 8-9 11-1 *3-3 15-5 17-7 20-0 | 2 2-5 5-1 7-6 10-1 12-7 15-2 17-7 20-3 22-8 ft 2* 2-9 5-7 8-3 11-4 14-3 17-1 20-0 22-8 25-7 | 2-i 3-2 6-3 9-5 12-7 15.-8 19-0 22-2 25-4 28-5 PRACTICAL TABLES. 123 TABLE III. FLAT IRON. Th'k. Wid. 10ft' lift 12ft 13ft 14ft 15ft 16ft 17ft 18ft inch. inch. Ibs. Ibs. Ibs. Ibs. Ibs. Ibs. Ibs. Ibs. Ibs. ^ 1 8-5 9-3 10-1 Jl-0 11-8 12-7 13-5 14-4 15-2 4 H 10-6 11-6 12-7 13-7 14-8 15-8 16-9 17-9 19-0 k U 12-7 13-9 15-2 1G-5 17-7 19-0 20-3 21-5 22-8 i 11 14-8 16-3 17-7 19-2 20-7 22-2 23-7 25-1 26-6 j 2 16-9 18-6 20-3 22-0 23-7 25-4 27-0 28-7 30-4 ^ 2i 19-0 20-9 22-8 24-7 2G-6 28-5 30-4 32-3 34-2 ^ 2 21-1 23-2 25-3 27-5 29-6 31-7 33-8 35-9 38-0 1 21 23-2 25-6 27-9 30-2 32-5 34-9 37-2 39-5 41-8 3 26-3 27*9 30-4 33-0 35-5 38-0 40-6 43-1 45-6 3* 27-5 30-2 33-0 35-7 38-5 41-3 43-9 46-7 49-4 | a* 29-6 32-5 35-5 38-5 41-4 44.4 47-3 50-3 53-2 i 31 31-7 34-9 38-0 41-2 44-4 47-5 507 53-9 57-0 ^ 4 33-8 37-2 40-6 43-9 47-3 50-7 54-1 57-5 60-8 4| 35-9 39-5 43-1 46-7 50-3 53-9 57-5 61-0 64-6 \ ;>8-o 41-8 45-6 49-4 53-2 57-0 60-8 64-6 68-4 k 4| 40-1 44-1 48-2 52-2 56-2 60-2 64-2 68-2 72-2 | 5 42-2 46-5 50-7 54-9 59-1 63-4 65-6 71-8 76-0 i 44-4 48-8 53-2 57-7 62-1 66-5 71-0 75-4 79-9 54 46-5 51-1 55-8 60-4 65-1 69-7 74-4 79-0 83-6 i 51 48-6 53-4 58-3 63-2 68-0 72-9 77-7 82-6 87-5 i 6 50-7 55-8 60-8 65-9 70-9 76-0 81-1 86-2 91-2 | I 12-7 13-9 15-2 16-5 17-7 19-0 20-3 21-5 22-8 i 11 15-8 17-4 19-0 20-6 22-2 23-8 25-3 28-9 28-5 8 3 -4 19-0 20-9 22-8 24-7 26-6 28-5 30-4 32-3 34-2 8 1 22-2 24-4 26-6 28-8 31-1 33-3 35-5 37-7 39-9 . 2 25-3 27-9 30-4 33-0 35-5 38-0 40-6 43-1 45-6 i 28-5 31-4 34-2 37-1 39-9 42-8 45-6 48-5 51-3 8 1 2i 31-7 34-9 38-0 41-2 44.4 47-5 50-7 53-9 57-0 ft i 124 PRACTICAL TABLES, TABLE ill. FLAT IRON. Th'k. Wid. 1ft 2ft ! 3ft 4ft 5ft 6it 7ft 8ft 9ft inch. inrh. Ibs. . Ibs. Ibs. Ibs. Ibs. i Ibs. Ibs. | Ibs. Ibs. 1 21 3-5 7-0 10-5 13-9 17-4 20-9 24-4 27-9 31-4 1 3 3-8 7-6 11-4 152 19-0 22-8 26-6 30-4 34-2 1 34 4-1 8-2 12-4 16-5 20-6 24-7 28-8 33-0 37-1 f 3d 4.4 8-9 13-3 17-7 22-2 26-6 31-1 35-5 39-9 f 31 4-8 9-5 14-3 19-0 23-8 28-5 33-3 38-0 42-8 4 5-1 10-1 15-2 20-3 25-3 30-4 35-5 40-6 45-6 1 44 5-4 10-8 16-1 21-5 26-9 32-3 37-7 43-1 48-5 4i 5-7 11-4 17-1 22-8 28-5 34-2 39-9 45-6 51-3 f 41 6-0 12-0 18-1 24-1 30-1 30- 1 42-1 48-2 54-2 5 f>-3 12-7 19-0 25-3 31-7 38-0 44-4 50-7 57-0 1 54 G-7 13-31 20-0 1 26-fi 33-3 39-9 46-fi 53-2 59-9 f 5 7-0 13-9 20-9 27-9 34-9 41-8 48-8 55-8 62-7 f 51 7-3 14-6 2J-9 29-2 36-4 43-7 51-0 58-3 65-6 6 7-6 15-2 22-8 30-4 38-0 45-6 53-2 60-8 68-4 i 1 1-7 3-4 5-1 6-8 8-5 10-1 11-8 13-5 15-2 i M 2-1 4-2 6-3 8-4 10-6 12-7 14-8 1G-9 190 1} 2-5 5-1 7-6 10-1 12-7 15-2 17-7 20-3 22-8 h 11 3-0 5-9 8-9 1J-8 14-8 17-7 20-7 23-7 2G-6 | 2 3-4 6-8 10-1 13-5 16-9 20-3 23-7 27-0 30-4 g 2| 3-8 76 11-4 15-2 19-0 22-8 26-6 30-4 34-2 } 2d 4-2 8-4 12-7 109 21-1 1 25-3 29-6 33-8 3S-0 4 21 4-6 9-3 13-9 18-6 23-2 27-9 32-5 37-2 4i-8 4 3 5-1 10-1 15-2 20-3 25-3 30-4 35-5 40-6 45-6 34 5-5 11-0 16-5 22-0 27-5 32-9 38-4 43-9 49-4 4 34 5-9 11-8 17-7 23-7 29-6; 35-5 41-4 47-3 53-2 4 31 6-3 12-7 19-0 25-3 31-7 38-0 44-4 50-7 57-0 4 4 6-8 13-5 20-3 27-0 33-8 40-6 47-3 54-1 60-8 PRACTICAL TABLES. 125 TABLE III. FLAT IRON. Th'k. Wid. 10ft lift 12ft 13ft 14ft 15ft 16ft 17ft 18ft inch inch. Ibs. Ihs. Ihs. Ihs. Ib*. Ibs. Ibs. Ibs. Ibs. 1 2| 34-9 36-3 41-8 45-3 48-8 52-3 55-8 59-3 62-7 3 38-0 41-8 45-6 49-4 53-2 57-0 60-8 64-6 68-4 3| 41-2 45-3 49-4 53-6 57-7 61-8 65-9 70-0 74-2 | 44-4 48-8 53-2 57-7 62-1 66-5 71-0 75-4 79-9 1 32 47-5 52-3 57-0 61-8 66-5 71-3 76-0 80-8 85-5 | 4 50-7 55-8 60-8 65-9 70-9 76-0 81-1 86-2 91-2 1 44 53-9 59-3 64-7 70-0 75-4 80-8 86-2. 91-6 97-0 1 44 57-0 62-7 68-4 74-2 79-9 85-6 91-3 97-0 102-7 1 42 60-2 66-2 72-2 78-3 84-3 90-3 96-3 102-3 108-4 I 5 63-3 69-7 76-0 82-4 88-7 95-0 101-4 107-7 114-0 i *M 66-5 73-2 79-8 86-5 93-1 99-8 106-5 113-1 119-8 1 Si 69-7 76-7 83-7 90-6 97-6 104-5 111-5 118-5 125-5 1 51 72-9 80-2 87-5 94-7 102-0 109-3 116-6 123-9 131-2 I 6 76-0 83-6 91-2 98-9 106-5 114-1 121-7 129-3 136-9 1 16-9 18-6 20-3 22-0 23-7 25-4 27-0 28-7 30-4 H 21-1 23-2 25-3 27-5 29-6 31-7 33-8 35-9 38-0 i M 25-3 27-9 30-4 33-0 35-5 38-0 40-6 43-1 45-6 1 H 29-6 3^-5 35-5 38-5 41-4 44-4 47-3 50-3 53-2 i 2 33-8 37-2 40-6 43-9 47-3 50-7 54-1 57-5 60-8 i 2| 38-0 41-8 45-6 49-4 53-2 57-0 60-8 64-6 68-4 I 2 42-2 46-5 50-7 54-9 59-1 63-4 65-6 71-8 76-0 i 21 46-5 51-1 55-8 60-4 65-1 69-7 74-4 79-0 83-6 3 50-7 55-8 60-8 65-9 70-9 76-0 81-1 86-2 91-2 i 34 54-9 60-4 65-9 71-4 76-9 82-4 87-9 93-3 98-8 1 3 59-2 65-1 71-0 76-9 82-8 88-7 94-6 100-6 106-5 i 31 63-3 69-7 76'0 82-4 88-7 95-0 101-4 107-7 114-0 i 4 67-6 74-4 84-1 87-9 94-6 101-4 108-2 114-9 121-7 1*26 PRACTICAL TABLES. 'ABLE III. FLAT IRON Th'k. Wd 1ft 2ft 3ft ft 5 5ft 6ft J7 8ft 9ft inch. inc'i. Ibs. Ibs. Ibs. Ibs. Ibs. Ibs. Ibs. Ibs. Ibs. i 41 7-2 14-4 21-5 28-7 35-9 43-1 50-3 57-4 64-6 i 4 s . Ibs. Ibs. Ibs. Ibs. Ibs. Ibs. 1 41 71-8 7'J-O 86-2 93-4 100-5 107-7 114-9 122-1 129-3 i 44 76-0 83-B 91-2 98-9 106-5 114-1 121-7 129-3 136-9 i 41 80-3 88-3 96-3 104-3 112-4 120-4 128-4 136-4 144-5 i 5 84-5 92-9 101-4 109-8 118-3 126-7 135-2 143-6 152-1 i 51 88-7 97-6 106-5 115-4 124-2 133-1 142-0 150-8 159-7 i 54 93-0 102-2 111-5 120-8 130-1 139-4 148-7 158-0 167-3 i 5| 97-2 106-9 116-6 126-3 136-0 145.8 155-5 165-2 174-9 i 6 101-4 111-5 121-7 131-8 141-9 152-1 162-2 172-4 182-5 l 1 21-1 23-2 25-3 27-5 29-6 31-7 33* 35-9 38-0 i H 26-4 29-0 31-7 34-3 37-0 39-6 42-2 44-9 47-5 i 14 31-7 34-8 38-0 41-2 44.4 47-5 50-7 53-9 57-0 t H 37-0 40-7 44-4 48-1 51-8 55-5 59-2 62-8 66-5 t 2 42-2 46-5 50-7 549 60-1 63-4 67-6 71-8 76-0 I 21 47-5 52-3 57-0 51-8 66-5 71-3 76-0 80-8 85-5 t 24 52-8 58-1 63-4 68-6 73-9 79-2 84-5 89-8 95-0 t 21 58-1 63-9 69-7 75-5 81-3 87-1 92-9 98-7 104-5 i 3 63-3 69-7 76-0 82-4 88-7 95-0 101-4 107-7 114-0 i 31 68-7 75-5 82-4 89-3 96-1 103-0 109-9 116-7 123-6 t 34 73-9 81-3 88-7 96-1 103-5 110-9 118-3 125-7 133-1 i 31 79-2 87-1 95-1 103-0 110-9 118-8 126-8 134-7 142-6 i 4 84-5 92-9 101-4 109-8 118-3 126-7 135-2 143-6 152-1 i 41 89-8 98-8 107-8 116-7 125-7 134-7 143-7 152-6 161-6 i 44 95-1 104-6 114-1 123-6 133-1 142-6 152-1 161-6 171-1 $ 41 100-3 110-4 120-4 130-4 140-5 150-5 160-5 170-6 180-6 t 5 105-6 116-2 126-8 137-3 147-9 158-4 169-0 179-6 190-1 51 110-9 122-0 133-1 144-2 155-3 166-4 177-5 188-5 199-6 i 54 116-2 127-8 139-4 151-0 162-6 174-3 185-9 197-5 209-1 i 51 121-5 133-6 145-7 157-9 170-0 182-2 194-3 206-5 218-6 128 PRACTI^L TABLES. TABLE III FLAT IRON Thk. Wid. 1ft 2ft 3ft 4ft 5ft 6ft 7ft 8ft 9ft inch. inch. Ibs. Ibs. Ibs. Ibs. Ibs. Ibs. Ibs. Ibs. Ibs. 1 6 12-7 25-3 38-0 50-7 63-4 76-0 88-7 101-4 114-1 1 2-5 5-1 7-6 10-1 12-7 15-2 17-7 20-3 22-8 3-2 6-3 9-5 12-7 15-8 19-0 22-2 25-4 28-5 14 3-8 7-6 11-4 15-2 19-0 22-8 266 30-4 24-2 1 11 4-4 8-9 13-3 17-7 22-2 26-6 31-1 35-5 39-9 2 5-1 10-1 15-2 20-3 25-3 30-4 35-5 40-6 45-6 f 5-7 11-4 17-1 22-8 28-5; 34-2 39-9 45-0 51-3 f 24 6-3 12-7 19-0 25-3 31-7 38-0 44-4 50-7 570 1 7-0 13-9 20-9 27-9 34-9 41-8 48-8 55-8 62-7 a 3 7-6 15-2 22-8 30-4 38-0 45-6 53-2 60-9 68-4 4 a 34 8-2 16-5 24-7 33-0 41-2 49-4 57-7 65-9 74-2 4 34 8-9 17-7 26-6 35-5 44-4 53-2 62-1 71-0 79-9 1 31 9-5 19-0 28-5 38-0 47-5 57-0 66-5 76-1 85-6 3 4 10-1 20-3 304 40-6 50-7 60-8 70-9 81-1 91-2 10-8 21-5 32-3 43-1 53-9 64-6 75-4 86-2 97-0 41 11-4 22-8 34-2 45-6 57-0 68-4 79-9 91-3 102-7 1 ^2 41 12-0 24-1 36-1 48-2 60-2 72-2 84-3 96-3 108-4 , 5 12-7 25-3 38-0 50-7 63-4 76-0 88-7 101-4 114-0 | 54 13-3 26-6 39-9 53-2 66-5 79-8 93-1 106-5 119-8 | "4 54 13-9 27-9 41-8 55-8 69-7} 83-7 97-6 111-5 125-5 1 51 14-6 29-1 43-7 58-3 72-9 87-4 102-0 116-6 131-2 1 6 15-2 30-4 456 60-8 76-0 91-2 106-5 121-7 136-9 I 14 5-1 10-1 15-2 20-3 25-3 30-4 35-5 40-6 45-6 I 2 6-8 13-5 20-3 27-0 33-8 40-6 47-8 54-1 60-8 I 3 10-1 20-3 30-4 40-6 50-7 60-8 70-9 81-1 91-2 1 4 13-5 27-0 40-6 54- 67-6 81-1 94-6 108-1 121-7 1 5 16-9 33-8 50-7 67-G 84-5 101-4 118-3 135-2 152-1 1 6 20-3 40-6 608 81-1 101-4 121-7 141-9 162-2 182-5 ^=^= PRACTICAL TABLES. TABLE III PLAT IRON. Th'k. Wid. 10ft lift 12ft 13ft 14ft 15ft IGft 17ft 18ft inch. inch. Ibs. Ibs. Ibs. Ibs. Ibs. Ibs. Ibs. Ibs. Ibs. ft 6 126-7 139-4 152-1 164-8 177-4 190-1 202-8 215-4 228-1 1 25-3 27-9 30-4 33-0 35-5 38-0 40-6 43-1 45-6 1 u 31-7 34-9 38-0 41-2 44-4 47-5 50-7 53-9 57-0 1 li 38-0 41-8 45-6 59-4 53-2 57-0 60-8 64-6 68-4 1 11 44-4 48-8 53-2 57-7 62-1 66-5 71-0 75-4 79-9 I 2 50-7 55-8 60-8 65-9 70-9 76-0 81-1 86-2 91-2 1 24 57-0 62-7 68-4 74-2 79:9 85-5 91-3 97-0 102-7 I 2 63-3 69-7 76-0 82-4 88-7 95-0 101-4 107-7 114-0 1 21 69-7 76-7 83-7 90-6 97-6 104-5 111-5 118-5 125-5 I 3 76-0 83-6 91-2 98-9 106-5 114-1 121-7 129-3 136-9 1 34 82-4 90-6 98-9 107-1 115-3 123-6 131-8 140-0 148-3 88-7 97-6 106-5 115-4 124-2 133-1 142-0 150-8 159-7 1 31 95-1 104-6 114-1 123-6 133-1 142-6 152-1 161-6 171-1 1 4 101-4 111-5 121-7 131-8 141-9 152-1 162-2 172-4 182-5 1 44 107-7 118-5 129-3 140-1 150-8 161-6 172-4 183-2 193-9 | 114-1 125-5 136-9 148-3 159-7 171-1 182-5 193-9 205-3 1 4| 120-4 132-4 144-5 156-5 168-6 180-6 192-6 204-7 216-7 1 5 126-7 139-4 152-1 164-8 177-4 190-1 202-8 215-4 228-1 1 54 133-1 146-4 159-7 173-0 186-3 199-6 212-9 226-2 239-5 | 139-4 153-3 167-3 181-2 195-2 209-2 223-1 237-0 250-9 1 51 145-7 160-3 174-9 189-5 204-0 218-6 233-2 247-8 262-3 1 6 152-1 167-3 182-5 197-7 212-9 228-1 243-3 258-5 273-7 1 H 50-7 55-8 60-8 65-9 70-9 76-0 81-1 86-2 91-2 1 2 67-6 74-4 81-1 87-9 94-6 101-4 108-1 114-9 121-7 1 3 101-4 111-5 121-7 131-7 141-9 152-1 162-2 172-4 182-5 1 4 135-2 148-7 162-2 175-7 ! 189-3 202-8 216-7 229-8 243-3 1 5 169-0 185-9 202-8 219-7 236-6 253-5 270-4 287-3 304-2 1 6 202-8 223-1 243-3 263-6 283-9 304-2 324-4 344-7 365-0 130 PRACTICAL TABLES. The tables are all calculated to the nearest tenth of a pound. To the weights of bars of Wrought Iron, ado T |-_th part for bars of Soft Steel ; and from the same weights subtract -J f th part for bars of Cast Iron. Proportional Breadths for hexagonal or six-sided Nut* for Wrought- Iron Bolts. Dia. of bolts. Breadth of nuts, Dia. of bolts. Breadth of nut? inch. 1 g- 1 [ j* inch. i I " U 2ft " I 14-" It 2J " f IA " u 2 A H " 1| 2| " 1 If " . If 3 A'ofe.'Thc thickness of the nut is equal the bolt's diam WEIGHTS OF IRON, COPPER, ETC. 13) Thicknes5s in parts of an inch. V.**o w ;H-a^H^^ ^ M OOlO^CnK/O-'JCnJOO^lCn en en en en en s i p Thickness by the wire gauge. ^ p tpcoeo.to.enenqjoi-JOpopoE i 1 I Q CJ ep .&. en en 05^J^J 00 <0 - 10 tOd5eOodbentOob-J>&.t-idi-q J *. 00 Cfl 10 o s 1 CCWh*krffc in OiO-sJ OOOOtDh- tO c3 CO ca n t-*(tfc*-OOUii 'OOtJilOCOOi H^ JO g Thickness by the wire gauge. SggS3g88!gS5; K3 s p" _ C5 2 tO tO Ol C5 ^ OD 01 3 ia g 3 s i C3 iss-^^s-^^SSs^s a P w o o *3 * > a TJ 2 w B g JO *) > 2 5! > O P w o g Bfl W B H A r ote. JSo. 1 wire gauge equal -j^ths of an inch. " 4 " " " 7 " T 3 (T ' 11 " | " " 16 " T V " 22 & The jrreat variety of thicknesses into v, r hich copper is manufactured, cause in trade the weight to be named whereby to determine the thickness required, the unit 12 132 COMPARATIVE WEIGHTS OF BODIES. II It U U tt u u a ft tt u n being- taat of a common sheet, so designated, viz., 4 feet by 2 feet, in Ibs., thus : A 70 Ib. plate is -j^ths of an inch in thickness. " 46 " " " F " " " " " "23 " "4 " " " " 6 The thickness of lead is also in common determined or understood by the weight ; the unit being that of a square or superficial foot ; thus : 4 Ibs. lead is y^th of an inch in thickness. 6 " " -i. " U COMPARATIVE WEIGHTS OF DIFFERENT BODIES Bar iron being 1, Cast iron being 1, Cast iron = -95 Bar iron = 1-07 Steel = 1-02 Steel = 1-08 Copper =1-16 Brass = 1-16 Brass = 1-09 Lead = 1-48 Sr = 1-21 = 1-56 1. Suppose I have an article of plate iron, the weight of which is 728 Ibs., but want the same of copper, and of similar dimensions, what will be its weight ? 728 x M6 =844-48 Ibs. & A model of dry pine, weighing 32 Ibs., and in which the iron for its construction forms no material portion of the weight, what may I anticipate its weight to be in cast iron ? 32-5 X 16 = 520 Ibs. Note. It frequently occurs, in the formation or construc- tion of models, that neither the quality nor condition of the timber can be properly estimated ; and, in such cases, it may be a near enough approximation to reckon 15 Ibs. of cast iroi Jb each Ib. of model. COPPER PIPES, ETC. 133 TO ASCERTAIN THE WEIGHTS OF PIPES OF VARIOUS METALS, AND ANY DIAMETER REQUIRED. Thickness : in parts of an inch. Wrouht iron. Copper. Lead. A 326 11 Ibs. pJate, -38 2 Ibs.lead, -483 As 653 23 -76 > 4 " " -967 A 976 35 " ". 1-14 5 " " 1-45 * 1-3 46 1-52 8 " " 1-933 A 1-627 58 1-9 9| " " 2-417 A 1-95 70 " " 2-28 11 " 2-9 A 2-277 80 " 2-66 13 " " 3-383 i 2-6 93 " " 3-04 15 " 3-867 . To the interior diameter of the pipe, in inches, add the thickness of the metal; multiply the sum by the decimal numbers opposite the required thickness, and under the metal's name; also, by the length of the pipe in feet; and the product is the weight of the pipe in Ibs. 1. Required the weight of a copper pipe whose in- terior diameter is 1\ inches, its length 6 feet, and the metal \ of an inch in thickness. 7-5 + -125 = 7-625 X 1-52 X 6-25 = 72-4 Ibs. 2. What is the weight of a leaden pipe 18<| feet in length, 3 inches interior diameter, and the metal \ of an inch in thickness ? 3 + -25 = 3-25 x 3 867 X 18-5 = 232-5 Ibs. Note. Weight of a cubic inch of Lead equal -4103 Ib. Copper, sheet " -3225 Brass, do. " -3037 " Iron, do. " -279 Iron, cast -263 " Tin, do. -2636 Zinc, do. -26 Water -03617 1 134 BALLS. WEIGHT OF CAST IRON BALLS. Diameter Weight Diameter Weight Diameter Weight in inches, in Ibs. in inches, in Ibs. in inches. in Ibs. 2 1-10 6 29-72 10 137-71 24 1-57 64 33-62 104 148-28 2A 2-15 6| 37-80 io| 159-40 2j 2-86 6| 42-35 wi 171-05 3 3-72 7 47-21 11 183-29 34 4-71^, 74 52-47 114 19610 3* 5-80 7J 58-06 "I 209 13 3| 7-26 7| 64-09 111 223-40 4 8-81 8 70-49 12 237-94 44 10-57 84 77-32 124 253-13 4A 12-55 8} 84-56 12* 268-97 4| 14-76 8| 92-24 12| 285-37 5 17-12 9 100-39 13 302-41 64 19-93 94 108-98 134 320-80 5A 22-91 9j 118-06 13| 338-81 5| 26-18 9| 127-63 13| 357-93 1. What will be the weight of a hollow ball or shell of cast iron, the external diameter being 9<| , and in- ternal diameter 8| inches ? Opposite 9A are 118-06, and Opposite 8| aie 92-24, subtract 25 82 ibs ., weight required. 2. Requiring to remove a cast iron ball 37-8 Ibs. in weight, and in diameter 6 inches, and replace it by one of lead of an equal weight, what must be the diameter of the leaden ball ? Weight of lead to that of cast iron =1-56 (see Table, page 132.) Then = 3^/176 = 5-f inches the diameter. 1-56 TIMBER MEASURE. 135 TABLES BY WHICH TO FACILITATE THE MEN- SURATION OF TIMBER. 1. Fled or Board Measure. Breadth n inches. Area of a lineal foot. Breadth in inches. Area of a lineal foot. Breadth in inches. Area of a lineal foot. A 0208 4 3334 8 6667 | 0417 4i 35 i2 81 6875 | 0625 41 375 8A 7084 1 0834 4| 3958 8f 7292 u 1042 5 4167 9 75 u 125 54 4375 91 7708 if 1459 5j 4583 9$ 7917 2 1667 of 4792 03 8125 2 i 1875 6 5 10 8334 2| 2084 6 i 5208 101 8542 2| 2292 3 5416 10* 875 3 25 6| 5625 10| 8959 31 2708 7 5833 11 9167 3! 2916 7^ 6042 Hi 9375 3| 3125 7j 625 nJ 9583 7f 6458 llf 9792 Application and Use of the Table. 1. Required the number of square feet in a board 01 plank 16 feet in length, and 9| inches in breadth. Opposite 9| is -8125 x 16-5= 13-4 square feet. 2. A board 1 foot 2| inches in breadth, and 21 feet in length ; what is its superficial content in square feet ? Opposite 2| is -2292, to which add the 1 foot. Then 1-2292 X21 = 25-8 square feet. 3. In a board 15^ inches at one end, 9 inches at the ather, and 14<| feet in length, how many square feet ? 15-5 4- 9 Z- 124, or 1-02085 and 1-0208 X 145 = 12* : 14-8 sq. ft. 136 TIMBER MEASURE. Cubic or Solid Measure. Mean I girth in inches. Cubic ft. j in each ! li.ieal ft. ! Mean girth in inches. Cubic ft. j in each ' lineal ft. Mean k gn' in inches. Cubic ft. in each lineal ft. 6 25 14 1-361 22 3-362 6 4 272 141 141 224 3-438 6j 294 4| 1-46 22j 3-516 61 317 4*| 1:511 92* 3-598 7 340 5 1-562 23 3-673 74 364 54 1-615 234 3-754 7* 39 5$ 1-668 tsl 3-835 7| 417 54 1-722 23| 3-917 8 4U 16 1-777 24 4- 84 472 164 1-833 244 4-084 gl 501 16j 1-89 24.J 4-168 8| 531 161 1-945 24| 4-2i>4 9 562 17 2-006 25 4-34 94 594 174 2-066 251 4-428 oT 626 1 7 I 2-126 25| 4-516 94 659 17| 2-187 2^ 4-605 10 694 18 2-25 26 4-694 73 18$ 2-313 264 4-785 10A 766 2-376 26J 4-876 io| 803 18| 2-442 26| 4-969 11 84 19 2-506 27 5-062 m 878 194 2-574 274 5-158 nl 918 m 2-64 27 5-252 ni 959 19| 2-709 27| 5-348 12 ! 20 2-777 28 5-444 124 12J 12| 1-042 1-085 1-129 20| 2-898 2-917 2-99 28,^ 28A 28| 5-542 6-64 574 13 1-174 21 3-062 29 5-84 13J 1-219 214 3-136 291 5-941 13A 1-265 21A 3-209 29A 6-044, 13j 1-313 2l| 3-285 291 6-146 CAST METAL CYLINDERS. 137 In the cubic estimation of timber, custom has estab- lished the rule of { the mean girth being the side of the square considered as the cross sectional dimensions* hence, multiply the number of cubic feet per linea, foot, as in the Table of Cubic Measure, opposite the i girth, and the product is the solidity of the given dimensions in cubic feet. Suppose the mean \ girth of a tree 21$ inches, and its length 16 feet, what are its contents in cubic feet ? 3-136 X 16 = 50-176 cubic feet. CAST METAL CYLINDERS. The cylinders are solid, each 1 foot in length. Diam. Iron. Copper. Brass. Lead. inches. Ibs. Ibs. Ibs. Ibs. 1 2-5 3-0 2-9 3-9 2 9-8 12-0 114 155 3 22-1 27-0 25-8 34-8 4 39-3 47-9 45-8 61-9 5 614 74-9 71-6 96-7 6 884 107-8 103-0 139-3 7 120-3 146-8 140-2 189-6 8 157-1 191-7 183-2 347-7 9 198-8 242-7 231-8 3134 10 2454 299-5 286-2 387-0 ! CAST IRON PIPES. This table shows the weight of pipes 1 foot long, of bores from 1 inch to 12 inches in diameter, advancing by of an inch; and of thicknesses from | of an inch to 1| inches, advancing by J of an inch. 138 CAST IRON PIPES. bore. i 1 i 8 1 i 1 11 li in. Ibs. Ibs. Ibs. Ibs. Ibs. lb. Ibs. Ibs. KM. 1 3-1 5-1 7-4 10-0 12-9 101 19-6 23-5 27-6 ] 4 3-7 6-0 8-6 11-5 14-7 18-3 22-1 26-2 30-7 n 4-3 6-9 9-8 13-0 16-6 20-4 24-5 29-0 33-7 M 4-9 7-8 11-1 14-6 18-4 22-6 27-0 31-8 36-8 a 5-5 8-8 12-3 1O1 20-3 24-7 29-5 34-5 39-9 2 * 6-1 9-7 13-5 17-6 22-1 26-8 31-9 37-3 43-0 1 6-7 7-4 10-6 11-5 14-7 16-0 19-2 20-7 23-9 25-7 28-9 31-1 34-4 36-8 40-0 42-8 46-0 49-1 3 8-0 12-4 17-2 22-2 27-6 33-3 39-3 45-6 522 31 8-6 12-3 18-4 23-8 29-5 35-4 41-7 48-3 55-2 Si 9-2 14-2 19-6 25-3 31-3 37-6 44-2 51-1 58-3 33 9-8 15-2 20-9 20-9 33-1 39-7 46-6 53-8 61-4 4 10-4 16-1 22-1 28-4 35-0 41-9 49-1 56-6 64-4 4 4 11-1 17-1 23-4 30-0 36-9 44-1 51-6 59-4 67-6 4 I 11-7 18-0 24-5 31-4 38-7 46-2 54-0 62-1 70-6 4? 12-3 18-9 25-8 33-0 40-5 48-3 56-5 64-9 73-6 5 12-9 19-8 27-0 34-5 42-3 50-5 58-9 67-6 76-7 51 13-5 20-7 28-2 36-1 44-2 52-6 61-4 70-4 79-8 5| 14-1 21-6 29-5 37-6 46-0 54-8 63-8 73-2 82-8 5 3 14-7 22-6 30-7 39-1 47-9 56-9 66-3 76-0 85-9 6 15-3 23-5 31-9 40-7 49-7 59-1 68-7 78-7 88-8 6| 16-0 24-4 33-1 42-2 51-5 61-2 71-2 81-2 92-0 6| 16-6 25-3 34-4 43-7 53-4 63-4 73-4 84-2 95-1 64 17-2 202 35-6 45-3 55-2 65-3 701 87-0 98-2 7 17-8 27-2 36-8 46-8 56-8 67-7 78-5 89-7 101-2 7 $ 18-4 28-1 38-1 48-1 58-9 69-8 81-0 92*5 104-2 3 19-0 29-0 39-1 49-9 60-7 72-0 83-5 95-3 1074 H 19-6 29-7 40-5 51-4 62-6 74-1 85-9 98-0 110-5 8 20-0 30-8 41-7 52-9 64-4 76-2 88-4 100-8 113-5 81 209 31-7 43-0 54-5 66-3 78-4 90-8 103-5 11O6 8 21-7 32-9 44-4 56-2 68-3 80-8 93-5 106-5 119-9 83 22-1 33-6 45-4 57-5 70-0 82-7 95-7 109-1 122-7 9 22-7 34-5 46-6 59-1 71-8 84-8 98-2 111-8 125-8 9 i 23-3 35-4 47-9 60-6 73-6 87-0 100-6 114-6 128-9 9i 23-9 304 49-1 62-1 75-5 89-1 103-1 117-4 131-9 91 24-8 37-3 50-3 63-7 77-3 91-3 105-5 120-1 1350 10 25-2 38-2 51-5 65-2 79-2 93-4 108-0 ! 122-8 138-1 10} 25-8 39-1 52-8 66-7 81-0 95-6 110-4 125-6! 141-1 io| 26-4 40-0 54-0 68-3 82-8 97-7 112-9 128-4 144-2 io| 27-0 41-0 55-2 69-8 84-7 99-9 115-4' 131-2 147-3 11 27-6 41-9 56-5 71-3 805 102-0! 117-8 133-9 150-3 111 28-2 42-8 57-7 72-9 88-4 104-2 i 120-3 136-7 153-4 111 28-8 43-7 58-9 74-4 90-2 1003 ! 122-7 139-4 1504 113 29-5 44-6 60-1 75-9 92-0 108-5 125-2 142-2 159-5 <2 30-1 45-6 61-4 77-5 93-6 i 110-6 i 127-6 145-0 162-6 , , ___ . j DEGREES OF HEAT. 139 TABLE FOR COMPOSITIONS OF BRASS, &C. 3 parts copper, tin, I zinc, for yellow brass. 1 1 " for Spelter, for lathe bushes. 1 1 still harder. h " " " for bearings of shafts, for harder bearings, fit for pulley blocks, fit for wheels. a gun metal The effect of different degrees of heat on different bodies, according to Fahrenheit's scale, are shown below: Degrees Cast iron thoroughly melted, 20577 Cast iron begins to melt, 17U77 Greatest heat of a common smith's forge, . . . 173117 Flint glass furnace, strongest heat, 158*17 Welding heat of iron, greatest, 131"27 Swedish copper melts, .... 4 45H7 Brass melts ^ 3807 Iron red-hot in the twilight, 884 Heat of a common lire, 790 Iron bright red in the dark, 752 Zinc melts, , 700 Mercury boils, 672 Lead melts, 94 The surface of polished steel becomes uniformly a deep blue, 58C The surface of polished steel becomes a pale straw color, 4(10 A mixture of 3 tin and 2 lead melts, 33^ CENTRE, In a general sense, denotes a point equally remote from the extremes of a line, surface, or solid. 140 CENTRES. CENTRE OF ATTRACTION Of a body, is that point into which, if all its matter is collected, its action upon any remote particle would still be the same. CENTRE OF EQUILIBRIUM Is the same, -in respect to bodies immersed in a fluid as the centre of gravity is to bodies in free space. CENTRE OF FRICTION Is that point in the base of a body on which it re- volves, into which, if the whole surface of the base and the mass of the body were, collected, and made to revolve about the centre of the base of the given body, the angular velocity destroyed by its friction would be equal to the angular velocity destroyed in the given body by its friction in the same time. CENTRE OF GRAVITY Of any body, or system of bodies, is that point upon which the body, or system of bodies, acted upon only by the force of gravity, will balance itself in all posi- tions ; hence it follows, that, if a line or plane, passing through the centre of gravity, be supported, the body or system will be also supported. CENTRE OF GYRATION Is that point into which, if the whole mass were collected, a given force, applied at a given distance, would produce the same angular velocity in the same time as if the bodies were disposed at their respective distances. This point differs from the Centre of Oscillation only m this, that, in the latter case, the motion is produced COHESION. 141 by the gravity of the body ; but, in the former, the body is put in motion by some other force, acting at one place only. COHESION Is that species of attraction which, uniting particle to particle, retains together th * component parts of the same mass ; being thus distin ruished from adhesion, or that species of attraction which takes place between the surfaces of similar or dissimilar bodies. The absolute cohesion of solids is measured by the force necessary to pull them asunder. Thus, if a rod of iron be suspended in a vertical position, having weight attached to its lower extremity till the rod breaks, the whole weight attached to the rod, at the time of frac- ture, will be the measure of its cohesive force, or abso- lute cohesion. The particles of solid bodies, in their natural state, are arranged in such a manner, that they are in equi- librium in respect to the forces which operate on them ; therefore, when any new force is applied, it is evident that the equilibrium will be destroyed, and that the particles will move among themselves till it be restored. When the new force is applied to pull the body asunder, the body becomes longer in the direction of the force, which is called the extension ; and its area, at right angles to the direction of the force, contracts. When the force is applied to compress the body, it becomes shorter in the direction of the force, which is called the compression ; and the area of its section, at right angles to the force, expands. In either case, a part of the heat, or any fluid that occupies the pores or interstices of the body, before the new force was made to act upon it, will be expelled. CASE-HARDENING. The hardness and polish of steel may be united, ic a certain degree, with the firmness and cheapness of 14*2 CASE-IIAUDENKN'G. malleable iron, by what is called case-hardening; an operation much practised, and of considerable use. It is a superficial conversion of iron into steel, and only differs from cementation in being carried on for a shorter time. Some artists pretend to great secrets in the practice of this art, using saltpetre, sal-ammoniac, and other fanciful ingredients, to which they attribute their success. But it is now an established fact, that the greatest effect may be produced by a perfectly tight box, and animal carbon alone. The goods intended to be case-hardened, being pre- viously finished, with the exception of polishing, are stratified with animal carbon, and the box containing them luted with equal parts of sand and clay. They are then placed in the fire, and kept at a light red heat for half an hour, when the contents of the box are emptied into water. Delicate articles, like files, may be preserved by a saturated solution of common salt, with any vegetable mucilage, to give it a pulpy con- sistence! The carbon here spoken of is nothing: more than any animal matter, such as horns, hoofs, skins, or leather, just sufficiently burned to admit of beim* re- duced to powder. The box is commonly made of iron, but the use of it, for occasional case-hardening upon a small scale, may easily be dispensed with, as it will answer the same end to envelop the articles with the composition above directed to be used as a lute, drying it gradually before it is exposed to a red heat, other- wise it will probably crack. It is easy to infer, that the depth of the steel, induced by case-hardening, will vary with the time the operation is continued. It may be varied from one hour to four, according to the depth of steel required. In one hour, it will scarcely be the thickness of a fourpence, and therefore may be re- moved by violent abrasion, though sufficient to answer well for fire-irons, and a multitude of other utensils, in the common usage of which its hardness prevents its being easily scratched, and its polish preserved by friction with so soft a material as leather. STEAM-ENGINES. 143 To estimate, by means of an indicator, t.e amount of effective power produced by a steam-engine. Rule. Multiply the area of the piston in square inches by the average force of the steam in Ibs., and by the velocity of the piston in feet per minute ; divide the product by 33,OuO, and y 7 ^ths of the quotient equal the effective power. Ex. Suppose an engine with a cylinder of 37 inches diameter, a stroke of 7 feet, and making 17 revolutions per minute, or 238 feet velocity, and the average indi- cated pressure of the steam 1O73 Ibs. per square inch , required the effective power. Area = 1104-^87 inches x 16-73 Ibs., x 238 feet. 33000 133.% y 7 = 93-282 horses' power. 10 To determine, the proper velocity for the piston of a. steam-engine. Rule. Multiply the logarithm of the nth part of the stroke at which the steam is cut off by 2-3, and to the product of which add 7. Multiply the sum by the dis- tance in feet the piston has travelled when the steam is cut off, and 120 times the square root of the product equal the proper velocity for the piston in feet per minute. Ex. Let the steam be cut oft in an 8-feet stroke when the piston has travelled 4th of the length ; re- quired its proper velocity. Logarithm of 4 = 0-60206 Multiplied by 2-3 1-384738 To which add -7 2-084738 2 V 4-169476 = 2-04 x 120 = 245 feet, velocity 1 3 per minute 144 STEAM-ENGINES. Table of Approximate Velocities for the Pistons oj Steam* Engines. Condensing Engines. Non-condensing Engines. Length of stroke Velocity in feet per Number of revolutions Length of stroke Velocity in feet per Number of revolutions in feet. minute. per nun. in feet. minute. per nun. 2 160 40 4 186 62 2 177A 35k 2 200 50 3 192 32 a 2124 42 203 29 21 217J 3D| 4 214 26} 3 222 37 24j 31 231 33 5^ 230 23 4 236 29A Q 236A 21A 4 243 27 6 240 20 5 247^ 21-^ 7 245 171 51 253 23 S 2.56 16 6 264 22 Of the Parallel Motion in a Steam-Engine. When the power from the piston is communicated by means of a beam or lever moving upon an axis, the parallel motion becomes a very important portion of the machine ; for then it forms the link of connection, and by its properties renders the action of alternate circular motion, and reciprocating vertical motion, mutually agreeable, thereby properly insuring to the piston rod a truly direct line to that of the cylinder; but to effect this, the greatest degree of exactitude of the various parts is required, otherwise extra friction is created, and the effective powe* of the engine proportionately dimin- ished. PARALLEL MOTIONS. 145 Table by which to determine the various Distances of tht Movable Points in a Parallel Motion. 15 j 2 1 4| 10 = 6J 4 is; iP o 53 4 6 1 4 11> -Zi 4 8g 3 71 2 9 2 1 1 U 3 10 3 2 3| 1 9.1 1 41 1 3 33 3 1 . 4 1 4| j 81 4 11 3 3 2 6j 2 Oi o 5 4 4 4 3 6 3 2| 2 3 1 9 1 4| i 0'; 9g 4 6| 3 9 3 0^ 2 6 2 1 7 1 3 ll.i 5 4 4 3 9 1 5l 91 6 0^ 5 63 4 3 3 6| 2 11J 2 53 ??! 6 3 5 35 4 6 3 9| Q Ol 1 If 2 25 1 10 J__6_ 5 6| 4 9 * si 2 10 7 2 5| 2 04 5 9. 5 4 3 3 8 3 1 2 8 2 3 1 10 li 6 0^ 5 3 4 6 3 11 3 3| 2 10J 6 34 5 6 4 94 4 2 3 3 2 7g 6 61 5 9 5 Oi 4 5 3 10| 3 4 2 10$ 2 6 6 8) 6 5 2\ 4 7| 4 1 3 6^ 3 1 5*1 140 LOGARITHMS. LOGARITHMS. LOGARITHMS literally signify ratios of numbers ; hence Logarithmic Tables may be various, but those ir. com- mon use for the facilitating 1 of arithmetical operations generally are of the following corresponding progres- sions, viz. : Arithmetical, 0, 1, 2, 3, &c., or series oflogaritmns. Geometrical, 1, 10, 100, 1000, &c., or ratio of numbers. And thus it may be perceived, that if the log. of JO be J, the log. of any number less than 10 must consist wholly of decimals, because increasing by a decimal ratio. Again; if the log. of 100 be 2, the log. of any intermediate number between 10 and 100 must be 1. with so many decimals annexed ; and in like manner, the log. of any intermediate number between 100 and 1000, must be 2, with decimals annexed proportionally, as before. APPLICATION AND UTILITY OF COMMON LOGA- RITHMIC TABLES. The whole numbers of the series of logarithms, aa I, 2, 3, &c., are called the indices, or characteristics of the logarithm, and which must be added to the logarithm obtained by the Table, in proportion to the number of figures contained in the given sum. Thus, suppose the logarithm be reqaired for a sum of only two figures, the index is 1 ; if of three figures, the index is 2; and if of four figures, the index is 3, &c. ; being always a number less by unity than the number of figures the given sum contains. LOGARITHMS. 14? Ex. The index of 8 is 0, because it is less than 10 The index of 80 is 1, because it is less than 100. The index of 800 is 2, because it is less than 1000. The index of 8000 is 3, because it is less than 10,000, &c. The index of a decimal is always the number which denotes the significant figure from the decimal point, and is marked with the sign, thus, , to distinguish it a whole number. Ex. The index of -32549 is 1, because the first sig- nificant figure is the first decimal. The index of -032549 is 2, because the first signi- ficant figure is the second decimal. The index of -0032549 is 3, because the first sig- nificant figure is the third decimal, &c., of any other sum. If the given sum for which the logarithm is required contains or consists of both integers and decimals, the index is determined by the integer part, without having any regard to the other. 1. To Jind the logarithm of any whole number under 100. Look for the number under N in the first page of any Logarithmic Table ; then immediately on the right of it is the logarithm required, with ts proper index. Thus the log. of 64 is 1-806180, and the log. of 72 is 1-857332. 2. To Jind the logarithm of any number between 100 and 1000, or any sum not exceeding 4 figures. Find the first three figures in the left-hand column of the page under N, in which the number is situated, and the fourth figure, at the top or bottom of the page ; then the logarithm directly under the fourth figure, and in a line with the three figures in the column on the 1 3ft, with its proper index, is the logarithm re- 1 48 LOGARITHMS. quired. Thus, the log. of 450 is 2-653213- and the log of 7464 is 3-872972. Or, the log. of 378-5 is 2-57806$ and that of -7854 is 1-895091. 3. To find ibt number indicated by a given logarithm Look for the decimal part of the given logarithm in the different columns, and if it cannot be found exactly, take the next less. Then under N in the left-hand column, and in a line with the logarithm found, are three figures of the number required, and on the top of the column in which the found logarithm stands is one figure more; place the decimal point as indicated by the logarithmic index, which determines the sum, prop- erly valued, as required. If the logarithm cannot be found exactly ir. the Tables, subtract from it the next less that can be found, and divide the remainder by the tabular difference ; the quotient will be the rest of the figures of the given number, which, being annexed to the tabular number already found, is the proper number required. Ex. Required the number answering to ihe loga- rithm 3-233568. Given logarithm . . . . = 3-233568 Next leas is the log. of 1712 = 3-233604 Remainder 64 Tab. n;r 553 an d = -25 253 Hence the number required =1712-25. For practical purposes in mechanics, logarithms are seldom resorted to, unless for the raising of the powers of numbers or extraction of their roots. These opera- tions, when tables are at hand, they very nmch facili- tate ; involution, or the raising of powers, being per- formed simply by multiplication, and evolution, or the extraction of roots, by division, as in simple arithmetic. LOGARITHMS. 149 Ex. 1. Required the square or second power of 25791. Log. of 25-791 = 1-411468 Multiplied by 2 the power required. Logarithm 2 822936 indicated number or square re- quired = 665-115. Ex.2. What is the cube of 30-7146? Logarithm = 1-487345 Multiplied by 3 the power required. Logarithm 4-462035 indicated number or cube required = 28975-7. Ex. 3. Required the square root of 365. 2-56^293 Log. = = l-28?14b indicated number or root = 19-105. 2 Ex. 4. Find the cube root of 12345. 4-091491 Log. = = 1-363830 indi-?atwi number or root 150 LOGAK1THMS. Table of Logarithms Jrorn 1 to 100. N. Log. N. Log. N. Log. N. Log. 1 0-000000 26 1-414973 51 1-707570 re 1-880814 2 0-301030 27 1-431364 52 1-716003 ",7 1-886491 3 0-477121 28 1-447158 53 1-724276 73 1-892095 4 0-602060 29 1-462398 54 1-732394 79 1-897627 5 0-698970 30 1-477121 55 1-740363 80 1-903090 6 0-778151 31 1 491362 56 1-748188 81 1-908485 7 0-845098 32 1-505150 57 1-755875 82 1-913814 8 0-903090 33 1-518514 58 1 763428 83 1-919078 9 0-954243 34 1-531479 59 1-770852 84 1-924279 10 1-000000 35 1-544068 60 1-778151 85 1-929419 11 1-041393 36 1-556303 61 1-785330 86 1-934498 12 1-079181 37 1-568202 62 1-792392 87 1-939519 13 1-113943 38 1-579784 63 1-799341 88 1-944483 14 1-146128 39 1-591065 64 1-806180 89 1-949390 15 1-176091 40 1-602060 65 1-812913 90 1-954243 16 1-204120 41 1-612784 66 1-819544 91 1-959041 17 1-230449 42 1-623249 67 1-826075 92 1-963788 18 1 255273 43 1-633468 68 1-832509 93 1-968483 19 1-278754 44 1-643453 69 1-838849 94 1-973128 20 1-301030 45 1-653213 70 1-845098 95 1-977724 21 1-322219 46 1-662758 71 1-851258 96 1-982271 22 1-342423 47 1-672098 72 l-&>7332 97 1-986772 23 1-361728 48 1-681241 73 1-863323 98 1-991226 24 1-380211 49 1-693196 74 1-869232 99 1-995635 25 1-397940 50 1-698970 75 1-875061 100 2-000000 Note. The best Tables of Logarithms are those by Taylor, Gardiner, Hutton, Babbage, and Gail let. The smaller work* are those by Lalande, Hassler, Renaud, Christison, and Wai lace, and those published in the " Library of Useful Kuowiecge. WATER IN PIPES. TABLE -WATER IN PIPES. This table shows the quantity and weight of water contained in one fathom of length of pipes of different bores from 1 inch to 12 inches in diameter, advancing by half inch. The weight of a cubic foot of water ia taken at 1000 ounces avoirdupois, and the imperial gallon at 10 Ibs. Diameter in inches. Quantity in cubic inches. Quantity in imperial gallons. Weight in Ibs avoirdupois. i 14-14 0-051 0-51 1 56-55 0-205 2-05 J 12723 0-460 4-60 2 226-19 0-818 8-18 ft 35343 1-278 12-78 3 508-94 1 841 1841 34 692-72 2-506 25-06 4 904-78 3272 32-72 4 1145-11 4-142 41-42 5 1413-72 5-113 51-13 5* 1710-60 6-187 61-87 6 2035-75 7-363 73-63 6 2389-18 8-641 86-41 7 2770-88 10-022 100-22 *J 3180-86 11-505 115-05 8 3619-11 13-090 130-90 8| 4085-64 14-777 14777 9 4580-44 16-567 16567 * 5103-52 18-459 184-59 10 5654-87 20-453 204-53 10 6234 49 22-550 225-50 11 6842-39 24748 247-48 ii| 7478-56 27-049 270-49 12 8143-01 29-452 294-52 152 CHANGES IN THE STRUCTURE OF IRON. CHANGES INDUCED IN THE STRUCTURE OP IRON SUBSEQUENT TO MANUFACTURE. The important purposes to which iron is applied have a.ways rendered it a subject of peculiar interest ; and at no period has its importance been so general and extensive as at the present time, when its application is almost daily extending, and there is scarcely any thing connected with the arts to .which, either directly or indirectly, it does not in some degree contribute. My object is to point out some peculiarities in the habitudes . of iron, which appear to have almost wholly escaped the attention of scientific men, and which, although in some degree known to practical mechanics, have been generally considered by them as isolated facts, and not regarded as the results of a general law. The circum- stances, however, well deserv^,the attention of scientific men, on account of the very important consequences to which they lead. The two great distinctions, which exist in malleable wrought iron, are known by the names of red-short and cold-short qualities. The former of these comprises the tough, fibrous iron, which generally possesses con- siderable strength when cold ; the latter shows a bright, crystallized fracture, and is very brittle when cold, but works ductile while hot These distinctions are per- fectly well known to all those who are conversant with the qualities of iron ; but it is not generally known that there are several ways by which the tough, red-short iron becomes rapidly converted into the crystallized; and that, by this change, its strength is diminished to a very great extent. The importance which attaches to this subject will not be denied. The principal causes which produce this change are percussion, heat, and magnetism ; and it is doubtful whether either of these means will produce this effect; and there appear strong reasons for supposing that, generally, they are all in CHANGES IN THE STRUCTURE OF IRON 153 some degree concerned in the production of the ob- served results. The most common exemplification or* the effect of heat, in crystallizing fibrous iron, is by breaking a wrouo-ht-iron furnace-bar ; which, whatever quality it was of in the first instance, will, in a short time, invariably be converted into crystallized iron; and, by heating, and rapidly cooling by quenching with water a few times, any piece of wrought iron, the same effect may be far more speedily produced. In these cases, we have at least two of the above causes in operation heat and magnetism. In every instance of heating iron to a very high temperature, it under- goes a change in its electric or magnetic condition; for, at very high temperatures, iron entirely loses its magnetic powers, which return, as it gradually cools to a lower temperature. In the case of quenching the heated iron with water, we have a still more decisive assistance from the electric and magnetic forces ; for Sir Humphrey Davy long since pointed out, that all cases of vaporization produced negative electricity in the bodies in contact with the vapor ; a fact which has lately excited a good deal of attention, in conse- .quence of the discovery of large quantities of negative electricity in effluent steam. These results, however, are practically of but little consequence ; but the effects of percussion are at once various, extensive, and ot high importance. We shall trace these effects under several different circumstances. In the manufacture of some descriptions of ham- mered iron, the bar is first rolled into shape, and then one-half the length of the bar is heated in a furnace, and immediately taken to the tilt-hammer and ham- mered ; and the other end of the bar is then heated and hammered in the same manner. In order to avoid tiny unevenness in the bar, or any difference in its color where the two distinct operations have terminated, the workman frequently gives the bar a few blows with the hammer on that part which he first operated upon. That part of the bar has, however, by this time, 154 CHANGES IN THE STRUCTURE OF IRON. become comparatively cold; and, if this cooling 1 pro- cess has proceeded too far when it receives this addi- tional hammering 1 , that part of the bar immediately becomes crystallized, and so extremely brittle that it will break to pieces by merely throwing it on the ground, though all the rest of the bar will exhibit the best and toughest quality imaginable. This change, therefore, has been produced by percussion as the primary agent. We here see the effects of percussion in a very instructive form. And it must be observed, that it is not the excess of hammering which produces the effect, but the absence of a sufficient degree of heat at the time the hammering takes place ; and the evil may probably be all produced by five or six blows of the hammer, if the bar happens to be of a small size. In this case, we witness the combined effects of percussion, heat, and magnetism. When the bar is hammered at the proper temperature, no such crystal- lization takes place, because the bar is insensible to magnetism ; but, as soon as the bar becomes of that lower degree of temperature at which it can be affected by magnetism, the effect of the blows it receives is tc produce magnetic induction ; and that magnetic in- duction, and consequent polarity of its particles, when assisted by further vibrations from additional percussion, produces a crystallized texture. For it is perfectly well known that, in soft iron, magnetism can be almost instantaneously produced by percussion ; and it is probable that, the higher the temperature of the bar at the time it receives the magnetism, the more likely will it be to allow of that rearrangement of its mole- cules vvhich would constitute the crystallization of the iron. It is not difficult to produce the same effects by repeated blows from a hand-hammer on small bars of iron; but it appears to depend upon something peculiai in the blow, which, to produce the effect, must occasion B. complete vibration among the particles in the neigh borhood of the part which is struck. And it is re niarkable that the effects of the biows, in all cases, CHANGES IN THE STRUCTURE OF IRON 155 ueem to be confined within certain limited distances of the spot which receives the strokes. Dr. Wollaston first pointed out that the forms in which native iron is disposed to break, are tl.ose of the regular octahedron and tetrahedron, or rhomboid, consisting of these forms combined. The tough and fibrous character of wrought iron is entirely produced by art ; and we see, in these changes that have been described, an effort at returning to the natural and primal form; the crystalline structure, in fact, being the natural state of a large number of metals ; and Sir Humphrey Davy has shown, that all those which are fusible by ordinary means assume the form of regular crystals by slow cooling. The general con- clusion, to which these remarks lead us, appears to leave no doubt that there is a constant tendency in wrought iron, under certain circumstances, to return to the crystallized state ; but that this crystallization is not necessarily dependent upon time for its develop- ment, but is determined solely by other circumstances, of which the principal is, undoubtedly, vibration. Heat, within certain limits, though greatly assisting the rapidity of the change, is certainly not essential to it ; but magnetism, induced either by percussion or other- wise, is an essential accompaniment of the phenomena attending the change. 14 156 STRENGTH OF JOURNALS OF SHAFTS. STRENGTH *)F JOURNALS OF SHAFTS. Mr. Buchanan's rule is The cube root of the vveignt in cwts. is nearly equal to the diameter of the journal; it being prudent to make the journal a little more than less, and to make a due allowance for wear- ing. JEx. What is the diameter of a journal of a water- wheel shaft, 13 feet long, the weight of the wheel being 15 tons ? By Mr. B.'s rule, V 15 X 20 = 6-7, or 7 inches diameter. By Mr. Tredgold's rule, 3360 Weight in the middle. X 13 = 873 3 A/873 = 9A inches 500 diameter. Weight equally distributed, 33600 X 13 = 436800 = 7-65 inches. 10 To resist Torsion or Twisting. It is obvious that the strength of revolving shafts* are directly as the cubes of their diameters and revqlu- tions; and inversely, as the resistance they have to overcome. Mr. Robertson Buchanan, in his essay on the Strength of Shafts, gives the following data, deduced from several experiments, viz.: That the fly-wheel shaft of a 50- horse-power engine, at 50 revolutions per minute, re- quires to be 7 inches diameter ; and therefore, the cube of this diameter, which is 421 -875, seives as a multi- * Shafts, here, are understood as the journals of shafts, the bodies of shafts being generally made square. STRENGTH OF JOURNALS OF SHAFTS. 157 plier to all other shafts in the same proportion ; and, taking this as a standard, he gives the following multi- pliers, viz. : For the shaft of a steam-engine, water-wheel, or any shaft connected with a first power, 400 For shafts in inside of mills, to drive smaller machinery, or connected with the shafts above, 200 For the small shafts of a mill or machinery, 100 From the foregoing, the following rule is derived, viz. : The number of horses' power a shaft is equal to, is directly as the cube of the diameter and number of revolutions ; and inversely, as the above multipliers. Ex. 1. When the fly-wheel shaft of a 45-horse-power steam-engine makes 90 revolutions per minute, what is the diameter of the journal ? 4.5 v 400 Q A = 200 3V200 = 5 T 8 o- inches diameter. 90 Ex. 2. The velocity of a shaft is 80 revolutions per minute, and its diameter is 3 inches ; what is its power ? 33x80 = 5-4 horses 7 power. 400 Ex. 3. What will be the diameter of the shaft in the first example, when used as a shaft of the second multi- plier ? * 5-8 3^45 x 200 . 6 . = 4-64, or = 4^77 inches diameter 1-25 90 The following is a table of the diameters of shafts, oeing the first movers, or having 400 for their multi- pliers. * The diameters of the second movers will be found by dividing tht nunbers in the Table by 1-25, and the diameters of the third movers, >y dividing the numbers by 1-56. 158 DIAMETERS OF THE II T Revolutions. 10 15 20 25 30 | 35 40 45 50 55 Inches Diameter. 5.5 4-8 4-5 4- 37 3-H 35 3-3 32' 3-1 5 6 5-9 6-3 5-1 5-5 4-7 5- 44 41 3-9 37 36 35 3-3 3-6 46 44 41 4- 38 3-7 7 6-6 5-8 5-2 5-5 4-9 46 44 4-2 4- 3-9 37 8- 9 10, 12 6!) 6- 6-3 51 4-8 46 4-4 45 42 41 4- 41 42 4-6 47 5- 72 5-7 5-9 63 5-5 56 5- 4-8 4-4 46 42 7-4 7-9 6-6 6-9 52 4-9 47 44 5-8 6-2 5-6 5-4 5-2 5- 4-8 5- 14 16 8-3 72 67 5-9 5-6 5-4 5-2 8-7 76 71 66 61 5-8 56 5-4 5-2 18 20 25 9- 93 10- 7-9 75 7-7 7- 66 62 5-8 5-6 5-4 52 54 8-1 8-5 72 6-8 64 5-9 57 56 8- 7-4 71 6-8 6-3 6- 5-9 56 30 10-7 9-3 8-4 8-9 7-9 74 71 74 6-9 67 65 63 65 67 68 73 35 40 114 117 12- 12-6 9-8 10-5 10-6 8-4 7-9 71 6-9 72 66 9-3 9-7 10- 8-8 8-3 7-8 7-4 6-9 45 50 92 8-7 8-1 7-6 7-4 7- 11- 9-3 9- 8-5 8- 7-8 7-4 55 60 13-4 11-4 10-4 9-8 9-1 8-8 8-4 8- 7-5 7-4 7-6 136 12- 10-8 10- 9-3 9- 8-6 8-2 7-7 JOURNALS OF FIRST MOVERS. 159 I 1 ' T 5 Revo utions. - 60 65 70 75 80 85 | 90 | 95 100 1C5 Inches Diameter. 3- 2-9 2-9 2-8 2-7 27 26 2-6 26 2-5 33 32 3-1 3- 3- 29 2-9 2-8 2-8 2-7 6 7 8 35 35 3-4 33 32 32 3- 3- 2-9 2-9 36 3-9 36 35 34 34 33 35 3-3 3-4 32 3-1 3-1 3-8 3-7 3-6 3-5 3-4 33 32 9 10 12 4- 3-8 3-7 37 3-6 3-6 3-5 3-5 3-4 3-3 41 44 4- 3-9 3-8 3-7 3-7 36 3-6 35 34 43 42 41 4 42 3-9 3-8 3-8 3-7 3-6 14 16 18 20 25 30 45 4.4 44 46 4-3 41 4- 4- 3-9 3-8 4-8 5- 52 5-5 47 45 44 4-4 4-5 43 44 42 4-1 4- 4-9 48 4-7 46 4-3 4-2 4-2 51 5- 4-8 4-6 46 4-5 4-5 44 4-4 46 54 53 5-2 5-1 4-9 4-8 4-7 4-6 5-9 63 5-8 61 5-7 56 5-5 5-3 5-2 5-4 5-7 51 5- 4-9 35 5-9 5-7 5-6 5-9 55 5-8 6- 5-3 5-2 5-2 40 15 6-6 6-7 6-4 6-2 6-4 6- 5-6 56 5-5 6-5 69 6-2 61 5-9 5-8 5-7 56 5-8 50 7-2 6-8 66 6-5 6-4 6-2 6- 5-9 55 60 7-3 7-2 7- 6-7 66 65 6-3 62 6-1 6-4 6- ~ei 7-4, 7-3 72 6-9 6-8 6-8 67 66 14* 10 J STRENGTH OF WHEELS. It is ?i well known fact, that a cast iron rod will BUS- tain more torsional pressure than a malleable iron rod of the same dimensions ; that is, a malleable iron rod will be twisted by a less weight than what is required to wrench a cast iron rod of the same dimensions. When the strength of malleable is less than that of cast iron to resist torsion, it is stronger than cast iron to resist lateral pressure, and that is in proportion as 9 is to 14. From the foregoing, it is easy for the millwright to make his shafts of the iron best suited to overcome the resistance to which they will be subject, and the pro- portion of the diameters of their journals, according to the iron of which they are made. Ex. What will be the diameter of a malleable iron journal to sustain an equal weight with a cast iron jour- nal of 7 inches diameter. 73=343. A* 14 : $13 : : 9 :220 j now 3 V 220 5 = 6-04 inches diameter. STRENGTH OF WHEELS. The arms of wheels are as levers fixed at one end, and loaded at the other; and, consequently, the greatest strain is upon the end of the arm next the axle. For that reason, all arms of wheels should be strongest at that part, and tapering toward the rim. The rule for the breadtb and thickness of arms, ac- cording to their length and number in the wheel, is as follows : Multiply the power or weight acting at the end of the arm by the cube of its Jength ; the product of which, divided by !2(j56 times the number of arms mul- tiplied by the deflection, will give the breadth, and cube of the depth. Ex. Suppose the force acting at the circumference of a spur-wheel to be 1600 Ibs., the radius of wheel 6 STRENGTH OF WHEELS. 161 feet, and number of arms 8, and let the deflection not exceed T \yth of an inch. X GS = 1G3 = breadth and cube of the deptli 2656 X 8 x 1 Let the breadth be 2-5 inches ; therefore, = 65-2 j 2-5 which is equal to the cube of the depth. Now the cube root of 65-2 is nearly 4-03 inches : this, conse- quently, is the depth or dimension of each arm in tho direction of the force. Note. __ When the depth at the rim is intended to be hall that of the axes, use 1640 as a divisor instead of 2656. The teeth are as beams, or cantilevers, fixed at one end and loaded at the other. The rule applying directly to them where the length of the beam is the length of the teeth, and the depth the thickness of the teeth. For the better explanation of the rule, the following example is given. Ex. The greatest power acting at the pitch line ot the wheel is 6000 Ibs., and the thickness of the teeth 1 inch, the length of the teeth being 0-25 feet; it is required to determine the breadth of the teeth. 6000X0*5^ 1500 = ^ . ncheg> the breadth required< 212 X 1-52 477 In order that the teeth may be capable of offering a sufficient resistance after being worn by friction, the breadth thus found should be doubled ; therefore, ir the above example, the breadth should be 64, or say 6 inches. The following data are gleaned from experiments, which are, therefore, valuable, and of much use to the practical mechanic. Rule. _ Multiply the breadth of the teeth by the square of the thickness, and divide the product by the length ; the quotient will be the proportional strength in horses' power, with a velocity of 2-27 feet per second. STRENGTH OF WHEELS. Ex. What is the power of a wheel, the teeth of which are 6 inches broad, J -5 inch thick, and 1-8 inch long, and revolving at the velocity of 3 feet per second 5 'b 2 x 6 13'5 = = 7-5, strength at 2-27 feet per second ; then 1-8 1-8 7*5 X 3 2-27 : 7-5 : : 3 = = 991 horses' power. 2'27 Hide. The pitch is found by multiplying the thick- ness by 2*1, and the length is found by multiplying the thickness by 1-2. Ex. The thickness being 2 inches, what is the pitch 4nd length ? 2x 2-1=4-2, pitch. 2x 1-2 = 2-4, length Note. The breadth of the teeth, as commonly executed by the best mechanics, seems to be from about twice to thrice the pitch. .2 e . o . ff| ^5-^- |X ga ^ m tn oj gjg JS *"" 35 _ 0) OJ^ CL n S C j ^3 CL 0- = a^i Si O -So 5-f? .:% a . OJ O " <8 1 .s.S g.s e.S l|l w CO an |i B h M 3 o ^ S cs O *j ffi ca o ffi ca 4-2 2- 8- 2-40 13-33 17-61 35-23 3-99 1-9 7-6 2-28 13-03 15-90 31-80 378 1-8 7-2 2-J6 10-80 14-27 28-54 3-57 1-7 6-8 2-04 9-63 12-72 25-54 3-36 1-6 6-4 1-92 8-53 11-27 22-54 3-15 1-5 6- 1-80 7-50 9-91 19-82 2-94 1-4 5-6 1-68 653 8-63 17-26 2-73 1-3 5-2 1-56 5-63 7-44 14-88 2-52 1-2 4-8 1-44 4-80 6-34 12-68 2-31 1-1 4-4 1-32 4-03 5-32 10-64 2-10 1- 4- 1-20 3-33 4-40 8-81 1-89 9 3-6 1-08 2-70 3-57 7-14 168 8 3-2 96 2-13 2-81 5-62 1-47 7 2-8 84 1-63 2-15 4-30 1-26 6 2-4 72 1-20 1-59 3-18 1-05 5 2- 60 83 1-10 2-20 CIRCUMFERENCES OF CIRCLES. 163 TABLES OF THE CIRCUMFERENCES OF CIRCLES, TO THE NEAREST FRACTION OF PRACTICAL MEASUREMENT, ALSO THE AREAS OF CIRCLES IN INCHES AND DECIMAL PARTS, LIKEWISE IN FEET AND DECIMAL PARTS, AS MAY BE REQUIRED. Rules that may render the following Talks more gen erally useful. 1. Any of the areas in inches multiplied by '04328, or the areas in feet multiplied by 0-232, the product is the number of imperial gallons at 1 foot in depth. 2. Any of the areas in feet multiplied by -03704, the product equal the number of cubic yards at 1 foot in depth. 3. The area of a circle in inches multiplied by the length or thickness in inches, and by -263, the product equal the weight in Ibs. of cast iron. oe. _ The French cubic metre, or unit of solid measure, equal 35-31716 English cubic feet. Also the litre, or unit for measures of capacity, equal 61-028 English cubic inches, or about -463 of an imperial gallon, lOl CIRCUMFERENCES AND 1 Dia. in inch. Circuin. in iiidi. Area in q. inch. -icieof Dia. in inch. Cir. in ft. in. Area in q. inch. Ar.in sq. ft. TV 196 0030 0554 3m. 9| 7-068 2| i 392 0122 1107 3J 9| 7-669 2| T5 589 0276 1661 3^ 10^ 8-295 2 & 785 0490 2115 3^ 10| 8-946 3 in. A 981 0767 2669 3d 11 9-621 3& 1 1-178 1104 3223 3| Hi 10-320 H T 7 ? 1-374 1503 3771 31 ill 11044 3| 1-570 1963 4331 3^ 12^ 11-793 3y 7 B & * 1-767 1-963 2485 3068 4995 5438 4 in. o^ 12-566 13-364 14-186 0879 0935 0993 TF 2-159 3712 6093 4| ]| 15-033 1052 2-356 441? 66-46 $ 2| 15-904 16-800 1113 1176 TF 2-552 5185 7200 4| 2 17-720 1240 2-748 6013 7754 4 ^ 3 i 18-665 1306 i 2-945 6903 8308 5 in. 3 I 19635 1374 20-629 1444 lin. 34 7854 7 4 4 21-647 1515 *^8 53 4? 22-690 1588 H 34 9940 B & 32" 3 5! 23-758 1663 U 3& 1-227 1 in. ^i 5| 24-850 1739 C feo HN 4 4 1-484 1-767 A iA af 6 6| 25-967 27-108 1817 1897 6m. 65 28-274 1979 It 5J 2-074 irV 7| 29-464 2062 If 5 2-405 i 9 64 7| 30-679 2147 1| 2-761 Hi 6 i 8 31-919 33-183 2234 2322 2 in 6J 3-141 11 G l 83 34-471 35-784 2412 2504 2J 61 3-546 ii fi i 9 4 37-122 2598 2 7 3-976 2 in. 7 in. 10 38-484 2(593 ! 2f 7f 4-430 2J 74 7} 10| 39-871 41-282 2791 2889 2 7| 4-908 2y 3 ^ 7f ll| 42-718 2990 81 gi 5-412 2-A 71 Hi 44-178 3092 21 8| 5-939 2fV ll 2 Of 45-663 47-173 3196 3299 2& 9 6-491 2y 9 F 7| 2 Of 48-707 3409 AREAS OF CIRCLES. 165 Dia. in Cir. in Area in Area in! Dia. in Cir. in Area in Area in inch. ft. in. sq. inch. ,q. ft. inch. ft. in. sq. inch. sq. ft. Sin. 2 H 50-265 3518 13m. 3 4| 132-732 9291 8$ 2 1A 51-848 3629 134 3 54 135-297 9470 ft 2 \l 53-456 3741 3 58 137-886 9642 8j 2 24 55-088 3856 131 3 6 140-500 9835 & 2 2g 56-745 3972 13A 3 6 143-139 1-0019 8! 2 3 58-426 4089 131 3 6| 145-802 1-0206 8 ; 2 3 60-132 4209 13| 3 71 148-489 1-0294 8 i 2 3 61-862 4330 13* 3 7A 151-201 1-0584 9 in. 2 44 63-617 4453 14 in. 3 11 153-938 1-0775 9^ 2 4f 65-396 4577 14| 3 8f 156-699 1-0968 94 2 5 67-200 4704 144 3 8f 159-485 1193 9$ 2 5| 69-029 4832 14| 3 9 1 162-295 1360 4 2 5| 70-882 4961 14 A 3 9j| 165-130 1569 9l 2 64 72-759 5093 14* 3 9? 167-989 1749 9| 2 6f 74-662 5226 14$ 3 10J 170-873 1961 9| 2 7 76-588 5361 14J 3 103 173-782 2164 10 in. 2 7| 78-540 5497 15 in. 3 11 176-715 2370 10 2 7l 80-515 5636 15 3 ll| 179-672 2577 10^ 2 8| 82-516 5776 15^ 3 111 182-654 2735 id 2 8^ 84-540 5917 158 4 Oj 185-661 2996 10* 2 8^ 86-590 6061 15A 4 Of 188-692 3208 lOJ 2 9f 88-664 6206 15| 4 1 191-748 3422 10* 2 9| 90-762 6353 1,53 4 1 194-828 3637 wl 2 1Q I 92-855 6499 1/>| 4 if 197-933 3855 11 in. 2 10A 95-033 6652 16 in. 4 24 201-062 4074 Mi 2 10J 97-205 6804 16 4 2| 204-216 4295 n 2 114 99-402 6958 164 4 3 207-394 4517 ill 2 ll| 101-623 7143 161 4 3 210-597 1-4741 nj 3 Of 103-869 7270 164 4 3| 213-825 1-4967 n 3 OA 106-139 7429 1GJ 4 44 217-077 1-5195 n 3 01 108-434 7590 16| 4 4g 220-353 1-64-24 *i ' 3 ij 110-753 7752 16| 4 5 223-654 1-5655 12 in. 3 1| 113-097 7916 17 in. 4 5 226-980 1-5888 I 6 ' A 3 2 115-466 8082 17 4 53 230-330 1-6123 124 3 2 117-859 8250 174 4 6| 233-705 1-6359 12$ 3 2| 120-276 8419 171 4 6^ 237-104 1-6597 12A 3 34 122-718 8590 17 i 240-528 1-6836 12| 3 3| 125-185 8762 17| 4 7| 243-977 1-7078 12* 3 4 127-676 8937 17| 4 7| 247-450 1-7321 12| 3 4j| 130-192 9113 2f 4 8| 250-947 1-7566 166 CIRCUMFERENCES AND Dia. in inch. Cir. in ft. in. Area in sq. inch. Area in sq. ft. Dia. in inch. Cir. in ft. in. Area in sq. inch. Area in sq. ft. 18 4 8 254-469 1-7812 23 6 OJ 415-476 2-8903 18| 4 8f 258-Olfi 1-8061 23 6 0| 420-004 2-9100 18.4 4 94 261-587 1-8311 23^ 6 1 424-557 2-9518 181 4 9| 265-182 1 -8562 23| 6 1| 429-135 2 9937 UU 4 10| 268-803 1-8816 23A 6 1| 433-737 3-0129 181 4 10A 272-447 1-9071 23| 6 2j 438-363 3-0261 18| 4 10 276-117 1-9328 23| 6 2| 443-014 3-0722 18| 4 llj 279-811 1-9586 23$ 6 3 447-690 3-1081 19 4 11| 283-529 1-9847 2 6 3f 452-390 3^1418 ! 19ft 5 287-272 1-99-11 2 Oi 6 4} 461-864 3-2075 1 19* 5 OA 291-039 2-0371 2 OA 6 4g 471-436 3-2731 I 19f 5 Oi 294-831 2-0637 2 03 6 5i| 481-106 3-3410 | 19 5 14 298-648 2-0904 2 1 6 6j 490-875 3-4081 19 5 if 302-489 2-1172 2 1| 6 1\ 500-741 3-4775 1 19| 5 2 306-355 2-1443 2 l| 6 8^ 510-706 3-5468 iy| 5 2f 310-245 2-1716 2 if 6 8 520-769 3-6101 20 5 2g 314-160 2-1990 2 2 6 9| 530-930 3-6870 20 5 34 318099 2-2265 2 2^ 6 10| 541.-189 3-7583 204 5 3g 322i*53 2-2543 2 C 4 6 114 551-547 3-8302 20f 5 4 326-04 2-2822 2 2| 7 562-002 3-9042 2o| 5 4| 330-6 I 2-3103 2 3 1 Of 572-556 3-9761 20| 5 4| 334-101 2-3386 2 3^ 7 If 583-208 4-0500 20| 5 5f 338-163 2-3670 2 3A 7 2| 593-958 4-1241 2o| 5 5 342-250 2-3956 2 3^- 7 3 604-807 4-2000 21 5 5 346-361 2-4244 2 4 7 3? 615-753 4-2760 2U 5 6f 350-497 2-4533 2 44 7 41 626-798 4-3521 214 5 6f 351-G.V7 2-4824 2 4| 7 6A 637-941 4-4302 21| 5 7| 358-841 2-5117 2 4| 7 64 649-182 4-5083 21 5 7 I 363-051 2-5-112 2 5 7 7 660-521 4-5861 21f 5 7| 367-284 2-5708 2 54 7 7S 671-958 4-6665 21| 5 84 371-543 2-6007 2 5A 7 8f 683-494 4-7467 2l| 5 8| 375-826 2-6306 2 | 7 9j 695-128 4-8274 22 5 9 380-133 2-6608 2 6 7 10| 706-860 4-9081 224 5 9| 384-465 2-6691 2 64 7 11 718-690 4-9901 221 5 9^ 388-822 2-7016 '2 6A 7 111 730-618 5-0731 22f 5 104 393-203 2-7224 2 6| 8 0| 742-644 5 1573 22A 5 10| 397-608 2-7632 2 7 8 l| 754-769 5-2278 22f 5 11 402-038 2-7980 2 74 8 2j 766-992 '5-3264 2<2f 5 1U 406-493 2-8054 2 7A 8 2 ',79-313 5-4112 22| 5 11J 410-972 2-8658 2 7| 8 3| | ^1-732 5-4982 AREAS OF CIRCLES. 167 Dia. in ft. in. Cir. in ft. in. Area in sq. inch. Area in sq. ft. Dia. in ft. in. Cir. in ft. in. Area in sq. in. Area in sq. ft- 2 8 8 4 804-249 5-5850 3 6 10 m 1385-44 9-6212 2 84 8 5 816-8(55 5-6729 3 6^ 11 0| 1401-98 9-7364 2 8j 8 6J 829 '578 5-7601 3 6 11 i| 1418-62 9-8518 2 m 8 6< 842 o90 5-8491 3 6M 11 24 143536. 9-9671 2 9 8 7-| 855-300 5-9o!;cJ 3 7 U 3 145220 10-084 2 9| 8 8j 868-308 6-0:291 3 74 11 3g 1469-14 10-202 2 9A 8 94 881-415 6-1201 3 7* 11 4 1486-17 10-320 2 9| 8 10 894-619 6-2129 3 7f 11 5| 1503-30 10-439 2 10 8 1(J 907-922 6-3051 3 8 11 54 1520-53 10559 2 104 8 ll| 921 -3T3 6-3981 3 81 11 7 1537-86 10-679 2 1(2 9 if 934 822 6-4911 3 8 4-890 5 24 16 3j; 3043-47 21-135 4 4'| 13 8i 2164-75 13 OS-? 5 2A 16 4; 30(57-96 21-305 4 42 13 9f 2185-42 15176 5 2| 16 6J 3092-56 21-476 4 5 13 10 2206-18 o 3l\) 5 3 16 5| 3117-25 21-647 4 54 13 114 2227-05 15-165 5 34 16 64 314204 21-819 4 5j 14 o 2248-01 15-611 5 3A 16 7A 316692 21-992 4 5^ U f-jf 2269-06 15-757 5 3| 16 8| 3191-91 22-166 4 6 14 1 2290-22 15-90* 5 4 16 9 3216-99 22-333 4 64 14 2g 2311-48 16-051 5 4 16 9| 3242-17 22-515 4 6j 14 3i 2332-83 16-200 5 4j 16 I0 3267-46 22-621 4 64 14 4 2354-28 16-349 5 4J 16 111 3292-83 22-866 4 7 14 4| 2375-83 16-498 5 5 17 0| 3318-31 23-043 4 7| 14 5 2397-48 l/i-649 5 54 17 t)| 3343-88 23-221 4 g 14 6f 2419-22 16-800 5 5A 17 1| 3369-56 23-330 4 H 7i 2441-07 16-951 5 5| 17 2| 3395-33 23-578 4 8 14 7 24 ^3-01 f7-104 5 6 17 38 3421 -20 23-758 4 8j 14 8| 2485-05 17-257 5 64 17 4! 3447-16 23-938 4 8 14 9 A 2507-19 17-411 5 6| 17 42 3473-23 24-119 4 8| 14 10J 2529-42 17565 5 l| 17 5f 3199-39 24-301 4 9 14 11 2551-76 17-720 5 7 17 6A |352,3-66 24-483 4 94 14 llg 2574-19 17-876 5 74 17 74 3552-01 24-666 4 9 15 0{j 2596-72 18-033 5 7A 17 8 357847 24-U50 4 9$ 15 If 261935 18-139 5 7| 17 8| 3605-03 25-034 4 10 15 4 2642-08 18-3t7 5 8 17 9g 3631-68 25-220 4 10J 15 f 2664-91 18-506 5 84 17 108 9656-44 25-405 4 10J 15 8 2687-83 18-665 5 8j 17 11| 3685-29 25-692 4 10-f 15 4 2710-85 18-825 5 8| 17 11 3712-24 25-779 4 11 15 5^ 2733-97 18-985 5 9 18 0| 3739-28 25-964 4 114 15 6J 2757-19 19-147 5 94 18 1A 3766-43 26-155 4 111 15 62 2780-51 19-309 5 9l 18 24 3793-67 26-3-14 4 llf 15 7| 2803-92 19-471 JLJ! 18 3| 3821-02 26 534 5 ? 5 8} 2827-44 19-635 j 10 18 31 3848-46 26-725, 5 01 15 9} 2851-05 19-798 5 104 18 4 3875-99 26-916 5 15 10 2874-76 19-963 5 10| 18 5A 3903-63 27-108 5 Of 15 10| 2898-56 20-128 5 10| 18 64 3931-36 J27-301 5 1 15 111 2922-47 20-294 5 11 18 7 3959-20 27-494 5 1.4 16 2946-47 20-461 5 114 18 7| 3987-13 27-688 5 1A 16 ij 2970-57 20-629 5 111 18 8f 4015-16 27-883 5 If 16 l| 2994-77 20-797 5 11| 18 9| 4045-28 28-078 AREAS OF CIRCLES. 169 Dia. in Cir. in Area in Area in |Dia. in Cir. in Area in Area in ft. in. ft. in. sq. inch. sq. ft. ft. in. ft. in. sq. in. sq. ft. 6 18 104 4071-51 28-274 6 6 20 5 4778-37 33-183 6 0| 18 104 4099-83 28-471 1 6 64 20 53 4809-05 33396 c o| 18 111 4128-25 28-668 6 6] 20 6A 4839-83 33-619 6 0| 19 Oj 415677 28-866 6 6| 20 7| 4870-70 33-824 6 1 6 \i 6 U 19 ll 19 2| 19 24 4185-39 4214-11 4242-92 29-065 29-264 29-466 6 7 6 71 6 7A 20 8 20 8l 20 9} 4901-6834-039 4932-7534-255 4963-9234-471 6 if 19 3 4271-83 29-665 6 7| 20 10^ 4995-19 34-688 6 2 19 4 4300-85 29-867 6 8 20 114 5026-26 34-906 6 24 19 54, 4329-95 30-069 6 84 21 0|l5058-02|35 125 6 2j 19 6 4359-16 30-271 6 8| 21 02 5089-51: 135-344 6 2f 19 6| 438847 30-475 6 8| 21 l| 5121-2435-564 6 3 19 7c 4417-87 30-679 6 9 21 2|' 5 153-00 35-784 6 34. 19 8$ 4447-37 30-884 6 94 21 345184-8636-006 6 3 19 9i 4476-97 31-090 6 9j 21 4 5216-82;36-227 6 3| 19 9 4506-67 31-296 6 9| 21 4| 5248-87 36-450 6 4 19 10| 453647 31-503 6 10 21 5 5281-02 36-674 6 44 19 llj 4566-36 31-710 6 104 21 6| 5313-27 36-897 6 4j "20 04, 4596-35 31-919 6 10A 21 7| 5345-62 37-122 6 4| 20 \\ 4626-44 32-114 6 10| 21 7^ 5378-07 37-347 6 5 20 if 4656-63 32-337 6 11 21 815410-62 37-573 6 54 20 2f 4686-92 32-548 6 114 21 9j 5443-26 37-700 6 5| 20 & 4717-30 32-759 6 ll| 21 10J 5476-00 38-027 6 flj 20 4| 4747-79 32-970 6 11| 21 11 5508-8438-256 170 CIRCUMFERENCES AND Dianrr in ft. and in. ft. and in. Area in feet. Diam. in ft. and in. Circum. in ft. and in. Area in feet. 7 21 Hi 38-4846 10 31 5 78-5400 1 22 3 39-4060 1 31 8| 79-8540 2 22 6J 40-3388 2 31 Hi 81-1795 3 22 94 41-2825 3 32 2f 82-5160 4 23 Of 42-2367 4 32 5 83-8627 5 23 2 43-2022 5 32 8| 85-'.?t> 6 23 6| 44-1787 6 32 Hi 86v. ( 7 23 11 45-1656 7 33 2| 87-96J7 8 24 1J 46-1638 8 33 6k 89-3608 9 24 4 47-1730 9 33 9i 90-7627 10 24 7 48-1926 10 34 0| 92-1749 11 24 10| 49-2236 11 34 3 93-5986 8 25 1 50-2656 11 34 6| 95-0334 1 25 4f 51-3178 1 34 9| 964783 2 25 7i 52-3816 2 35 97-9347 3 25 11 53-4562 3 35 4i 99-4021 4 26 2fr 54-5412 4 35 74 100-8797 5 26 51 55-6377 5 35 10| 102-3689 6 26 8| 567451 6 36 li 103-8691 7 26 Hi 57-8628 7 36 4 105-3794 8 27 2| 58-9920 8 36 7| 106-9013 9 27 5| 60-1321 9 36 lOf 108-4342 10 27 9 61-2826 10 37 2| 109-9772 11 28 62-4445 11 37 5| 111-5319 9 28 3| 63-6174 12 37 8| 113-0976 1 28 6| 64-8006 1 37 1H 114-6732 2 28 94 65-9951 2 38 2| 116-2607 3 29 Oi 67-2007 3 38 5| 117-8590 4 29 31 684166 4 38 8| 119-4674 5 29 7 69-6440 5 39 121-0876 6 29 10* 70-8823 6 39 34 1227187 7 30 l^ 72-1309 7 39 6| 124-3598 8 30 4| 73-3910 8 39 9| 126-0127 9 30 7 74-6620 9 40 Of 127-6765 10 30 111 75-9433 10 40 31 129-a r >04 11 31 ll 772362 11 40 61 131 3360 AREAS Ol CIRCLES. 171 Di:im. in ft. and in. Circmn. in ft. and in. Area in feet. Diam. in ft. and in. Circum. in ft. and in. Area in feet 13 40 10 132-7326 16 50 3 201-0624 1 41 li 1344391 1 50 6^ 203-1615 2 41 4| 136-1574 2 50 9$ 205-2726 3 41 71 137-886? 3 51 207-3946 4 41 10| 139-6260 4 51 31 209-5264 5 42 1| 141-3771 5 51 64 211-6703 6 42 41 143-1391 6 51 10 213-8251 7 42 8 144-9111 7 52 U 215-9896 8 42 11J 146-6949 8 52 44 218-1662 9 43 24 148-4896 9 52 7| 220-3537 10 43 54 150-2943 10 52 10A 222-5510 11 43 8| 1521109 11 53 1| 224-7603 14 43 111 153-9384 17 53 41 226-9806 1 44 2& 155-7758 1 53 8 229-2105 2 44 6 157-6250 2 53 11J 231 -4625 3 44 9$ 159-4852 3 54 2i 233-7055 4 45 04 1613553 4 54 of 235-9682 5 45 3 163-2373 5 54 8 2382430 6 45 6| 1651303 6 54 11| 240-5287 7 45 91 167-0331 7 55 2$ 242-8241 8 46 0$ 168-9479 8 55 6 2451316 9 46 4 170-8735 9 55 9 247-4500 10 46 7J 172-8091 10 56 0| 249-7781 11 46 Hi 174-7565 11 56 3% 2521184 15 47 1^ 1767150 18 56 64 2544696 1 47 4| 1786832 1 56 91 2568303 2 47 71 180-6634 2 57 01 2592033 3 47 10^ 1826545 3 57 4 2615872 4 48 24 1846555 4 57 7\ 263-9807 5 48 5i 1866684 5 57 10.1 2663864 6 48 8i 1886023 6 58 1| 268-8031 7 48 11| 190-7260 7 58 44 271-2293 8 49 2 1927716 8 58 7j 273-6678 9 49 51 194-8282 9 58 10} 2761171 10 49 8| 1968946 10 59 2 278-5761 11 50 198-9730 11 59 5 281-0472 15* 172 SQUARE AND CUBE ROOTS OF NUMBERS. No. S. R. C. R. No. I S. R. C. R. No. S. R. l C. R. No. S. R. C. R. l 1-0000 1-0000 55 | 7-4 161 |3-8029 109 10-4403! -7768 163 12-7671 5-4625 2 1-4142 1-2599 56 7-4833 : 3-S'2JS 111) 10-4880 7914 164 12-8062 5-4737 3 7320 1-4422 57 7-5498 3-6485 HI 10-5356 8058 166 12-8452 5-4848 4 2-0000 1-5874 to 7-6157 3 bTV- 112 10-5830 820:2 i.6fl 12-8840 5-4958 5 2-2360 1-7099 59 7-6811 38929 118 10-6301 8345 !67 12-9228 5-5068 6 2-4494 1-8171 60 7 7459 3-9i48 114 10-6770 84b8 168 12-9614 5-5178 7 2-6457 1-9129 61 7-8102 3-9364 115 10-7238 8629 169 13-0000 5-5287 8 2 -8284 2-0000 62 7-8740 3-9578 116 10-7703 876y 170 13-0384 5-5396 9 30000 2-0800 u 7-9372 3-S7i,0 111 10-81S6 8909 171 13-0766 5-5404 10 3-16-22 2-1544 64 8-0000 4-0000 Us 10-86-27 9048 172 13-1148 5-5612 11 3-3166 2-2239 8-0622 4-0207 119 10-9087 918-3 173 13-1529 5-5720 13 3- 16n 2-2894 16 8-1-240 4-0412 126 10-9514 93v } 4 174 13-1909 5-53-27 13 J-6055 2-3513 67 8-1853 4-0515 121 11-0000 9460 178 13-2287 5-5934 14 3-7413 2-4101 K 8-2462 4-0316 122 11-0453 9596 i:.i 13-2664 5-50-10 15 3-87^9 2-4562 99 8-3066 4-1015 1-3 11-0905 9731 177 13-3041 5-6416 16 0000 2-5198 70 83666 4-1212 124 1 -1355 9866 178 13-3416 5-6-252 17 1231 2-5712 71 8-4261 4-1408 125 1 -1803 0000 171 13-3790 5-6357 18 "2426 2-6207 72 84852 4-1601 126 1 -2249 5-0132 (80 13-4164 5-6462 19 3588 2-6684 73 8-5440 4-1793 127 1 -2694 5-0265 181 13-4536 5-6566 20 4721 2-7144 7-1 8-6023 4-19a3 1-2- 1 -3137 5-03S6 183 13-4907 5-8670 21 5825 2*7589 78 8-6602 4-2171 129 1 -3578 5-0527 183 13-5-277 5-6774 22 6904 2-8020 7b 8-7177 4-2358 130 11-4017 5-0657 184 13-5646 5-6877 23 7958 2-8438 77 87749 4-2543 131 1-4455 5-0787 186 13-6014 5-6980 24 8939 2-8844 78 8-8317 4-2726 132 11-4891 5-0916 186 13-6331 5-7082 25 0000 2-9240 79 8-8881 4-2908 133 1-5325 5-1044 181 13-6747 5-7184 26 5-0990 2-9624 w 8-9442 4-3088 13! 11-5758 5-1172 188 13-7113 5-7286 27 5-1961 3-0000 bi 9-0000 4-3267 I3S 1-6189 5-1299 ! 8 13-7477 5-7387 28 5-2915 3-0365 b2 9-0553 4-3444 !:;> 11-6619 5-1425 190 13-7840 5-74S8 29 53851 3-0723 S3 9-1104 4-3620 137 11-7046 5-1551 194 13-8202 5-7589 30 5-4772 3-1072 8! 9-1651 4-3795 138 11-7473 5-1676 192 13-8564 5-7689 31 55S77 3-1413 BS 9-2195 4-3968 139 11-7898 5-1801 193 13-8924 5-7789 3-2 565S3 3-1748 ^ 9-2736 4-4UO 140 11-8321 5-1924 194 13-9283 5-7889 33 5-7445 3-2075 87 9-3273 4-4310 I-il 11-8743 5-2048 199 13-9642 5-7988 34 5-8309 3-2396 S3 9-3808 4-4479 11, : 11-9163 5-2171 196 14-0000 5-8087 35 5-9160 3-2710 BI 9-4339 4-4647 149 1-9582 5-2293 ; 7 14-0a56 5-8186 36 6-0000 3-3019 M 9-4868 4-4814 144 12-0000 5-2414 i 98 14-0712 5-8284 37 6-0827 3-3322 91 9-5393 4-4979 I -1-1 12-0415 5-2535 198 14-1067 5*382 38 6 1644 3-3619 92 9-5916 4-5143 146 1-2-0830 5-2656 200 14-1421 5-8480 39 6-2449 3-3912 93 9-6436 4-5306 147 2-1243 5-2776 201 14-1774 5-8577 40 6-3245 3-4199 91 9-6953 4-5468 148 12-165~> 5-2895 202 14-2126 5-8674 41 6-4031 3-4482 05 9-7467 4-5629 148 12-2065 5-3014 303 14-2478 5-8771 42 6-4807 3-4760 B6 9-7979 4-5788 150 12-2474 5-3132 204 14-2828 5-8867 43 6-5574 3-5033 W 9-8488 4-5947 151 12-2882 5-3250 205 14-3178 5-8963 44 6 -6332 3 5303 98 9-8994 4-6104 152 2-3288 5-336fr 206 14-3527 5-S059 45 6-7r82 3-55K8 99 9-9198 4-6260 153 2-3693 5-3484 an 14-3874 5-9154 46 6-7823 3-5830 loo 10-0000 4-6415 154 2-4096 5-360! 208 14-42-22 5-9249 47 6-8556 3-60M8 !;,! 10-0498 4-6570 155 2-4498 5-3716 209 14-4568 5-9344 48 6-928-2 3634-2 ioa 10-0995 4-6723 156 2-4899 5-3832 210 14-4913 5-S439 49 7-0000 3-6593 103 10-1488 4-6375 157 2-5299 5-3946 21.1 14-5258 5-9533 50 70710 3-6840 104 10-1980 4-70'26 158 2-5698 5-4061 ,-1-2 14-5602 5-9627 51 7 1414 3-7084 105 10-2469 4-7176 159 12-6095 '5-4175 213 14-5945 5-9720 52 7-2111 3-7325 106 10-2956 4-7326 160 12-6491 1 5-4288 21! 14-6287 5-9814 53 7-2801 3-7562 107 10-3440 4-7474 161 12-6885 5-4401 215 1 4 -6628 ! 5 -9907 54 7-3484 3-7797 108 10-3923 4-7622 162 12-7279 5-4513 216 14-6969 6-0000 To find the gquare or cube root of a number consisting of integers and decimate. Rule. Multiply the difference between the root of the integer part of the jrjven number, ami the root of the next higher number, by the decimal part of the give number, and add the product to t!ie root of the given integer number; the sum is th loot required. Ex. Required the square root of 20-321. Square root of 21 4-5825 M 20=4-4721 Di - -1 104 X -321+ 4-4721 -4-507, 4c., the root required. VARNISHES, 173 MISCELLANEOUS NOTES VARNISHES. [From Dr. lire's Dictionary of Arts and Manufactures.] White Spirit Varnish. Sandarach, 250 parts ; mas tie in tears, 64 ; elemi resin, 32 ; Venice turpentine, 64; alcohol of 85 per cent, 1000 parts by measure The turpentine is to be added after the resins are dis- solved. This is a brilliant varnish, but not so hard as to bear polishing. Varnish for the Wood Toys of Spa. Tender copal, 75 parts ; mastic, 12-5 ; Venice turpentine, 6*5 ; alcohol of 95 per cent., 100 parts by measure ; water, ounces for example, if the other be taken in ounces. The alcohol must be first made to act upon the copal, with the aid of a little oil of lavender or camphor, if thought fit; and, the solution being passed through a linen cloth, the mastic must be introduced. After it & dissolved, the Venice turpentine, previously melted in a water bafh, should be added. The lower the tem- perature at which these operations are carried on, the more beautiful will the varnish be. This varnish ought to be very white, very drying, and capable of being smoothed with pumice-stone and polished. Varnish for Cabinet-Makers. Pale shellac, 750 parts ; mastic, 64 ; alcohol of 90 per cent., 1000 parts by measure. The solution is made in the cold, with the aid of frequent stirring. It is always muddy, and is employed without being filtered. With the same resins and proof spirit, a varnish is made for the book- binders, to do over their morocco leather. Crystal Varnish. Procure a bottle of Canada bal- eam, which can be had at any druggist's ; draw out the cork and set the bottle of balsam at a little distance 174 MISCELLANEOUS NOTES. from the fire, turning it round several times, until tho heat has thinned it ; then have something that wil} hold as much as double the quantity of balsam ; carry the balsam from the fire, and, while fluid, mix it with the same quantity of good turpentine, and shake them together until they are well incorporated. In a few days, the varnish is fit for use; particularly if it is poured into a half-gallon glass or stone bottle, and kept in a gentle warmth. This varnish is used for maps, prints, charts, drawings, paper ornaments, &c. The, Chinese Varnish is obtained from a tree which grows in Cochin-China, China, and Siam. It forms the best of all varnishes. Gold Lacker. Put into a clean four-gallon tin 1 Ib. ground turmeric, 1 oz. powdered gamboge, 3 Ibs. powdered gurn sandarach, f Ib. snellac, and 2 galls, spirits of wine. Afler being dissolved and strained, add 1 pint of turpentine varnish, well mixed. Red Spirit Lacker. 2 galls, spirits of wine; 1 Ib. dragon's-blood; 3 Ibs. Spanish annotto; 3 Ibs. gum sandarach ; 2 pints turpentine ; made exactly as the gold lacker. The Famish of Watin, for Gilded Articles. Gum la* in grain, 125 parts ; gamboge, 125 ; dragon's-blood, 125; annotto, 125; saffron, 32. Each resin must be dissolved in 1000 parts by measure of alcohol of 90 per cent. Two separate tinctures must be made with the dragon's-blood and annotto, in 1000 parts of such alcohol ; and a proper proportion of each should be added to the varnish, according to the shade of golden color wanted. Transfer Varnish. For fixing engravings or litho- graphs upon wood, a varnish called mordant is used in France, which differs from others chiefly in containing more Venice turpentine, to make it sticky. 1. consists of sandarach, 2~>0 parts; mastic in tears, 64; rosin, 125; Venice turpentine, 250; alcohol, 1000 parts b) measure. Common Mastic Varnish. Put as much gum mastic, VARNISHES. 175 unpicked, into the gum-pot, as may be required; and to every 2| Ibs. of gum, pour in 1 gall, of cold turpen- tine ; set the pot over a very moderate fire, and stir it Be careful, when the steam of the turpentine rises near the mouth of the pot, to cover with a piece of woollen cloth, and carry it out of doors, as the vapor is very ap< to catch fire. A few minutes' low heat will perfectly dissolve 8 Ibs. of gum, which will, with 4 galls, of turpentine, produce, when strained, 4^ galls, of varnish; to which add, while yet hot, 5 pints of pale turpentine varnish, which improves the body and hardness of the mastic varnish. Pale Brass Lacker. 2 galls, spirits of wine ; 3 oz. Cape aloes ; cut small 1 Ib. fine pale shellac ; 1 oz. gamboge, cut small ; no turpentine ; varnish made exactly as before. But observe, that those who make lackers frequently want some paler and some darker; and sometimes inclining more to the particular tint of certain of the component ingredients. Therefore, if a 4 oz. phial of a strong solution of each ingredient be prepared, a lacker of any tint can be produced at any time. Iron-Work Black. Put 48 Ibs. asphaltum into an iron pot, and boil for 4 hours ; during the first 2 hours, introduce 7 Ibs. litharge, 3 Ibs. dried copperas, and 10 galls, boiled ; add 1-eighth Ib. run of dark gum, with 2 galls, hot oil. A tier pouring the oil and gum, con- tinue the boiling 2 hours, or until it will roll into hard pills, like Japan. When cool, thin it off with 30 galls. turpentine, or until it is of proper consistence. This varnish is intended for the iron- work of coaches and other carriages, &c. To make Cloth, Silk, fyc. water-proof. Mix equal quantities of alum and acetate of lead, and dissolve the mixture in a gallon and a half of boiling water When the solution has cooled, remove the supernatant liquid from the sediment, which consists of sulphate of lead, and it is ready for use. Any article of dress, wnen well saturated in this liquid, and allowed to dry 176 SOLDERS. slowly, bears the action of boiling water, and does not permit it to pass through, although steam and air pene- trate it freely. Cement for China, Glass, tyc. To 1 oz. gum mastic add as much spirits of wine as will dissolve it ; soak 1 oz. isinglass in water till it is quite soft, then dis- solve it in pure brandy till of the consistence of glue ; to this add | oz. gum ammoniac, well rubbed and mixed. Put now the two mixtures together in a vessel over a gentle heat, till properly united, and the cemen' is ready for use. It must be kept in a phial wel stopped ; and, when about to be used, it ought to bi set in boiling water to soften. Preparation for Silver Solution. Take 1 pint of pure rain or distilled water; add to it 2 oz. cyanide oi potassium ; shake them together occasionally, until the hitter is entirely dissolved, and allow the liquid to become clear ; then add 4 oz. oxide of silver, which will very speedily dissolve ; and, after a short time, 8 clear, transparent solution will be obtained. Preparation of Gold Solution. Warm a pint of pure rain water, and dissolve in it 2 oz. cyanide of potassium ; then add | oz. oxide of gold ; the solution will at first be yellowish, but will soon subside to white SOLDERS. For Lend. Melt 1 part of block tin, and, when in a state of fusion, add 2 parts of lead. Resin should be used with this solder. For Tin. Pewter, 4 parts ; tin, 1 ; bismuth, 1 ; melt them together. Resin is also used with this solder. For Iron. Tough brass, witn a small quantity of borax. SCREWS. 177 CAPACITY OF CISTERNS IN GALLONS. For each 10 Inches in Depth. 2 feet diameter, 2A " 3 " " 3 " " 4 i{ ll 44 " " b~ " u ?: 74 19-5 8 feet diameter. . 313-33 30-6 8 353-72 4-1-06 9 " u 396-56 59-97 9A " it 461-40 78-33 10 u 489-2C 99-14 11 tt 592-4C 122-40 12 " ii 705- 148-10 13 tt 827-4 176-25 14 it 959-6 206-85 15 tt 1101-6 '239-88 20 tt 1958-4 275-40 25 " u 3059-9 SCREWS. Table showing the Number of Threads to an Inch in V -thread Screws. Diam. in inches, . . * lV t iVf I I I * 1* No. of threads, . . 20 18 16 14 12 11 10 9 8 7 *i 7 Diam. in inches, . . 1 No. of threads, . . 6 5 5 4^ 4 4 2| 3 3^ 3 34 Diam. in inches, . . 3| 4 No. of threads, . . 3 3 4| 5 2^ 2| 5| 6 The depth of the threads should be half their pitch. The diameter of a screw, to work in the teeth of a wheel, should be such, that the angle of the threads does not exceed 10. 178 WEIGHTS OF VARIOUS SUBSTANCES. RECAPITULATION OF WEIGHTS OF VARIOUS SUBSTANCES. Names. Cubic foot in Ibs. Cubic inch in Ibs Cast iron . . . Wrought iron . . Steel 450-55 486-65 489-8 26*07 2816 2834 Copper .... Lead Brass . . . . . 555- 708-75 5I57-75 32118 41015 3112 Tin 456- 263 White pine . . . Salt water (sea) . Fresh water . . Air 29-56 64-3 62-5 07529 0171 03721 03616 Steam .... 03689 CAST IRON expands -i^Vinj- of its length for one degree of heat ; greatest change in the shade, in this climate, YTTZT f * ts length ; exposed to the sun's rays, B TU I ?T pursuits for which they are wholly .incapacitated by talents, dispo- sition or education ; and what is still more un- reasonable, they expect them to be happy in situations which are totally uncongenial to their nature. One reason why parents and guardians fall so frequently into errors on this point, errors, too, which they lead those under their charge to embrace, is the vain imagination that there is a great and essential difference in the respecta bility of those pursuits which are generally admitted to be honest. The respectability of a profession, I suppose it will be admitted, must depend in a great measure on the respectable character of its members, taken collectively, or regarded with reference to the most brilliant examples. If we adopt this standard, it will be found no easy matter to establish a claim to superior respectability in favour of any one COMPARISON OF PROFESSIONS. Jg] trade, or profession, or of any class of trades or professions, j If it should be asserted that the learned pro- fessions of law, physic and divinity are more respectable than the pursuits of commerce, me- chanics or agriculture, it might be easily shown that taken collectively, the members of these latter professions or trades possess more wealth, ease and independence than those of the learn- ed ones ; and moreover, that among them as brilliant examples of mental pre-eminence, pa- triotism and public spirit may be pointed out as among those of the more learned professions In fact, in a country like ours, such a claim of superior respectability on behalf of any pro- fession is preposterous ; and yet it is constantly assigied by purse-proud fathers and silly mothers & a reason for determining their chil- dren's pursuits in life. There is a very general impression tnat a merchant, a clergyman, doc- tor or lawyer stands higher, and should stand higher, in the social scale than a mechanic or tanner. But such is not the fact, as a general principle; or, which results in the same thing, it in a particular instance, a particular merchant, for example, stands higher in social estimation man a particular mechanic, it is not on accoun-* 182 INTRODUCTION. of the respective means by which they earn then livelihood., but because the merchant in this instance has claims by wealth, family in- fluence or education, which the mechanic has no! ; ami by passing into the next street, and taking another example, you will find the tables completely turned, and the mechanic in the enjoyment of a social position to which the merchant cannot aspire. This fact is sufficient to prove that a man of one trade or profession does not take a lower position in society than another of a different profession, simply on account of the di fie rent modes by which they subsist, but by reason of other circumstances which are wholly independent of this conside- ration. Mr. A., who is a merchant, does not, for example, decline an intimate acquaintance and social intercourse with Mr. B., because Mr. B. is a mechanic, but because their favourite topics of conversation, their tastes and pursuits, are different; and this is clearly apparent from another fact, viz. : that whenever two persons of totally different professions happen to meet frequently upon some common ground of science or the fine arts, in their leisure hours they immediately recognise each other's natu- ral equality and become familiar companions RESPECTABILITY OF TRADES. Jg3 They collect plants, or minerals, or perform chemical or philosophical experiments together; they unite in the same pursuits during their leisure hours, and become daily moie and more assimilated in mind and character, as well as in their favourite recreations, until they are hound together by the strictest bonds of friend- ship. There is, therefore, no necessary or es- sential difference in the respectability of differ- ent trades and professions; and there is no social estrangement between their members, which may not be overcome by precisely the same means which constitute the cause of inti- macy in other circumstances. In our country, therefore, in point of real and essential respect- ability, all trades and professions are equal ; and the social position which a man enjoys, and the degree of respect which he is able to com- mand, depend not upon his trade, but upon his individual character. 4 If, in every part of the United States, the stupid prejudice which would exclude the me- chanic or the farmer from any society to which his intelligence and good manners - entitle him, is not thoroughly exploded, the time has cer- tainly arrived when it is no longer to be avowed bv well bred people. In fact, the rule which 14 INTRODUCTION. would exclude a man from any drawing-room in the land, on the simple ground of his being a mechanic', would have excluded from the same drawing-room such men as Nathaniel Bowditch, who was a mariner by trade ; Roger Sherman, who was a shoemaker by trade ; Ben- jamin Franklin, late ambassador to the Court of Versailles, who was a printer by trade ; and George Washington, a very respectable man of the last century, who was a surveyor by trade, But the imaginary respectability which a man may happen to enjoy from his position in so- ciety, is not by any means the first and most mip^rtant thing to be considered in the choice of a profession. It should not be the leading motive in determining the choice of the parent ; neither should it be the main consideration in the mind of the young person himself. There is another, and a much more important poin<- which claims and should receive the prece- dence. Every parent in making choice of a profession for his son, and every son in making the same choice for himself, should seriously and deliberately inquire, what profession affords the best chance for happiness ; happiness, in ile noblest and broadest sense happiness which consists in contentment, independence RESPECTABILITY OF TRADES. Jg/J and real usefulness happiness, which begins in the conscientious and successful discharge of duty on earth, and reaches forward to the unerring retribution of a future world. The inquiry which is thus presented is a very extensive one. It admits of whole years of investigation whole volumes of disquisi- tion to treat it at large, and apply it to any considerable portion of the cases that might arise. In order, therefore, to avoid running into useless generalities, I shall devote the short space which is allotted to me on the present occasion, to a very small part of this great sub- ject, and shall consider that part in a single point of view. I propose, in the outset of the present work, to inquire what opportunities are afforded for usefulness, happiness, and real re- spectability by the mechanical trades in other words, to inquire how a mechanic may be use- ful, happy and respectable. In the succeeding chapter I shall consider the first branch of the subject. THE YOUNG MECHANIC CHAPTER L THE MECHANIC SHOULD BE MASTER OF HIS TRADE. IN order to become useful, respectable, and nappy, it appears to me to be necessary, IN THE FIRST PLACE, that the mechanic should be- come a thorough master of his trade. Having made a deliberate choice of that pursuit, by which he is to gain his livelihood, it is a mat- ter of the utmost importance that he should devote the energies of his mind to the business unreservedly, until he has mastered all its prin- ciples and details. It is by this means only that hft can use it with ease and satisfaction as the instrument of success in the world. The incapable, or half taught mechanic, always works at a ruinous disadvantage. He can neither command the highest prices for the pro- ducts of his art, nor superintend with intelli- gence and authority the workmen under his care. He is in constant danger of failure in his business, or of abandoning it, through sheer disgust, only to take up some other pursuit for which he is totally unfitted by education. It APPRENTICESHIP. Jg^ is a laudable ambition, therefore, which makes him aspire to be first among his fellows. Jlut Ccesar aid nullus a master mechanic, or no mechanic at all should be his motto. 1. In order to render himself a thorough proficient in his trade, the mechanic should serve out his complete apprenticeship. Justice to himself, as well as to his master, dictates this course. Nor is it less a matter of policy than of moral duty. Even if he should deem him- self capable of undertaking the management of business for himself before he has half com- pleted his apprenticeship, it is a much safer and wiser course to remain in a subordinate capa- city till he has attained the age of manhood, than to rush upon the heavy duties an^l icarful responsibilities of active life before his judg- ment is matured, his understanding ripened, and his nerves hardened for the rough encoun- ter of conflicting interests and unforeseen emer- gencies. 2. At the same time that I counsel the ap- prentice to serve out his whole time, I would strenuously urge upon him the importance of devoting any leisure moments that he may have at his command, each day, to the cultivation of his mind. The parent or guardian, in becoming 188 THE YOUNG MECHANIC. a party to indentures, should be careful to ha\e a clause inserted by which a certain portion of time shall be secured to the apprentice for men- tal cultivation , and when this i& done the ap- prentice should regularly conseci ite this time' to its legitimate purpose. In our large cities facilities for this purpose are judiciously afford- ed by the beneficent provisions of Mechanics' Institutes, Lyceums and Libraries; but even in situations where such opportunities are not af- forded, we know by many illustrious examples that knowledge may be pursued and attained under the most discouraging difficulties. Where that good seed, the love of science, has been once implanted, it will spring up and grow and flourish, though pelted by storms of adversity, and chilled by the coldness of neglect. It is this consideration which encourages the teacher who has the future apprentice under his care, to instil into his opening mind the most liberal and exalted views of the real beauty, as well as utility, of science and literature. But why, it may be inquired, should the me- chanic be inspired with the love of science and literature ? I answer, that the mechanic should learn to love these intellectual pursuits for two MENTAL CULTIVATION. Jgg reasons : First, because he is a mechanic; and secondly, because he is a man. If the physician, the lawyer, the statesman, and the divine avail themselves of the assist- ance of science and literature in their several professions, the mechanic has still stronger in- ducements for doing the same thing ; for to none of these professions are the results of science so directly applicable, and for none of them are the recreations of literature so appro- priate or gratifying. By making himself mas- ter of those principles of science which are most intimately connected with his trade, the mechanic, while he is satisfying a liberal cu- riosity, may possibly be approaching some brilliant discovery, which will speedily conduct him to fortune and fame; and if the lighter reading, generally termed literature, promises no such result, it affords him the most dignified and innocent means of amusement, and pre- serves the vigour and increases the brightness of his intellect. He should, therefore, learn to appreciate such pursuits, because they are fitting and proper to him as a mechanic. He may also claim them as his own, upon the broad principle, that wherever there is a human intellect to be cultivated, there is a na- ]90 THE YOUNG MECHANIC tural and indefeasible right to the brightest de* gree of cultivation which it can attain. I remark, in the next place, that the mechanic, in order to render himself a complete mastei of his trade, should possess himself of new discoveries in science which are applicable to his purposes, and should actually apply them to the improvement of his trade. There never was a time since Lord Bacon first placed in the hands of philosophy the right instrument of investigation, when men of science were more actively and successfully engaged in developing the materials and pro- cesses directly applicable to the advancement of the mechanic arts, than the present. The forest and the mountain, the mine and the river, the deep bosom of the ocean itself all are literally ransacked by the ardent devotees of science, in pursuit of new substances which may minister to the sustenance or pleasure of man, or may open to the gaze of liberal cu- riosity the wonders of creative power. The Fcientific traveller brings home the products of vlistant lands to be naturalized in his own coun- try, and thus supply new materials for the use- ful arts ; the mechanical philosopher is con- stantly adding to the number of known motive USE OF LEISURE TIME. jgj powers ; the chemist is discovering new sub- stances, and making new developements and combinations of the powers of those already known ; while the press, by means of the ai t preservative of all arts, is bringing the icsult of all these labours and inquiries u home to the bosoms and business of men."" At such a time it becomes not the mechanic to be an idle or regardless spectator of all this activity. In the leisure moments which, by an ordinary arrangement of his labours, every man may redeem, he should direct his attention to the progress of discovery in chemistry, me- chanical philosophy and natural history, which have a direct bearing on his trade. He should attach himself to that mechanics' institute or lyceum which affords him the best means of improvement by its lectures, experiments, and library. He should cultivate the acquaintance of those scientific men who have the good sense to appreciate the society of intelligent practical mechanics, and he should apply the results of his inquiries, so far as it may be ju- diciously done, to the perfecting of his own manufactures. In recommending such a course to the young mechanic, I know that 1 am no< urging upon him vain speculations in visionary 17 192 THE YOUNG MECHANIC. schema. That such a course is precisely the one best calculated to improve and develope the mechanical arts, is clearly apparent when- ever an exhibition of the products of American industry is opened by any one of the societies constituted and supported by mechanics for this very purpose. A single exhibition of the Franklin Institute establishes with .more cer- tainty tfian a whole volume of arguments, the soundness of that policy which leads the me- chanic to devote his winter evenings to scientific pursuits, and to apply the result of his study to the improvement of his own trade. ADHERENCE TO TRADE. CHAPTER II. THE MECHANIC SHOULD REMAIN AT TACHED TO HIS TRADE. THIS is not all that is requisite for the use- fulness, happiness, and respectability of the mechanic. In order to secure these objects fully, I maintain, in the second place, that it is neces- sary for him to remain attached to his trade. Recent events in this country have, I think, sufficiently demonstrated the pernicious ten- dency of that ambitious restlessness which has lately pervaded all classes of people, and made almost every man regard his business whatever it happened to be, as merely the stepping stone to something apparently higher. Apparently, I say, for we have seen in many instances that mechanics, who were slowly and surely ac- quiring the means of independence and com- fort, have dashed into wild speculations, in hopes to rise to some imaginary height of wealth and importance ; but when the glittering bauble was almost within their reach, have found it suddenly eiude their grasp and leave 194 TTIE YOUNG MECHANIC. them to regret the loss of all which they had been toiling for years to acquire. Contentment, like every other Christian duty, has a great many excellent uses. Jt is good for the mind, for the body, and for the estate of every man. It tranquillizes the spirit, it pre- serves the health, and it promotes that steady economy which leads to competency ; often to affluence. The man who is satisfied with the position which Providence has assigned him, and endeavours to make himself useful in that position, presents a vastly more respectable figure than one who is constantly struggling to place himself in a different position. The fruits of this struggle are harassing cares, jealous heart-burnings, hazardous enterprises, and often debt and ruin. There is an old and homely saying, applicable to every one who has been brought up to a regular trade or profession a saying full of practical wisdom, which many have hitherto disregarded, but which will be better observed in years to come u Keep your shop, and your shop will keep you." This saying, as I have already intimated, is a whole- some one for any man who labours for his subsistence, whether it be with his head or hia KEEP YOUR SHOP. JQ^ hands; but for the mechanic it is the ark of safety. In some foreign countries it is the custom for mechanics to form associations, of which one of the leading objects is to retain all the mem- bers of each trade in the trade to which he belongs. For this purpose they not only aid all their brethren who are in distress, but they use every exertion to retain within their circle all the talent and all the wealth which has originated among them. Their public institu- tions, libraries and lecture rooms, their scienti- fic collections, their pictures and models, afford the means of gratifying the most refined taste ; and these and the tone which is imparted to their circle of society by this noble esprit de corps, make it wholly unnecessary for the most imbitious person to leave the trade in pursuit of any of these objects. Any one may see that under such circumstances it is a nobler ob- ject of ambition to be highly respected in the trade, than can be attained by means of any position out of it. The same principle holds good under all circumstances. If a man has surrounded himself with all the elegancies and luxuries which affluence can purchase by dili- gence and industry in his trade, he should 196 THE YOUNG MECHANIC. never abandon it under the impression that he will thus elevate himself in the estimation of his fellow citizens, by putting on a finer coat, and appearing in a different character. Such a course calls down a torrent of invidious remarks, not from his brethren of the trade, who are content, for the most part, to regret the deser- tion in silence, but the rest of that little world by whose Argus eyes the movements of each individual in society is watched. On the other hand, the mechanic who remains attached to his trade, when it is no longer absolutely ne- cessary for his support, is universally respected for this mark of steadiness, constancy and good sense. In connection with this part of my subject, I am strongly reminded of an old ac- quaintance of my own, in the old common- wealth of Massachusetts, who evidently takes an honest pride in his adherence to that trade which has long since given him the most ample means of luxury and ease. This gentleman is referred to by Governor Everett, in one of his recent public addresses, in the following terms: " I scarce know if I may venture to adduce an instance, nearer home, of the most praise- worthy and successful cultivation of useful knowledge, on the part of an individual with- THE ENLIGHTENED MECHANIC. ^97 out education, busily employed in mechanical industry. I have the pleasure to be acquainted, in one of the neighbouring towns, with a person, who was brought up to the trade of a leather-dresser, and has all his life work- ed, and still works, at this business. He has devoted his leisure hours, and a portion of his honourable earnings, to the cultivation of useful and elegant learning. Under the same roof, which covers his store and work- shop, he has the most excellent library of Eng- lish books, for its size, with which I am ac- quainted. The books have been selected with a good judgment, which would do credit to the most accomplished scholar, and have been im- ported from England by himself. What is more important than having the books, their proprietor is well acquainted with their contents. Among them are several volumes of the most costly and magnificent engravings. Connected with his library, is an exceedingly interesting series of paintings, in water-colours, which a fortunate accident placed in his possession, and several valuable pictures, purchased by himself. The whole form a treasure of taste and know- ledge, not surpassed, if equalled, by any thing of its kind in the country." 198 THE YOUNG MECHANIC Governor Everett might have added thai the leading traits in Mr. Dowsers character are sound sense and good taste ; and no more de- cisive proof of these characteristics could be given than his steady adherence to his original business. In the same address from which the above paragraph is quoted, the eloquent orator urges upon his hearers that every working man should cultivate his mind to the utmost of his ability ; and he quotes examples of many who have thus raised themselves to conspicuous offices and honours. I would urge upon all working men the same duty of mental cultiva- tion, not as affording the opportunity of aban- doning their trade ; but as giving them the means of dignifying and embellishing it. Lo- renzo de Medicis by commerce raised his family to princely rank they were the merchant kings of their age. The American mechanic has no occasion to seek any advancement of this sort, for every voter in our country is something greater than a king ; by virtue of the elective franchise he is a maker of kings. When I speak of adhering to one's trade, J' would by no means be understood to lay down a rule without exceptions. Emergencies may occur which shall render it a paramount duty to entel DUTY OF WORKING MEN. |gg upon a new and difficult profession. The me- chanic, like any other citizen, may be suddenly called upon to shoulder his musket and defend his country from invasion, as happened in the case of General Greene ; or he may be required to aid the same 'great cause by his wisdom in council, as in the case of Sherman and Frank- lin. When a country is to be saved by valour or Avisdom, it becomes a matter of absolute necessity that the working men should contri- bute a large contingent towards the grand army of defence as well as the council of the nation. For a time, at least, a new course of life must then be embraced. But the greatest, and most celebrated among those who have been detach- ed from their trade in this or in any other way, have always shown an honest pride in their original calling. Girard wrote, himself mariner in his will ; and Franklin called himself printer in his epitaph. 200 THE YOUNG MECHANIC. CHAPTER III. THE MECHANIC SHOULD HONOUR HIS TKADE. I HAVE already insisted that the mechanic in order to be useful, happy and respectable, should become a thorough master of his trade, and should remain attached to it. 1 would in the next place urge upon him the duty and policy which dictate that he should honour his trade. Tlrere are two ways in which this may be done : first, by seeking distinction in it; and secondly, by adorning it with intellectual re- creations. The love of distinction is common to nearly all men ; and the most remarkable and conspi cuous diversities of character are produced by the different modes in which this favourite ob ject is pursued. One man seeks it by brillian/ deeds in the public service, another by munifi cent institutions. Here we see distinction courted by eloquence, and there by learning Some hope to become distinguished by their , literary efforts, or their scientific discoveries, while others, with a less laudable, but not les* LOVE OF DISTINCTION 01 earnest ambition, seek to attract public atten* tion by mere eccentricity of character or extra- vagance in conduct, dress or equipage. Doubt- less this passion, so generally prevalent among men, has been implanted in the human breast for a wise and useful purpose ; and it is there- fore right to allow it a field for action, provided that field be a safe and honourable one. If this postulate be granted, I would ask what could afford a fairer and nobler field for any man^s ambition, than the pursuit of distinction by ex- traordinary excellence in his trade or profes- sion. Each of the mechanical trades affords ample room for the exercise of ingenuity in the improvement of its processes, and the con- sequent improvement of its products ; and the free institutions and abundant resources of our country, and the ease with which the workman may support himself, has already enabled Ame- rican industry and invention in many instances to claim the admiration of the world. It must be a proud reflection to the American mechanic, that one of his class has exacted the most un- equivocal homage to the genius of our country from the proud Sultan of the East, by his won- derful skill as a naval constructor ; and every Philadelphian may justly entertain a feeling oi 202 THE YOUNG MECHANIC exultation when he remembers that a mechanic of one of our cities is at this moment furnishing locomotive engines, acknowledged to be supe- rior to all others, for the use of British and Austrian rail road companies. Such distinction as this we must acknowledge to be fairly and honourably won. It is true that all may not hope to rise so high in the world's estimation as to attract applause from foreign countries. But every one may reap the reward of diligence, ingenuity and devotion to his business, in the applause of that valued circle, which is, in a certain sense, ail the world to him the circle of his associates and friends. Again, the mechanic may honour his trade by adorning it with intellectual recreations. It is not desirable, in fact it is not possible for a man to devote every moment of his time to the business by which he lives. Such intense ap- plication is injurious both to the body and the mind. It destroys health, racks the brain, and ruins the temper. The repose of the domestic circle, the quiet hour for reading or music, or relaxation of some other kind, seems absolutely necessary for the preservation of that greatest of earthly blessings a sound mind in a healthy body. The business of the mechanic is pre- EXAMPLE OF CHARLES LAMB. 203 cisely that which renders it most expedient foi birn to give his recreations an intellectual cast ; and it is owing to the circumstance that the alternation of mental and bodily labour is best suited to the human constitution, that some of the most beautiful and brilliant productions of the human intellect have proceeded from those persons who were compelled, for many hours of each day, to labour at a business which was purely mechanical. Cast your eye over the whole field of English literature, and see who it is that has brought the art of essay writing to its greatest perfection. Of course you in- stantly answer, Charles Lamb. He is univer- sally acknowledged to be in this department inimitable, unrivalled, unapproachable. The best critics say that we can never hope to see such essays produced by any other writer. Yet these beautiful productions were the work of leisure evenings. The composition of them served as a relaxation, after severe labour through the day at the India House in copy- ing commercial papers, which to him must have been a perfectly mechanical operation. Never- theless, he had the good sense to adhere to this, his trade, long after he was one of the most famous writers in England, and in fact until hi* 18 204 THE YOUNG MECHANIC. age and services entitled him to a retiring pen sion. I will not weary your patience by citing other examples, although there are thousands at hand, in proof of my position that intellectual recreations are particularly appropriate for the mechanic, and that they form the proper and legitimate ornament of his trade. Coleridge, an author by profession, tells us in plain terms that it is necessary, in order to be successful in works of imagination, to have some profession or trade which is to a certain extent mechanical, and he allectionately exhorts all young people to avoid his own profession if they would be useful and happy. I cite his observations, which are as remarkable as they are just. u An interest in the welfare of those who, at the present time, may be in circumstances not dissimilar to my own at my first entrance into life, has been the constant accompaniment, and, (as it were,) the under-song of all my feelings. Whitehead, exerting the prerogative of his lau- reateship, addressed to youthful poets a poetic charge, wh : ch is perhaps the best, and certainly the most interesting of his works. With no other privilege than that of sympathy and sin- cere good wishes* I would address an affectionate TRADE OF AUTHORSHIP. 205 exhortation to the youthful literati, grounded on my own experience, it will be but short ; for the beginning, middle, and end, converge to one charge: Never pursue literature as a trade, With the exception of one extraordinary man, I have never known an individual, least of all, an individual of genius, healthy or happy without a profession, i. e. some regular employment which does not depend on the will of the mo- ment, and which can be carried on so far me- chanically, that an average quantum only of health, spirits, and intellectual exertion, are requisite to its faithful discharge. Three hours of leisure, unannoyed by any alien anxiety, and looked forward to with a delight as a change and recreation, will suffice to realize in literature, a larger product of what is truly genial, than weeks of compulsion. Money and immediate reputation, form only an arbitrary and accidental end of literary labour. The hope of increasing them, by any given exertion, will often prove a stimulant to industry ; but the necessity of acquiring them will, in all works of genius, convert the stimulant into a narcotic. Motives by excess reverse ttoeir very nature, and, instead of exciting, stun and stu- pify the mind. For it is one contradistinction 2QQ THE YOUNG MECHANIC. of genius from talent, that its predominant end is always compromised in the means ; and this is one of the many points which establish an analogy between genius and virtue. Now, though talents may exist without genius, yet, as genius cannot exist, certainly not manifest itself, without talents, I would advise every scholar who feels the genial power working within him, so far to make a division between the two, that he should devote his talents to the acquirement of competence in some known trade or profession, and his genius to objects of his tranquil and unbiassed choice ; while tlu* consciousness of being actuated in both alike by the sincere desire to perform his duty, will alike ennoble both. My dear young friend, (I would say,) ' suppose yourself established in any honourable occupation. From the manu- factory, or counting-house, from the law court, or from having visited your last patient, you return at evening Dear tranquil time, when the sweet sense of home Is sweetest to your family, prepared for its social enjoy- ments, with the very countenances of your wife and children brightened, and their voice of welcome made doubly welcome by the know- TRADE OF AUTHORSHIP. 0? ledge that, as far as they are concerned, you have satisfied the demands of the day, by the labour of the day. Then when you retire into your study, in the books on your shelves you revisit so many venerable friends with whom you can converse. Your own spirit, scarcely less free from personal anxieties than the great minds that, in those books, are still living for you ! Even your writing desk with its blank paper, and all its other implements, will appear as a chain of flowers, capable of linking your feelings, as well as thoughts, to events and cha- racters past or to come ; not a chain of iron, which binds you down to think of the future, and the remote, by recalling the claims and feelings of the preremptory present. But why should I say retire ? The habits of active life and daily intercourse with the stir of the world, will tend to give you such self-command, that the presence of your family will be no inter- ruption. Nay, the social silence or undisturb- ing voices of a wife or sister, will be like a restorative atmosphere, or soft music, which moulds a dream without becoming its object If facts are required, to prove the possibility of combining weighty performances in literature with lull and independent employment, the IS* 208 TIIE YOUNG MECHANIC. works of Cicero and Xenophon among- the ancients, of Sir Thomas More, Bacon, Baxter, or, to refer, at once, to later and contemporary instances, Darwin and Roscoe, are at once deci- sive of the question. " Whatever be the profession or trade chosen, the advantages are many and important, com- pared with the state of a mere literary man, who, in any degree, depends on the sale of his works for the necessaries and comforts of life. In the former, a man lives ip sympathy with the world in which he lives. At least, he ac- quires a better and quicker tact for the know- ledge of that with which men in general can sympathize. He learns to manage his genius more prudently and efficaciously. His powers and acquirements gain him likewise more real admiration, for they surpass the legitimate ex- pectation of others. He is something besides an author and is not therefore considered merely as an author. The hearts of men are open to him, as to one of their own class ; and whether h^ exerts himself or not in the con versational circles of his acquaintance, his silence is not ettrbuted to pride, nor his com- municativenes to vanity. To these advantages I will venture tc add a superior chance of hap- TRADE OF AUTHORSHIP. piness in domestic life, were it only that it is as natural for the man to be out of the circle of his household during the day, as it is merito- rious for the woman to remain for the most part within it. But this subject involves points of consideration <*o numerous and so delicate, and would not only permit, but require such ample documents from the biography of literary men, that I now merely allude to it in transitu. When the same circumstance has occurred at very different times to very different persons, ill of whom have some one thing in common, there is reason to suppose that such circum- stance is not merely attributable to the persons concerned, but is in some measure occasion- ed by the one point in common to them all. Instead of the vehement and almost slanderous dehortation from marriage, which the 4 Miso- gyne Boccaccio' ( Vita e Coslumi di Dante, p. 12. 16) addresses to literary men, I would substitute the simple advice : be not merely a man of letters ! Let literature be an honour- able augmentation to your arms, but not con- stitute the coat, or fill the escutcheon ! " It would be a sort of irreligion, and scarce- ly less than a libel on human nature, to believe that there is any established and reputable pro- 210 THE YOUNG MECHANIC. fession or employment, in which a man may not continue to act with honesty and honour; and, doubtless, there is likewise none which may not at times present temptations to the contrary. But wofully will that man find him- self mistaken, who imagines that the profession of literature, 01 (to speak more plainly) the trade of authorship, besets its members with fewer or with less insidious temptations, than the church, the law, or the different branches of commerce.' " Charles Lamb himself subscribes to this opinion of Coleridge, and urges it upon one of his friends with great force ; and Herder is quoted by Coleridge in support of his own opinion, as follows : Translation. u With the greatest possible solicitude avoid authorship. Too early, or im- moderately employed, it makes the head waste and the heart empty, even were there no other worse consequences. A person who reads only to print, in all probability reads amiss ; and he who sends away through the pen and the press, every thought, the moment it occurs to him. will in a short time have sent all away, am) will become a mere journeyman of the printing office, a compositor." NECESSITY OF A TRADE. Ql] So much for the opinion of great authors on ft.e character of their trade. In all these observations you find it distinctly admitted that the fancy, the imagination, the creative powers of the mind are not to be taxed for the purposes of mere support. They say it is better to work for a living at some business which is mechanical, by way of a regular trade or profession, and to give the genius free ptay in the hours of recreation. That such a dis- tribution of one's time may produce the hap- piest effect is abundantly apparent from the experience of all ages. Without adverting to the busy life led by Cicero and Quinetilian, whom I esteem among the best authors of an- cient times, we may conie down at once to the moderns. Bacon, the prince of philosophers, was a lawyer laboriously active in his profes- sion during the greater part of his life ; Shaks- peare, the most admirable of all writers, was a player and manager, and was obliged to work hard at the mechanical part of these laborious employments ; Raleigh was a soldier and states- man, one of the most active of his age ; Cla- rendon was a busy statesman and lawyer; Addi- son was secretary of state while he ,vas writing the Spectator; Walter Scott was a writer for 212 THE YOUNG MECHANIC. the signet, and sheriff of the county ; and it is a curious fact that this writer, the most prolific as well as the best of our century, passed his days in bodily labour, riding about the county or working at his profession. It was remarked that nobody could conjecture when it was that he found time to write his voluminous works. if we come to our own country, the exam- ples are more numerous. All our best authors are working men. Prescott is a lawyer ; Ban- croft, a teacher for some years, and afterwards collector of the port of Boston ; Charles Sprague is a bank clerk; Halleck collects Mr. Astor's rents ; Dana is a lawyer; Longfellow, a teacher. In fact, with us, authorship is seldom a profes- sion. Most of our literature has been produced in the leisure hours rescued from laborious oc- cupations. Our scientific and useful inventions too have generally resulted from the very course which I am desirous to recommend to the mechanic, viz. : that of honouring his trade by adorning it with intellectual recreations. Fulton was a portrait painter, who amused himself in his idle hours with experiments on steam power ; Whit- ney, the inventor of the cotton gin, was a ma- chinist, whose judicious employment of his AMERICAN AUTHORS. leisure moments led him to an invention which has trebled the value of cotton lands at the South; Whittemore, of West Cambridge, who invented the machinery for the manufacture of cards, was, if 1 recollect right, a cabinet maker. The case of Franklin is familiar to all. All these examples tend to establish the same truth, that a mechanical business, a life of acti- vity and labour, is far from being unfavourable to the highest operations of the intellect ; and that relaxation from active labours is most ap- propriately found ia mental recreations. 214 THE YOUNG MECHANIC. CHAPTER IV THE MECHANIC SHOULD DEVOTE HIS LEI- SURE TO THE GENERAL INTERESTS OF HIS TRADE. ONE more duty I would urge upon the me- chanic, in order to the finishing of his charac- ter of a useful, happy and respectable man. Having attained wealth at the time of life when it is desirable to cease from active labour, I would have him devote himself to the general interests of his trade. There are many ways in which the wealthy mechanic may promote the general interests of his trade, when he has retired from all partici- pation in its labours or profits. He may give a tone to its society by exer- cising a refined and judicious hospitality. lit may make his house the resort of kindred spi- rits, who will unite with him in their endeavours to retain men of talent and influence in the trade. He may assist young men who are en- tering upon business for themselves with money, credit and good advice. He may save many a brother from ruin by interposing a friendly FRANKLIN. 215 voice, and a helping hand at the critical moment when they are most needed. He may become in his old age the Mecaenas, as well as the Nestor of his fraternity, by patronizing the in- tellectual efforts of their leisure hours. Such was the course of Franklin; and his munificent aid ceased not with his life. In his will a permanent fund was established for aiding the young mechanics of his native place by loans of money. The example of his life, however, has been of more value than a legacy of millions. He was a mechanic who fulfilled the several conditions which we have been considering as necessary to happiness, usefulness and respect- ability. He made himself a thorough master of his trade ; he adhered to it till the impera- tive call of his suffering country compelled him to relinquish it ; and he honoured his trade by seeking distinction in it, and by adorning it with intellectual recreations. Long may his example be imitated by his countrymen long may his race live and flourish in the land. Such mechanics are the bulwark of our free institutions. While we have men of the Frank- lin stamp among us, we shall never want a supply of heroes and statesmen to perform great and brilliant actions, or poets, historians and orators to celebrate them. 19 216 THE YOUNG MECHANIC. CHAPTER V. MISDIRECTION OF INDUSTRY PREJUDICES AGAINST THE MECHANICAL TRADES. AMONG the many causes which have led "to the present depressed state of affairs in oui country, there is one which appears to me an efficient one, although it has been in a great measure overlooked. This is the misdirection of industry of productive labour. All obser- vers readily perceive that capital has been thrown away ; few take notice of the fact that hands and heads have been employed on works that are now known to be utterly useless. Railroads, for example, have been constructed, which can never, by any possibility, be re- quired for the public accommodation to such an extent as to pay the expense of keeping them in repair and employing lines of cars upon them. Mines have been opened and wrought in situations where no veins of metal existed, although the imaginations of the stock- holders, aided by the fine stories of some cun- ning Dousterswivel, had made each of the re- MISAPPLICATION OF TIME AND TALENTS. 217 gions a perfect El Dorado. Even agricultural labour has been misapplied ; for trees have been planted and nursed with the greatest care, un- der the impression that their leaves were to be converted into silks which should rival the fabrics of Lyons and Benares ; and yet these very trees have subsequently been cut down as cumberers of the ground. The productive industry of this country might just as well have been employed in the con- struction of pyramids, like those of the ancient Egyptians, as on works of this nature. It is literally labour, time, and talents thrown away. But these are not the only ways in which labour, time and talent have been misdirected. Thousands of our young men have entered the learned professions when they were already crowded,, and are consequently wasting their lives in vain hopes ; and other thousands have devoted themselves to the pursuits of com- merce without capital, prudence, or intelligence sufficient to avoid the dangers of commercial enterprize ; and these men are now either bank- rupts, or involved in a series of embarrassments v^hich may last through their whole lives. An error in the choice of one's profession is one which 3 followed by painful consequences, as 2 1 S THfi YOUNG MECHANIC. many have found to their cost. In this coun- try we are apt to be too ambitious and restless. The freedom of our institutions, instead of im- pressing upon us the wholesome lesson that all men are naturally equal in dignity, and that consequently every trade and profession may be ennobled by the personal merit of its mem- bers, leads men to aspire to certain professions which they esteem genteel ; and to high offices which the constitution has made attainable by citizens of all classes. This is wrong. An American should respect himself. A citizen of this republic should deem himself a peer of the world one of nature's noblemen. He should consider that the cir- cumstance of his being an American citizen is sufficient to adorn with all proper dignity any trade or profession which he may adopt. Having settled this point with himself, he is left at perfect liberty to look around with ^an unprejudiced mind, upon the different modes of obtaining subsistence and making himself useful to the community ; and he can make his choice upon the same principles that should govern him in deciding any practical question. In taking a survey of some large community with reference to the success which has attend- MECHANICS AND MERCHANTS. 219 ed the exertions of other men, in order to aid his judgment in the choice of a profession, the youth or his adviser may peradventure, arrive at some results which he did not anticipate. Suppose, for example, that he should examine the comparative success of those men whom we know to have devoted themselves to me- chanical trades, and those who have become merchants. Would it not be apparent that where one mechanic has failed and caused extensive losses to his friends and the community, ten merchants have done the same thing ? On the other hand, would it not appear that where one merchant had acquired a competent fortune and retired from business in the decline of life, se- veral mechanics have done the same thing ? If we were to run over the list of persons taxed for real estate, should we not find more me- chanics than merchants living in their own houses, and deriving a handsome income from their rents ; If it be said that this not a fair test of com- parative success, let another be resorted to. Take the whole number of persons employed in mechanical trades, and the whole number of persons employed in commerce, say for the last twenty years ; then calculate what per centage THE YOUNG MECHANIC. of each class has failed, what per eentage has gained a decent subsistence without failing, and what per eentage has arrived at what is called independence. The result of such an inquiry would satisfy the inquirer that it is a safer course to become a mechanic than to be a merchant. The prejudice against the mechanical trades is a relic of feudalism unworthy of our free country. Considered with reference to those old feudal prejudices, ail the pursuits by which bread is earned in our country are equally base. Considered in the light of republican philosophy, they are all equally honourable. The baron of the middle ages, who could not read or write, looked down upon the merchant, the mechanic, and the lawyer with equal con- tempt; and the baron of modern days, who cannot even wield a lance, considers himself superior to the greatest, wisest, and best of those who were born commoners. These old feudal prejudices are ridiculous. But when we call one profession respectable^ and another less respectable, do we not adopt them ? When we talk of degrading ourselves by making tradesmen of our sons, do we not give sanc- tion to the stupid and exploded notions of the FEUDAL PREJUDICES. 221 dark ages ? When we admit that any citizen may lose caste by associating with any other honest and honourable man, do we not submit to a barbarism worse than Gothic^the bar- barism of Hindostan and China ? Such notions should be laid aside with other useless lumber, as unfit for an age and a coun- try where common sense gives law to society, and where real merit stamps the seal of respect- ability. It is but fighting shadows to offer ar- guments in opposition to such views. I gladly turn therefore from this to the more agreeable task of continuing the subject of my last lec- ture the mechanic. THE YOUNG MECHANIC. CHAPTER VI. INTELLECTUAL CULTIVATION OF THE MECHANIC ITS IMPORTANCE. I PROPOSE now to offer a few remarks on the intellectual cultivation of the mechanic, its im- portance, its means, and its rewards. That intellectual cultivation, as a means of moral and social elevation, is as important to the mechanic as it is to any other citizen, is a truth so obvious as not to require argument or illustration for its support. But this is not all He has stronger reasons for study than most other men. His very livelihood may depend in a great measure on a degree of skill in his art which cannot be acquired without a know- ledge of the scientific principles and natural laws on which the arts are founded. The whole system of mechanics' institutes, lyceums, lectures, and collections of specimens and machines, is nothing more nor less than an open confession made by the mechanics them- selves, that intellectual cultivation has become absolutely necessary, in order that they may COMPETITION. 22*1 keep pace with the spirit of the age an ac- knowledgment that the time has come when science and art shall be firmly united, and thy head and the hands shall work together. Competition imposes upon the mechanic ot the present day the necessity of study. Unless he keeps pace with the intelligence of the times, he will speedily find himself working at a ruinous disadvantage. While the workman who is content to remain stationary in scien tific intelligence, neglects the opportunities of information afforded by the institute, the read- ing room, and a constant social intercourse with the most intelligent of his trade; his neighbour, availing himself of these advantages, may possess himself of new processes, new materials, or new facts, which will enable him to reduce his prices, and in a great measure to carry off the custom of the place. It was not always thus. Monopoly and pre- scription formerly exerted an influence as inju- rious to the arts as that which is now exerted by competition is beneficial. Indeed, as has been ably shown by a learned authority,* much mischief has been occasioned * Governor Everett. Oration, p. 232. 224: THE ^IJNG MECHANIC. in past times by the ignorance of artizans. He says : " The history of the progress of the human mind shqws us, that for want of a diffusion of scientific knowledge among practical men, great evils have resulted, both to science and practice. Before the invention of the art of printing, the means of acquiring and circulating knowledge were few and ineffectual. The phi- losopher was, in consequence, exclusively a man of study, who, by living in a monastic seclusion, and by delving into the few books which time had spared, particularly the works of Aristotle and his commentators, succeeded in mastering the learning of the day ; learning, mostly of an abstract and metaphysical nature. Thus, living in a world not of practice, but speculation, never bringing his theories to the test of observation, his studied assumed a vi- sionary character. Hence the projects for the transmutation of metals ; a notion not origi- nating in any observation of the qualities of the different kinds of metals, but in reasoning, i priori, on their supposed identity of sub- stance. So deep rooted was this delusion, that a great part of the natural science of the mid- dle ages consisted in projects to convert the EVILS OF IGNORANCE. 225 baser metals into gold. It is plain, that such a project would no more have been countenanced by intelligent, well-informed persons, practi- cally conversant with the nature of the metals, than a project to transmute pine into oak, or fish into flesh. " In like manner, by giving science wholly up to the philosophers, and making the practical arts of life merely a matter of traditionary repeti- tion from one generation to another of uninform- ed artists, much evil of an opposite kind was occasioned. Accident, of course, could be the only source of improvement ; and for want of acquaintance with the leading principles of mechanical philosophy, the chances were inde- finitely multiplied against these accidental im- provements. For want of the diffusion of in formation among practical men, the principles prevailing in an art in one place were unknown in other places ; and processes existing at one period were liable to be forgotten in the lapse of time. Secrets and mysteries, easily kept in such a state of things, and cherished by their possessor as a source of monopoly, were so common, that mystery is still occasionally used as synonymous with trade. This also contri- buted to the loss of arts once brought to pet" 226 THE ^OUNG MECHANIC. fe^tion, such as that of staining glass, as prac- tised in the middle ages. Complicated ma- chinery was out of the question ; for it requires, for its invention and improvement, the union of scientific knowledge and practical skill. The mariner was left to creep along the coast, while the astronomer was casting nativities ; and the miner was reduced to the most laborious and purely mechanical processes, to extract the precious metals from the ores that really con- tained them, while the chemist, who ought to have taught him the method of amalgamation, could find no use for mercury, but as a men- struum, by which baser metals could be turned into gold, u At the present day, this state of things is certainly changed. A variety of popular trea- tises and works of reference have made the great principles of natural science generally accessible. It certainly is in the power of al- most every one, by pains and time properly bestowed, to acquire a decent knowledge of every branch of practical philosophy. But still, it would appear, that, even now, this part of education is not on the right footing. Gene- rally speaking, even now, all actual instruction in the principles of natural science is confined EDUCATION OF MECHANICS. 227 to the colleges ; and the colleges are, for the most part, frequented only by those intended for professional life. The elementary know- ledge of science which is communicated at the colleges, is indeed useful in any and every calling ; but it does not seem right that none but those intended for the pulpit, the bar, or the profession of medicine, should receive in- struction in those principles which regulate the operation of the mechanical powers, and lie at the foundation of complicated machinery; which relate to the navigation of the seas, the smelting and refining of metals, the composi- tion and improvement of soils, the reduction to a uniform whiteness of the vegetable fibre, the mixture and application of colours, the motion and pressure of fluids in large masses, the nature of light and heat, the laws of mag- netism, electricity, and galvanism. It would seem that this kind of knowledge was more immediately requisite for those who are to con- struct or make use of labour-saving machinery, who are to traverse the ocean, to lay out and direct the excavation of canals, to build steam engines and hydraulic presses, to work mines, and to conduct large agricultural and manufac- Uiring establishments. Hitherto, with some 20 228 THE YOUNG MECHANIC. partial exceptions, little has been done, syste- matically, to afford to those engaged in those pursuits, that knowledge which, however con- venient to others, would seem essenfial to them. There has been scarce any thing, which could be called education for practical life ; and those persons who, in the pursuit of any of the use ful arts, have signalized themselves by the em ployment of scientific principles for the inven- tion of new processes, or the improvement of the old, have been self-educated men." It is argued, in opposition to this view of the matter, that the greatest discoveries and inven- tions have oeen produced by self-taught men, or by accidental circumstances, and that educa- tion is therefore unnecessary for the mechanic. The fact is indisputable ; but the argument founded on it against the intellectual cultiva- tion of working men, is not sound. Another fact will sufficiently refute it. Before education became generally diffused among mechanics, useful discoveries and inventions were much rarer than they are at present. When the great mass of mechanics could neither read nor write, the progress of invention was exceedingly slow. Now it is astonishingly rapid. In the middle ages great discoveries in the arts were A LIFE OF LABOUR. 29 made at the rate of about one in a hundred years. Now they are made almost every year. Within the range of our own recollection two great motive powers, unknown before, have been rendered available in the arts of life, and scarcely a month passes without the announce- ment of some new contrivance for economizing the labour of man. This fact not only an- swers the argument already cited, but acts with tremendous power on the opposite side : thus, The increase of education among mechanics increases the number of discoveries and im- provements in the arts, by which human labour is abridged. This increase of power is an in- crease of happiness. It elevates the mechanic in the scale of social being, and adds to the comfort the essential happiness of society. By means of the recent improvements in the arts effected by ingenious and educated mecha- nics, the amount of severe bodily labour pre- viously imposed on that class of men is greatly diminished ; and this is no small gain. " We read," says a shrewd writer, " we read in many authors great encomiums on a life of labour, and of the superior blessings of peasants and hard-working men, whose temperate and abstemious lives nit jnly make them enjoy an 230 THE YOUNG MECIiAWlC. uninterrupted state of health, but throw a crimson on their cheeks, and give a vigour to their bodies, the sons of wealth and affluence, they tell us, may in vain sigh for. This sounds well ; but I own I am doubtful of the fact " If I compare the working part of mankind, who fare hard, with those who eat and drink of the * good things of the earth,' I think 1 can discern better complexions, choicer animal spi- rits, and stronger bodies in the latter than in the former. Incessant labour and coarse and scanty food, have certainly a tendency to weaken the bodies of mankind, and wear them out be- fore their time ; and this we see is the case. What becomes then of the fine-spun theories of visionary authors who so greatly extol a laborious life ? Why, they are destroyed, like other cobweb systems, that will not bear hand- ling." Education multiplies the inventions which lighten bodily labour. Education among me- chanics is, therefore, a great blessing ; and it should be a settled policy with this large and influential class of citizens, to encourage in every possible way the intellectual cultivation of all who compose their body. The kind of education which is suitable for APPLICATION OF SCIENCE TO ART. 33] a mechanic is that which is best accommodated to his circumstances. It should be liberal, not minute. To learn the practical application of every science to every art, is not in the power of any single individual ; but the me- chanic, as well as the professed scholar, may learn the general laws and principles of science; and subsequently carry out to any degree which may seem expedient for him, those details which are particularly applicable to his own trade. His general acquaintance with the physical laws will enlarge his sphere of usefulness, and in- crease his chances of success in any particular art. There are many good reasons why the Ame- rican mechanics, more than those of any other nation, should cultivate science. One reason of this is the exalted station in society which he enjoys here, compared with that assigned to the same class of men in other countries. In this connexion, I will again quote the au- thority of Governor Everett. And first, he says, it is beyond all ques- tion, that what are called the mechanical trades of this country are on a much more liberal footing than they are in Europe. This circum- stance not only ought to encourage those who 20* 232 THE YOUNG MECHANIC. pursue them, to take an honest pride in im- provement, but it makes it their incumbent duty to do so. In almost every country of Europe, various restraints are imposed on the mecha- nics, which almost amount to slavery. A good deal of censure has been lately thrown on the journeymen printers of Paris, for entering into combinations not to work for their employers, and for breaking up the power presses, which were used by the great employing printers. I certainly shall not undertake to justify any acts of illegal violence, and the destruction of pro- perty. But when you consider that no man can be a master printer in France without a license, and that only eighty licenses were granted in Paris, it is by no means wonderful that the journeymen, forbidden by law to set up for themselves, and prevented by the power presses from getting work from others, should be disposed, after having carried through one revolution for the government, to undertake another for themselves. Of what consequence is it to a man, forbidden by the law to work for his living, whether Charles X. or Louis Philip is king ? In England, it is exceedingly difficult for a mechanic to obtain a settlement in any town CONDITION OF FOREIGN MECHANICS. 333 except that in which he was born, or where he served his apprenticeship. The object of impos- ing these restrictions is, of course, to enforce on each parish the maintenance of its native poor ; and the resort of mechanics from place to place is permitted only on conditions with which many of them are unable to comply. The con- sequence is, they are obliged to stay where they were bora ; where, perhaps, there are already more hands than can find work ; and, from the decline of the place, even the established arti- sans want employment. Chained to such a spot, where chance and necessity have bound him, the young man feels himself but half free. He is thwarted in his choice of a pursuit for life, and obliged to take up with an employment against his preference, because there is no opening in any other. He is depressed in his own estimation, because he finds himself unprotected in society. The least evil likely to befall him is, that he drags along a discouraged and unproductive existence. He more naturally falls into dissi- pation and vice, or enlists in the army or navy ; while the place of his nativity is gradually be- coming a decayed, and finally a rotten borough, and, as such, enables some rich nobleman to 234 THE Y UNG MECHANIC. send two members to parliament, to make laws against combinations of wcrkmen. In other countries singular institutions exist, imposing oppressive burdens on the mechanical classes. 1 refer now more particularly to the corporations, guilds, or crafts, as they are called, that is, to the companies formed by the mem- bers of a particular trade. These exist, with great privileges, in every part of Europe ; in Germany, there are some features in the insti- tution, as it seems to me, peculiarly oppressive. The different crafts in that country are incorr porations recognized by law, governed by usages of great antiquity, with funds to defray the corporate expenses, and in each consider- able town, a house of entertainment is selected, as the house of call (or harbour, as it is styled,) of each particular craft. No one is allowed to set up as a master workman, in any trade, un- less he is admitted as a freeman, or member of the craft; and such is the stationary condition of most parts of Germany, that I understand that no person is admitted as a master work- man in any trade, except to supply the place of some one deceased or retired from business. When such a vacancy occurs, all those desirous of being permitted to fill it, present a piece of CONDITION OF FOREIGN MECHANICS. work, which is called their master-piece, being offered to obtain the place of a master work- man. Nominally, the best workman gets the place ; but you will easily conceive, that, in reality, some kind of favouritism must generally decide it. Thus is every man obliged to sub- mit to all the chances of a popular election, whether he shall be allowed to work for his bread; and that too, in a country where the people are not permitted to have any agency in choosing their rulers. But the restraints on journeymen, in that country, are still more op- pressive. As soon as the years of apprentice- ship have expired the young mechanic is obliged, in the phrase of the country, to wander for three years. For this purpose he is furnish- ed by the master of the craft in which he has served his apprenticeship, with a duly authen- ticated wandering book, with which he goes forth to seek employment. In whatever city he arrives, on presenting himself, with this cre- dential, at the house of call, or harbour, of the craft in which he has served his time, he is al- lowed, gratis, a day's food and a night's lodging. If he wishes to get employment in that place, he is assisted in procuring it. If he does not 236 THE YOUNG MECHANIC. wish to, or fails in the attempt, he must pursue his wandering ; and this lasts for three years, before he can be any where admitted as a mas- ter. I have heard it argued, that this system had the advantage of circulating knowledge from place to place, and imparting to the young artisan the fruits of travel and intercourse with the world. But however beneficial travelling may be, when undertaken by those who have the capacity to profit by it, I cannot but think that to compel every young man, who has just served out his time, to leave his home, in the manner I have described, must bring his habits and morals into peril, and be regarded rathei as a hardship than as an advantage. There is no sanctuary of virtue like home. You will see, from these few hints, the na- ture of some of the restraints and oppressions to which the mechanical industry of Europe is subjected. Wherever governments and corpo- rations thus interfere with private industry, the spring of personal enterprise is unbent. Men are depressed with a consciousness of living under control. They cease to feel a respon- sibility for themselves, and, encountering ob- stacles whenever they step from the beaten path, they give up improvement as hopeless. I neeJ CONDITION OF FOREIGN MECHANICS. 3^ Hot remark on the total difference of things in America. We are apt to think, that the only thing in which we have improved on other countries, is our political constitution, whereby we choose our rulers, instead of recognizing their heredi- tary rights. But a mi oh more important differ- ence between us an ! foreign countries is wrought into the very texture of our society ; it is that generally pervading freedom from re- straint, in matters like those I. have just speci- fied. In England, it is said that forty days undisturbed residence in a parish gives a jour- neyman mechanic a settlement, and consequent- ly entitles him, should he need it, to support from the poor rates of that parish. To obviate this effect, the magistrates are on the alert, and instantly r ipel a new comer from their limits, who d' js not possess means of giving security, such as few young mechanics command. A duress like this, environing the young man, on his entering into life, upon every side, and con- demning him to imprisonment for life on the spot where he was born, converts the govern- ment of the country, whatever be its name,- into, a despotism. Such is the condition of mechanics abroad ; such, thanks to our free institutions and the 238 THE YOUNG MECHANIC. bounty of a good Providence, is not the condi- tion of mechanics here. They may in fact they must neglect the cultivation of their minds ; but the American mechanic is inexcus- able if he neglects the great privileges Avhich distinguish him from the less fortunate Euro- pean. Another reason why the American mechanic should cultivate his intellectual powers as far as possible, is the vastly wider field which is opened to him by the extent and the resources of his country, and the ever active enterprize of its citizens. The European mechanic is hedged in on every side by restriction, and by competitors without number. All the trades there are full. In our country we see the re- verse. Here we have not men enou ^h to per- form the work required. The demand for me- chanical industry has never been fully met, and cannot be, for a long time to come. The im- mense amount of our land, the preponderance of agricultural industry, and the increasing de- mands of commerce, open an unlimited field to mechanical enterprise. We may infer what may yet be done from what has already been done. The service which the mechanical in- genuity of Americans has already rendered to TRIUMPHS OF AMERICAN INGENUITY. 239 .ihe country is at once a source of pride and .of hope. Take, for example, the service rendered to the cotton growing interest by Whitney's invention of the saw-gin ; or that rendered to internal commerce and to agriculture by Ful- ton's introduction of the steamboat into general use ; or that rendered to every consumer in the country by inventors and manufacturers con- cerned in the production of cotton and woollen fabrics. These inventions and improvements, by increasing the resources of the country, 'have greatly increased the demand for mechanical products. Whether, therefore, the American mechanic addresses himself to increasing the quantity or improving the quality of his manu- iactures, the field before him is wide enough for his greatest powers and his most unwearied activity. In entering upon this field, let him remember that knowledge is power, and he will neglect no opportunity of impr ing his mind. 21 240 THE YOUNG MECHANIC CHAPTER VII. MEANS OF INTELLECTUAL CULTIVATION ACCESSIBLE TO THE MECHANIC. SUPPOSING that the reasons why an American mechanic should be well educated are suffi- ciently established, let us next consider the means which are at his disposal or may be brought within his reach. 1. Of course the first and most important means of intellectual cultivation are the schools ; and those to the improvement of which the efforts of mechanics as a body can be most serviceably directed are the public schools. Wherever a system of public schools exists, it is the interest of the mechanic, in common with all other citizens, to aid in rendering it as perfect as possible. I believe that it is essen- tial to the perfection of a system of public schools, that not only elementary instruction should be dispensed to the children of all citi- zens who require it ; but that schools of a higher order should be placed within the reach of all pupils whose parents may wish to obtain SCHOOLS. the advantages of higher instruction for their offspring. Experience shows that it is not a difficult matter to create a supply of this highei instruction equal to the demand, even where the provision of primary instruction is most abundant. In Boston, where the population is over eighty thousand, and the primary and grammar schools are sufficient to accommodate every applicant for admission without delay, the High School for twenty years has averaged only ninety pupils ; this being the whole num ber of qualified candidates offered for admis sion. In Philadelphia the supply has certainly been hitherto equal to the demand, as all applicants for admission to the High School who were qualified for the higher studies at the time of their examination have been admitted. I be lieve that the number of scholars who will leave the school every year to enter upon the active business of life, will always be found equal to those who shall be qualified for admis- sion and shall present themselves for exami- nation. The advantages resulting from High Schools are not confined to the pupils who re- ceive instruction at those schools. The stimu- lus afforded by the hope of attaining admission 242 TIIE YOUNG MECHANIC. to them arts upon all the other schools, pro- ducing greater exertion and a more rapid pro- gress in learning. In fact the whole system is not only improved, but greatly extended, by the existence of higher classes of schools, This is apparent in this city,* where a greater number of primary and grammar schools have been created since the erection of the High School than at any previous period of the same length. The High School flinches to the future mechanic precisely the liberal kind of instruction which will be most available to him in his trade ; and in some instances gives mi- nute practical information directly applicable to the arts ; as for example, in the mathematical and drawing lessons, and the lessons, lectures and experiments on chemistry, natural philosophy and natural history ; other parts of the course of instruction, as the training in logic, rhetoric a.id composition, have more direct reference to the pupil's future position in the community as a citizen, a public officer, a parent, or a teacher. Such institutions it is the interest of every man to sustain ; of the rich, who do not avail them- selves of this advantage for their own children, * Philadelphia. MECHANICS' INSTITUTES. equally with those who are not rich, and there- fore need their aid. In fact, the laws which dis- tribute property equally among heirs, render it probable that the grand-children, or great-grand- children of the richest man in any of our com- munities will become pupils in the public schools. Jt is, therefore, the rich man's in- terest to pay heavy taxes, if need be, in ordei that the public schools may be rendered perfect, 2. The inheritance which he will thus trans- mit to his posterity, will last long after his wealth shall have been scattered to the winds I pass with reluctance from this interesting part of the subject, to the next means of intellec- tual improvement for the mechanic, viz. : the Mechanic's Institute. Any youth who has been taught to read and write, may derive ad- vantages from the lectures, experiments and library of the Mechanic's Institute; and the system of operations in these admirable insti- tutions is so liberally expanded, that the most accomplished scholar may also increase the amount of his practical knowledge by having recourse to the means of improvement which they afford. 3. But the best of all instruction is self instruction, and the most available means which the young man who is determined to 244 THE YOUNG MECHANIC. instruct himself can employ, are the library and the apparatus which are immediately at his own disposal under his own roof in his own apart- ment. The great secret of self improvement is to dedicate a portion of every day to private study. Consult the biographies of a long line of self taught men who have advanced science and the arts by their individual exertions, and you will find in most instances that the bril- liant discovery which astonished the w6rld was the result of private study and unassisted experiment. You will find also that the hour redeemed from ordinary business, and conse- crated to some favourite scientific inquiry, was the great discoverer's choicest recreation, the delight of the day, the great reward of many labours and cares. We all have our favourite enjoyments, apart from our daily labour. While one man reads for recreation, another plays upon the flute or takes a ride, or sketches a landscape, or talks politics, or tells stories to his children. All these amusements are excel- lent and refreshing in their season all are looked -forward to with pleasure ; but a sweeter recreation than any of these awaits the man who is at once a hard worker and a devotee of science. Often in the course of a busy day do MECHANICS' INSTITUTES. 245 his thoughts bound forward to the happy mo- ment when he shall enter the sanctuary of his own study, leaving his toils and cares behind, and, " the world forgetting, by the world for- got," shall busy himself in his favourite pur- suits, studying, experimenting, calculating, till his brain is weary with pleasurable excitement, and tired nature claims the right of repose. Jn order to profit by study it is not absolutely ne- cessary, but it is certainly very convenient and agreeable to have a place, a room, be it ever so small or so poorly furnished, which the stu- dent, the self instructer, may call his own his castle his sanctuary. Here he treasures up his little library of books, few perhaps, but choice and well beloved. Here he has his desk, papers, and his collection of curious or useful things, each fraught with associations, each the occasion of a lesson to himself. The mineral, which is but a common pebble to the visitor who comes in to look at his cabinet, has a magic power in it for the collector himself. It brings back to his recollection the glorious mountain towering to the skies the cataract the deep cavern, or the broad prairie, where the wonderful gem was found wonderful by the power of association which it has over the mind YOUNG MECHANIC. of its finder. The well worn volume, which ia mere paper and print to another, is a precious treasure to him, who has learnt from it the great laws of nature, the lore of antiquity, or the sweets of poetry. Every article in this retreat of studious leisure has a value to the owner, as it is connected with the developement of his higher faculties. - Every article is praised for having been, in its turn, the instrument of self cultivation. It would occupy too much time to enter here into a detailed review of the various means of self cultivation to which the student may have recourse in the retirement of his own room. These will form the subject of a future chapter. INTELLECTUAL CULTIVATION. 247 CHAPTER VIII. REWARDS OF INTELLECTUAL CULTIVA- TION ACCESSIBLE TO THE MECHANIC. I WILL now offer a few remarks on thewe- wards of intellectual cultivation. Liberal know- ledge, like virtue, is in a certain sense its own reward. The developement of the intellectual powers is attended with positive gratification, resulting from a sense of increased power, and the satisfying of curiosity respecting the laws of nature. The famous story of the rapture of Archimedes when he arrived at his beautiful demonstration of a well known mathematical truth, is but one among a thousand proofs that science rewards her votaries on the instant, pays her workmen, in solid coin, by the day by the hour. This is the sweetest and best reward of intellectual labour. It is that which is most diligently sought and most highly prized. But there are other rewards, only incidental and inferior, but still worthy of some conside- ration. 248 THE YOUNG MECHANIC. 1. Liberal knowledge and accomplishments confer the advantage of an elevated and influ- ential position in society. It is generally un- derstood that society exacts from each of its members some price of admission to its cote- ries and saloons. One brings fashion, another the wealth and consequence of his family, another his musical or conversational talents, another his celebrity as an author or traveller, or distinguished stranger. Among the rest the votary of science prefers his claim, and finding it admitted, takes a place in society on an inde- pendent and respectable ground. He is ad- mitted for what he is, not for what he has, or what his ancestors had. 2. Again, liberal knowledge gives its posses- sor the means of enjoyment in sickness, in retirement, and in old age. He who has learnt to converse with the master spirits of other times, is never at a loss for society or amuse- ment. Give him a book and he is happy or, failing the book, his previous cultivation makes the communion of his own thoughts or the practice of composition a sufficient occupation to pass delightfully those hours of loneliness and silence which are a weariness to the illite- rate man. INTELLECTUAL CULTIVATION. 49 3. To the advantages which the scientific mechanic enjoys in the prosecution of his trade we have already adverted. We will name but one more before closing the present considera- tion of the subject. It is this : The members of any particular trade, by earnestly uniting in the use of the various means of intellectual cultivation within their reach, may greatly in- crease the respectability, wealth and influence of that trade. By possessing their own library, reading room, museum and apparatus, and by stimulating the exertions of every member of the trade, master, journeyman, and apprentice, they will soon come to be recognised as a scientific body; and will not only insure to themselves the other rewards of science, but will receive the grateful acknowledgments of their fellow citizens as public benefactors. Such are the rewards of intellectual cultiva- tion attainable by those who are engaged in the mechanical trades. The example of Franklin, Watt, Arkwright, and a host of other illustrious men, show what mechanics have done. It re- mains for the rising generation in our own happy land to show what mechanics can do. 250 THE YOUNG MECHANIC CHAPTER DC THE MECHANIC'S STUDIES] BOOKS are, generally speaking,-too volumin- ous ; writers descend too much into minutiae ; and it is ?.n old observation, that where men are determined t> write every thing which can be said an any subject, they may write to eternity. Hence it is that a man of sense and erudition need but open a sf "ogle page of many a modern volume to lay it aside forever. It is said of Didymus, an ancient gramrrii^ian, that he had written so much that lie knew not his own productions, and having once abused a work for its absurdity, it was found to be his owri. I fear the race of Didymus is not extinct.* To read all books on all subjects would re- quire an uninterrupted attention during the longest life, even of an antediluvian. To read only the most celebrated, written in a few lan- guages, is an employment sufficient to fill up every hour of laborious application. For the * Northraore. CHOICE OF BOOKS. 5 fiake then of saving time, and of directing the judgment of the inexperienced, it becomes an useful attempt to suggest some general hints, which may tend to facilitate selection. One rule of the greatest consequence is, to read only, or chiefly, the original treatises in all the various departments of science or of literature. Nearly the same space of time, though not the same degree of attention, is necessary to peruse the faint copies of imitative industry, as would appropriate to the student the solid productions of native genius. This rule is more particu- larly to be observed on the first entrance on smdy. The foundation must be laid deeply, and formed of solid materials. The superstruc- ture will often admit slight and superficial ap- pendages. When we have studied the fine relics of those who have lived before us, we may derive much pleasure from attending to the additional labours of contemporary genius. But to begin with these is to found, like the fool recorded in the gospel, an edifice in the sand.* The merit of a book consists in, 1, New facts j 2. JN ew inferences from established facts ; * Ivnox's Essays. 22 252 THE YOUNG MECHAN C. 3. A better arrangement ; 4. A more complete collection of facts ; 5. information. When a book is destitute of these requisites, it may be condemned, without mercy, as of no use what- ever, and immediately sold by weight to the cheesemonger, or consigned to any other base or more ignoble purpose. When it is not des- titute of these, it should be reprieved, acquitted, or applauded, according to the requisites which it possesses.* On the choice of books, most excellent ad- vice is given by Dr. Watts, from whom, and other authors, has been compiled a pocket volume " on the Improvement of the Mind," in which various interesting matter relating to books, reading, conversation, study, &c. are treated of. Happy are they, says Fenelon, who being disgusted with all violent pleasures, know how to content themselves with the swaets of an innocent life. Happy are they, who are diverted, at the same time that they are instructed, and please themselves by en riching their minds with knowledge. Where- ever they may be thrown by adverse fortune, they will carry their own entertaii ment with * Dr. Mosley. CHOICE OF BOOKS. 253 them ; and the uneasiness, which preys on others, even in the midst of their pleasures, is unknown to those who can employ themselves in reading. Happy are they who love books and are not deprived of them. Among the other improvements of the pre- sent age, the art of puffing appears to have arrived at such perfection that it is impossible to select books by their titles, or from some of our booksellers' account of them in their ad- vertisements. A person who would make a preference and choose the best, must read much beyond the title page. From a hand bill which accidentally lies on the compiler's desk, the following encomiums are bestowed on very immethodical and inferior works. u A fasci nating introduction, superior to every preceding attempt of the kind, and deserving of universal preference." " The most approved and gene- rally adopted book ever published, and un- doubtedly the best extant." Such parade of applause may pass with those who do riot compare and discriminate, and their number is unfortunately not small. Mr. Pratt ingeniously laments the strange circumstance, that authors themselves have been the most bitter detractors of the talents 254 THE YOUNG MECHAN/C. and reputations or each othei. A grievance far more disgraceful, if not more injurious, to the literaiy chaiacter, than any other species of criticism. Indeed it would be difficult to find any set of enemies among men, any per- sons, whose passions and interests are at va- riance, so full of acerbity, of open violence, or of concealed malice, as the most eminent writers have proved themselves to each other, in their contentions of rivalry. The u republic of let- ters" is a very common expression among Eu- ropeans, and yet, when applied to the learned of Europe, is the most absurd which can be imagined, since nothing is more unlike a repub- lic, than the society which goes by that name In truth, almost every member of this fancied commonwealth is desirous of governing, and none willing to obey : each looks upon his fellow as a rival, not an assistant in the same pursuit. They calumniate, they injure, they despise, they riuicule, they worry, and assas- sinate each other. If one man write a book which pleases, others write books to show thai he might have given still greater pleasure, or should not have attempted to please. If one happen to hit upon something new, numbers are ready to assure the public that all this was CHOICE OF BOOKS. 255 no novelty to them or the learned ; that Car- danus, or Brunus, or some other author, too dull to be generally read, had anticipated the discovery. Their jarring constitution, instead of being styled the republic of letters, should be entitled the anarchy of literature. It is true, there are some of superior abilities, who reve- rence and esteem each other ; but their mutual admiration is not sufficient to shield off the contempt of the crowd. The wise are but few, and they praise with a feeble voice ; the vulgar many, and roar in reproaches. The trnly grrat seldom unite in societies, have few meetings, and no cabals : the dunces hunt in full cry, till they have run down a reputation, and then snarl and fight with each other about dividing the spoil." No task would be more easy to the most superficial observer, than that of producing numerous instances of glaring partiality in the journals of several of our cri- tics by profession. It appears sometimes from their neglect in reading with care the book which they undertake to criticize, so as to comprehend the author's views ; sometimes the narrowness of party spirit warps their decisions, in open contempt of the power of genius and originality. Sometimes a publisher's name on 22* 256 THE YOUNG MECHANIC. the cover, connected with the imprint of the book, is a clue by which neglect, injustice, narrow-minded selfishness, and misrepresenta- tion, may be unravelled ; and sometimes the critic's private jjique, as a contemporary author, is obvious. Poetic compositions, whether in ancient or modern languages, may be read at vacant hours, with some advantage, because many passages contain practical rules relating to moral econo- my and religion. Many elegant and ingenious sentiments and descriptions may also be found among the writings of poets, well worth com- mitting to memory ; and the measure of verse greatly assists recollection. The mere art of rhetoric never yet formed an English orator. It is one of those artificial assistances of genius, which genius wants not, and of which dullness can little avail itself. But as excellent books have been written on this subject, the general scholar will not fdil to pay it some attention. Let him then read Cicero on the Orator, and Quintilian's Insti- tutes, and he need not trouble himself with those meagre treatises which give a hard name to natural modes of expression, and teach us that, like Hudibras, we cannot open our mouths, ELOCUTION AND RHETORIC. 257 but out there flies a trope.* So much of rheto- ric as teaches the art of speaking and writing with elegance and dignity, in order to instruct, persuade and please, is certainly most valuable. Grammar teaches only propriety ; but rhetoric raises upon it purity and clearness of language, elegant thoughts, variety of expression, and lively figures. The duty of the orator is to stat3 interesting truths with such probability and evidence as may gain belief, and with such force and simplicity as may produce conviction. He must be able to demonstrate, to delight, and to work on the passions. Probably nothing has contributed more to generate apposite habits of mind than the early taste for reading. Books gratify and excite our curiosity in innumerable ways. They force us to reflect. They hurry us from point to point. They present direct ideas of various kinds, and they suggest indirect ones. In a well written book we are presented with the maturest re-< flections, or the happiest flights, of a mind of uncommon excellence. It is impossible tha< we can be much accustomed to such compa- Sj without attaining some resemblance oi Dr. 258 THE YOUNG MECHANIC. them. He who revels in a well chosen library, has innumerable dishes, and all of admirable flavour. His taste is rendered so acute, as to distinguish the nicest shades of difference. His mind becomes ductile, susceptible to every im- pression, and gains new refinement from each. His varieties of thinking baffle calculation, and his powers, whether of reason or imagination, become eminently vigorous.* - Exclusive of all regard to interest, and of preparation for the exercise of any art or pro- fession, says Dr. Knox, a taste for pleasing books is surely eligible, if it were only for the sake of enabling an ingenious man to pass his days innocently, calmly, and pleasurably. The pleasures of letters are certainly great to those who have been early devoted to them, and they are of all others the easiest to be obtained. For with respect to books we may say, u These are friends, no one of whom ever denies him- self to him. who calls ; no one takes leave of his visitor till he has rendered him happier and more pleased with himself. The conversation of no one of these is dangerous, neither is the respect to be paid to him attended with expense. * Godwin's Enquirer. ON A TASTE FOR READING. 5^ You may take what you please from them. What happiness, what a glorious old age awaits him who is placed under the protection of such friends ! He will have those whom he may con- sult on the most important, and the most trifling matter, whose advice he may daily ask concern- ing himself; from whom he may hear the truth without insult, praise without adulation, and to whose similitude he may conform himself."* As soon as we have obtained, by reading, a competent knowledge of a book or particular subject, it will contribute" greatly to animate us in proceeding still farther, if we talk of it either with our equals in attainments, or with the learned and experienced. In such conversation we venture to advance an opinion; our self- love renders us solicitous to maintain it, we seek the book as an auxiliary, we therefore read it with eager attention. In this manner an attachment to books and literary employ- ments is gradually formed, and what began in labour or necessity, becomes a choice, and con- stitutes the most agreeable pleasure. There is no study so dry, but by fixing oui attention upon it, we may at last n*~id it capa v: , * Seneca. 260 THE YOUNG MECHANIC tfle of affording great delight. Metaphysics and mathematics, even in their abstrusest parts, are known to give the attentive student a very exalted satisfaction. Those parts, then, of hu- man learning, which in their nature are more entertaining, cannot fail of being beloved in a high degree, when the mind is closely and con- stantly applied to them. In order to acquire the power and habit of fixing the attention, it will be first necessary to summon a very considerable degree of resolu- tion. In beginning the study of a new language, or any book of science, which presents ideas totally strange, the mind cannot but feel some degree of reluctance or disgust But let the student persevere; and in a very short time the disgust will vanish, and he will be reward- ed with entertainment. Till this takes place, let him make it an inviolable rule, however disagreeable, to read a certain quantity, or for a certain time, and he will infallibly find, that what he entered upon as a task, he will conti- nue as his best amusement. A due degree of variety will contribute great- ly to render reading agreeable. For though it be true that not more than one or two books should be read at once ; yet, when finished, it ON A TASTE FOR READING. 26 \ will be proper, if any weariness be felt, to take up an author who writes in a different style, or on a different subject; to change from poetry to prose, and from prose to poetry ; to inter- mix the moderns with the ancients ; alternately to lay down the book and take up the pen ; and sometimes to lay them both down, and enter with alacrity into agreeable company and pub- lic diversions. The mind, after a little cessa- tion, returns to books with all the voracious eagerness of a literary hunger. But the inter- missions must not be long, or frequent enough to form a habit of idleness or dissipation. The morning has been universally approved as the best time for study ;, but at all hours and in all seasons, if we can restrain the licentious rovings of imagination ; soothe the passion of the heart, and command our attention, so as to concentre it on the subject we examine, we shall find it amply rewarded. Attend closely; and close attention to any worthy subject will always prove solid satisfaction. But particu- larly in reading it may be depended on as ap- proved truth, that the degree of profit as well as pleasure, derived from it, will ever be pro- portioned to the degree of attention.* * Kmx's Essays, No. 82. 252 T1IE Y UNG MECHANIC. There are some mechanic aids in reading, which may prove of great utility. Montaigne placed at the end of the book which he intend- ed not to reperuse, the time he had read it, with a concise decision on its merits. He has obliged his admirers with giving several of these annotations. The striking passages in a book may be noted on a blank leaf, and the pages 1 referred to with a word of criticism. Seneca, in sending some volumes to his friend Lucilius, accompanied them with notes on particular passages, that, as he observes, you who only aim at the useful, may be spared the trouble of examining them entirely. I have seen books noted by Voltaire with a word of censure or approbation on the page itself, which was his usual practice ; and these volumes are precious to every man of taste.* I would have qyery one try to form an opinion of an author himself, though mo- desty may restrain him from mentioning it. Many are so anxious to have the reputation of taste, that they only praise the authors whose merit is indisputable. I am weary of hearing of the sublimity of Milton, the elegance and * D'Israeli's Miscellanies. ON A TASTE FOR READING. 263 harmony of Pope, and of the original, untaught genius of Shakspeare. Such hackneyed re- marks are made by those who know nothing of nature, and can neither enter into the spirit of those authors, nor understand them.* Temperance in eating and drinking, will con- tribute more to improve the natural, force or abilities of the mind, than any art or any ap- plication. It is related of the unfortunate young Chatterton, that he was remarkably abstemious, and that it was a frequent and favourite maxim with him, that a man might arrive at any height of improvf ment, or effect the most arduous un- dertaking by dint of industry and abstinence. He practised what he thought ; and this in some degree accounts for his uncommon attainments and productions, at an age when the full-fed heir can scarcely read and write. I recommend to all students the perusal of Dr. Cheney's Medical Advice ; or I will give it to them in a few words. "Take the least and the lightest food, under which you can be easy." Your 80^1 will thux feel fresh vigour, your life will be longer and happier, and your conduct wiser/f The neglect of writing in early life is the ' Mary Wollstonecraft. f Dr. Knox. 23 2(34 TI1E Y UNG MECHANIC. reason that almost every line of our scholars and gentry (who seem to pride themselves in their bad penmanship) stands in need of an in- terpreter. As this art is purely mechanical, and perfected by practice only, it is foreign from my purpose to prescribe rules for its attain ment. I will venture however to assert, that a plain, upright hand, resembling the round ro- man print is preferable to the ridiculous flour- ishes and slopes of writing-masters ; and my opinion is founded on a very simple reason, i* is more legible.* Plain writing, says Dr. Gregory, clear of flourishes, and very upright, is certainly the most proper for every station of life, and will remain intelligible longer than any other. It may be learned with less time and trouble, and may be written more expeditiously.^ I have long been of this opinion, and was happy to find it countenanced by the authority of Dr. Knox, and Dr. Beattie. Their popularity may perhaps be of weight in correcting the whimsi- cal and unintelligible mode of writing, which has been introduced by ignorant schoolmasters I perfectly agree with the latter, that the writing 'Yorke. ON THE ART OF WRITING. 265 which approaches nearest the Roman printed character, is the completest. Pope was taught to write by imitating and copying the Roman character of printed books, in which kind of writing he always excelled. [The Italic printed character appears better adapted for the purpose of writing than the Roman.] A gentleman in- form H, by letter, his country friend in Lin- colnshire, who had done him some recent fa- vour, how much he was obliged, and that he should soon send him an equivalent. Not being accustomed to fashionable scrawls, he read it that his friend would send him an elephant , and, building a barn at the time, actually fitted up a stall for the reception of his expected pre- sent. The arrival, however, of a barrel of oysters, a few days afterwards, helped him to the right reading, by' putting him in possession of a more suitable equivalent than an elephant, This is a fact, and occurred a few years since.* Rede's Anecdotes, 1799. 2(36 THE YOUNG MECHANIC CHAPTER X. THE MECHANIC'S STUDIES. To learn the rudiments of grammar by rote, is not the way to understand grammar. The mind must be addressed and convinced. Of what use is it to vex a boy's memory with the definition of a noun, when the definition itself is not clear to his understanding ? We may as well show him the figure of a triangle on pa- per, and expect him to comprehend its nature, by a definition of its properties. The fact is, the tender mind is not capable of abstract rea- soning; consequently, every subject which im- plies the generalization of ideas, should be first unfolded by evident and palpable demonstra- tion. Thus, a boy is taught in our schools to gabble that u a noun is the name of any per- son, place, or thing, as John, London, Honour;" yet J will venture to assert, that not one in ten thousand comprehends what he says. An analysis of language was never formed, until men were enabled to observe the turns of speech which custom authorizes ; there were ON LEARNING A LANGUAGE. 267 poets and orators before a grammar was ever thought of; it would be useless to teach either By stems of rhetoric or composition to a child, who had not learnt, by frequent use, the proper idioms of his own language ; and that there- fore the best models of beautiful writing should be set before him, previous to his being brought to judge of them by any determined rules.* If grammar be taught, it must be to one who can speak the language ; how else can he be taught the grammar of it? This is evident from the practice of the wise and learned na- tions among the ancients. They made it a part of education to cultivate their own, not foreign tongues. The Greeks counted all other nations barbarous, and had a contempt for their lan- guages. And though the Greek learning grew in credit among the Romans, towards the end of their commonwealth, yet it was the Roman tongue which was made the study of their youth, It was their own language which they were to make read it therefore by itself, is," as Ascham well observes, " tedious for the master, hard for the scholar, cold and uncomfortable for them both.' 7 274 THE "VOTING MECHANIC. It certainly is irksome for boys who have it to learn, because it conveys no pleasurable ideas, and much time is thus unnecessarily lost. Mr. Dyer in his life of Robinson, has observed that " Mr. Robinson's way of acquiring a knowledge of languages, was to sit down to an author, without any previous knowledge of the gram- mar, and to refer only to it in the same manner as the dictionary." This being premised, let us now suppose that my pupil is to be instruct- ed in the Greek language. He accordingly procures a grammar and dictionary ; but instead of labouring a twelvemonth in committing the former to memory, he reads it over once or twice merely to acquire some little insight into the nature of the language. His tutor then procures for him the best work of the purest Greek writer ; suppose the Republic of Plato, or the Cyropaedia of Xenophon, which is bet- ter adapted to youth. We now sit down to- gether, with our pens, ink and paper, to translate one of the easiest passages, making due refer- ence to our grammar and dictionary. Having done this we shut our books, and put our translations carefully by in our drawers. We then proceed to other business ; perhaps to the carpenter's chest, or the garden tools. The ON LEARNING A LANGUAGE. 275 next morning we take out our translations, and retranslate them into the best Greek we are able, which we compare with, and correct by the original text. This translation and retrans- lation, increasing gradually in quantity, we con- tinue to practise, till we become masters of the language, never omitting a single day, how small soever be the portion. It should be re membered, that, as we increase in knowledge* the version of one day is not retranslated till the interval of three or four days has elapsed, in order that the pupil may not translate by rote. By these means the language is learnt not only with greater facility, but to much greater perfection ; for the scholar acquires a knowledge of the peculiar cast of the language, and the particular points in which it differs from his own. Another advantage attending this system of translation, is, that the pupil cannot suffer from the ignorance of his tutor, both of them having the best possible standard for their guide. Nor perhaps is it a matter of small importance that the tutor is improving himself, at the very time that he is instructing his pupil ; and I am certain that the appearance only of studying one's-self, tends much to in- crease the love of study in youth. 24 276 THE *OUNG MECHANIC. In addition to translating, we must not omit to mention the advantages which accrue., par- ticularly to maturer minds, from reading and reciting the works of the great masters. By this we imbibe not only a taste for their purity and elegance of diction, but frequently partici- pate of their animation, and the fire of their genius.* Let none despair of acquiring, not only a competent but a critical knowledge of language, at whatever age a taste for such studies may be imbibed. Julius Scaliger, a profound critic, knew not the letters of the Greek alphabet at the age of forty years. Dr. Franklin learnt to speak French when upw r aros of seventy. Eu- gene Aram, without any assistance, learnt Latin, Greek, Hebrew, French, Chaldee, Arabic, and the Celtic. Whatever be the advantages, or defects of the English language, as it is our own language, it deserves a high degree of our study and at- tention, both with regard to the choice of words which we employ, and with regard to the syntax, or the arrangement of these words in a sentence, V\e know how much the Greeks and the Ro* * Northmore. THE ENGLISH LANGUAGE. 27*> mans, in their most polished and flourishing times, cultivated their own tongues. We know iiow much study both the French and the Ita- lians have bestowed on theirs. Whatever know- ledge may be acquired by the study of other languages, it can never be communicated with advantage, unless by such as can write and speak their own language well. Let the matter of an author be ever so good and useful, his compositions will always suffer in the public esteem, if his expression be deficient in purity and propriety. At the same time, the attain- ment of a correct and elegant style, is an ob- ject which demands application and labour. If any imagine they can catch it merely by the ear, or acquire it by a slight perusal of some of our good authors, they will find themselves much disappointed. The many errors, even in point of grammar, the many offences against purity of language, which are committed by writers who are far from being contemptible, demonstrate, that a careful study of the lan- guage is previously requisite, in all who aim at writing it properly.* The application of a child to a dead Ian- *Dr Blair. 278 THE YOUNG MECHANIC. guage, before he be acquainted with his own, is a lamentable waste of time, and highly de- trimental to the improvement of his mind. The general principles of grammar are common to all languages , a noun is the same in English, French, Latin, Greek, &,c. The varieties of languages are easily acquired by observation and practice, when a preliminary knowledge of our own grammar is obtained. But, the com- prehension of our native tongue, is not the only good preparative for the study of other languages. Some previous acqaintance with the general nature of things is necessary to the accomplishment of this end, in order that our literary progress may not be obstructed merely by words. For, although it be useful to leave some difficulties in the way of a child, that he may exercise his mind in overcoming them, yet he must not be disgusted by too many or too great impediments. Our whole attention should consist in proportioning the difficulties to his powers, and in offering them to his considera- tion individually. If Latin were made the pri mary object of a child's lesson, he would lose a vast portion of time in the study of grammar ; he would be incapable of perceiving the beau- ties of that language, because he would not THE EJVGLISH LANGUAGE. 7Q have acquired any previous knowledge. No benefit therefore could possibly accrue, from reading in the Latin tongue subjects which he could not understand in his own. But, by his becoming well acquainted with our best poets and prose writers, he will easily learn, inde- pendently of the number of ideas which he will gain thereby, the general rules of gram- mar ; several examples will unfold them, and a proper application of others may be soon made without difficulty. Besides, he will acquire taste and judgment, and be well prepared to feel the beauties of a foreign tongue, when he begins to feel the beauties of his own. His knowledge being also extended and diversified, it will be found that the sole difficulty attendant on the study of Latin, consists in learning words ; so that to obtain a just knowledge of things he must apply himself to such Latin authors only as are within the reach of his capacity, and whose writings he can compre- hend with the same facility as if they were written in his native language. By this plan, he will easily acquire the Latin tc ngue, trea- sure up fresh knowledge as he advances, and experience no disgusts in the study of it. Nothing can be more useless than to fatigue a 24* 280 THE YOUNG MECHANIC child, by filling his memory with the rules of a language which he does not yet understand, for, of what advantage is the knowledge of its rules, if he be unable to apply them ? We should wait, therefore, until reading has gradu- ally enlightened his mind, and the task becomes not irksome to him. When he has studied his own language, we should anticipate the princi- pal difference between the Latin and English syntax. His surprise in perceiving an unex- pected difference, will excite his curiosity, and effectually remove all distaste. After this, and not before, we may devote a part of each day to Latin ; but it ought never to be the first ob- ject of his studies.* The best English Gram mar for the purpose of self instruction is Frost's Practical Grammar, published by Thomas, Cowperthwait &. Co., Philadelphia. The Latin authors are possessed of uncom- mon excellence. One kind of excellence they possess which is not found in an equal degree in the writers of any other country : an exqui- site skill in the use of language ; a happy se- lection of words ; a beautiful structure of phrase , a transparency of style ; a precision * H. R. Yorke. THE LATIN LANGUAGE. gg] by which they communicate the strongest sen- timents in the directest form ; in a word, even 7 thing which relates to the most admirable polish of manner. Other writers have taken more licentious flights, and produced greater astonishment in their readers. Other writers have ventured more fearlessly into unexplored regions, and cropped those beauties which hang over the brink of the precipice of deformity. But it is the appropriate praise of the best Ro- man authors, that they scarcely present us with one idle and excrescent clause, that they con tinually convey their meaning in the choicest words. Their lines dwell upon our memory; their sentences have the force of maxims, every part vigorous, and seldom any thing which can be changed but for the worse. We wander in a scene where every thing is luxuriant, yet every thing vivid, graceful and correct. It is commonly said, that you may read the works of foreign authors in translations. But the excellencies above enumerated are incapa- ble of being transfused. A diffuse and volumi- nous author, whose merit consists chiefly in his thoughts, and little in the manner of attiring them, may be translated. But who can trans- late Horace ? who endure to read the transla- 2S2 THE YOUNG MECHANIC. tion ? Yet who is there, acquainted with hinv only through this medium, but listens with astonishment and incredulity to the encomiums he has received from the hour his poems were produced ? The Roman historians are the best which ever existed. The dramatic merit and the eloquence of Livy ; the profound philoso- phy of Sallust; the rich and solemn pencil of Tacitus, all ages of the world will admire. Add to this, that the best ages of Rome afford the purest models of virtue which are any where to be met with. Mankind are too much inclined to lose sight of all which is heroic, magnanimous and public spirited. Modern ages have formed to themselves virtue, rather polished than sublime, which consists in petty courtesies, rather than in the tranquil grandeur of an elevated mind. It is by turning to Fabri- cius, and men like Fab riciusy that we are brought to recollect what human nature is. Left to ourselves, we are apt to sink into effeminacy and apathy. It is by comparison only that we can enter into the philosophy of language. It is by comparison only that we can separate ideas, and the words by which those ideas are ordinarily conveyed. It is by collating one language with another that we detect all the THE LATIN LANGUAGE. 2S3 shades of meaning through the various inflec- tions of sense which the same word suffers, as it shall happen to be connected with different topics. He who is acquainted with only one lan- guage, will probably always remain in some degree the slave of language. From the im- perfectness of his knowledge, he will feel him- self at one time seduced to say what he did not mean, and at another time will fall into errors of this sort without being aware of it. It is impossible he should understand the full force of words. He will sometimes produce ridicule where he intended to produce passion. He will search in vain for the hidden treasures of his native tongue. He will never be able to. 2m ploy it in the most advantageous manner. He cannot be well acquainted with its strength and weakness. He is uninformed respecting its true genius and discriminating characteris- tics. But the man who is competent to, and exercised in the comparison of languages, has attained to his proper elevation. Language is not his master, but he is the master of language. Things hold their just order in his mind ; ideas, first, and then words. Words therefore are used by him as the means of communicating 284 THE YOUNG MECHANIC. or giving permanence to his sentiments ; and t.he whole magazine of his native tongue is sub- jected at his feet. Latin is a language which will furnish us with the etymology of many of our own words ; but it has perhaps peculiar recommen- dations as a praxis in the habits of investiga- tion and analysis. Its words undergo an un- common number of variations and inflexions. These inflections are more philosophically ap- propriated, and more distinct in their meaning, than the inflections of any language of a more ancient date. As the words in Latin composi- tion are not arranged in a philosophical or na- tural order, the mind is obliged to exert itself to disentangle the chaos, and is compelled to yield an unintermitted attention to the inflec- tions. It is therefore probable that the philoso- phy of language is best acquired by studying this language. Practice is superior to theory ; and this science will perhaps be more success- fully learned, and more deeply imprinted, by the perusal of Virgil and Horace, than by read ing a thousand treatises on universal grammar. Examples seem to correspond to what is here stated. Few men have written English with force and propriety, who have been wholly THE LATIN LANGUAGE. 285 unacquainted with the learned languages Our finest writers and speakers have been men who amused themselves during the whole of their lives with the perusal of the classics. Nothing is generally more easy than to discover by his style whether a man has been deprived of the advantages of a literary education. He who has not been accustomed to refine on words, and discriminate their shades of meaning, will think and reason after a very inaccurate and slovenly manner. Two qualities are especially necessary to any considerable improvement of human un- derstanding ; an ardent temper, and a habit of thinking with precision and order. The study of the Latin language is particularly conducive to the production of the last of these qualities. In this respect the study of Latin and geometry might perhaps be recommended for a similar reason. In the study of language and its in- flections, all is in order. Every thing is sub- jected to the most inflexible laws. The mind therefore which is accustomed to it, acquires habits of order, and of regarding things in a state of clearness, discrimination, and arrange- ment. The discipline of mind, here described, is 286 THE YOUNG MECHANIC of inestimable value. He who is not initiated in the practice of close investigation is con- stantly exposed to the danger of being deceived. His opinions have no standard, but are entirely at the mercy of his age, his country, the books he chances to read, or the company he happens to frequent. His mind is a wilderness. It may contain excellent materials, but they are of no use. He is unable to regulate his mind, and sails at the mercy of every breath of accident or caprice. Such a person is ordinarily found incapable of application or perseverance. All talent may perhaps be affirmed to consist of analysis and dissection, the turning a thing on all sides, and examining it in all its variety ol views. An ordinary man sees an object just as it happens to be presented to him, and sees no more. But a man of genius takes it to pieces, inquires into its cause and effects, remarks its internal structure, and considers what would have been the result, if its members had been combined in a different way, or subjected to different influences. The man of genius gains a whole magazine of thoughts, where the ordi nary man has received one idea; and hi* powers are multiplied in proportion to the number of ideas on which they are to be em- THE LATIN LANGUAGE. g7 ployed. Now there is perhaps nothing which contributes more eminently to this subtilizing and multiplication of mind, than an attention to the structure of language. Let it be taken for granted that the above ar- guments sufficiently establish the utility of classical learning ; it remains to be determined whether it be necessary that it should form a part of the education of youth. It may be alleged, that, if it be a desirable acquisition, it may with more propriety be made when a per- son is arrived at years of discretion; that it will then be made with less expense of labour and time, that the period of youth ought not to be burdened with so vexatious a task, and that our early years may be more advantageously spent in acquiring the knowledge of things, than of words. In answer to these objections it may be remarked, that it is not certain that, if the acquisition of the rudiments of classical learning be deferred to our riper years, it will ever be made. It will require strong inclina- tion and considerable leisure. A few active and determined spirits will surmount the difficulty ; but many who would derive great benefit from the acquisition, will certainly never arrive at it. The age of youth seems particularly adapted 25 THE YOUNG MECHANIC to the learning of words. The judgment is then small, but the memory is retentive. In our riper years we remember passions, facts, and arguments ; but it is for the most part in youth that we retain the very words ir which they are conveyed. Youth easily contents itself with this employment, especially where it is not enforced with particular severity. Acquisi- tions which are disgustful in riper years, art often found 'to afford young persons no con Cemptible amusement. It is not perhaps true that, in teaching languages to youth, we are imposing on them an unnecessary burden. ]f we would produce right habits in the mind, it must be employed. Our early years must not be spent in lethargic indolence. An active ma- turity must be preceded by a busy childhood. It has often been said that classical learning is an excellent accomplishment m men devoted to letters, but that it is ridiculous, in parents whose children are destined to more ordinary occupations, to desire to give them a superficial acquaintance with Latin, which in the sequel will infallibly fall into neglect. A conclusion opposite to this is dictated by the preceding reflections. We can never foresee the future destination and propensities of our children; THE LATIN LANGUAGE. yet, no portion of classical instruction, however small, need be wholly lost. Some refinement of mind, some clearness of thinking 1 , will al- most certainly result from grammatical studies. Though the language itself should ever after be neglected, some portion of a general science has thus been acquired, which can scarcely be forgotten. Though our children should be destined to the humblest occupation, that does not seem to be a sufficient reason for our de- nying them the acquisition of some of the most fundamental documents of human understand- ing.* The following method of teaching Latin, re- commended by R. L. Edgeworth, F. R. S., ap- pears exceedingly simple, natural, and pleasing, and furnishes useful hints for those who desire to teach themselves. u When children have by gentle degrees, and by short and clear conver- sations, been initiated in general grammar, and familiarized to its technical terms, the first page of tremulous Lilly will lose much of its horror. It is taken for granted, that the pupil can read and understand English, and that he has been eccustomed to employ a dictionary. He may * Godwin's Enquirer. 290 TIIE YOUNG MECHANIC. now proceed to translate from some easy book, a few short sentences : the first word will pro- bably be an adverb or conjunction ; either of them may be readily found in the Latin dic- tionary, and the young scholar will exult in having translated one word of Latin ; but the next word, a substantive or verb, perhaps will elude his search. Now the grammar may be produced, and something of the various termi- nations of a noun may be explained. If musam be searched for in the dictionary, it cannot be found, but musa catches the eye, and with the assistance of the grammar it may be shown, that the meaning of words may be discovered by the united helps of the dictionary and gram- mar. After some days' patient continuation of this exercise, the use of the grammar, and of its uncouth collection of words and syllables, will be apparent to the pupil ; he will perceive that the grammar is a sort of appendix to the dictionary. The grammatical formulae may then, by gentle degrees, be committed to me- mory ; and when once got by heart, they should be assiduously preserved in the recollection. After the preparation which we have recom mended, the singular number of a declension will be learnt in a few minutes, by a child oi THE LATIN LANGUAGE. 29 1 ordinary capacity, and after two or three days' repetition, the plural number may be added. The whole of the first declension should be well fixed in the memory before a second be attempted. During this process a few words at every lesson may be translated from Latin to English, and such nouns as are of the first de- clension may be compared with musa, and may be declined according to the same form. Te- dious as this method may appear, it will in the end be found expeditious. Omitting some of the theoretic or didactic part of the grammar, which should only be read, and which may be explained with care and patience, the whole of the declensions, pronouns, conjugations, the list of prepositions, conjunctions, interjections, some adverbs, the concords, the common rules of syntax, may be comprised with sufficient repetitions in about two or three hundred les- sons of ten minutes each : that is to say, ten minutes' application of the scholar in the pre- sence of the teacher. A young boy should never be set to learn a lesson by heart when alone. Forty hours ! Is this tedious ? If you are afraid of losing time, begin a few months earlier ; but begin when you will, forty hours is surely no great waste of time ; th^ whole, or ' 25* 292 THE YOUNG MECHANIC. even half of this short time, is not spent in the labour of getting jargon by rote; each day some slight advance is made in the knowledge of tneir combinations. What we insist on is, that nothing be done to disgust the pupil : steady perseverance, with uniform gentleness, will in- duce habit, and nothing should ever interrupt the regular return of the daily lesson. If ab- sence, business, illness, or any other cause, pre- vent the attendance of the teacher, a substitute must be appointed ; the idea of relaxation on Sunday, or a holiday, should never be permitted. In most public seminaries above one third, in some nearly one half, of the year is permitted to idleness : it is the comparison between severe labour and dissipation which renders learning hateful. Johnson is made to say, by one of his female biographers, that no child loves the per- son who teaches him Latin ; yet the writer would not take all the doctor's fame, and all the lady's wit and riches, in exchange for the hourly, unfeigned, unremitting friendship which he enjoys with a son who had no other master than his father. So far from being laborious or troublesome, he has found it an agreeable em- ployment to instruct his children in grammar and the learned languages. In the midst *>f a THE LATIN LANGUAGE. 293 variety of other occupations, half an hour every morning for many years, during the time of dressing, has been allotted to the instruction of boys of different ages in languages, and no other time has been spent in this employment," It has been objected, that a classical educa- tion loses time in acquiring words only, when ideas ought to be acquired. This objection (though in a great measure unjust ) would cer- tainly be without any colour of reason, if a plan could be proposed for uniting both these purposes ; if by a proper choice of books we could contrive to store the mind at different periods with such useful, moral ideas as are adapted to its capacity. The first branch of sci- ence which youth is capable of comprehending appears to be history. On the knowledge of facts, all moral reasoning must depend ; and facts learned in youth are certainly better re- tained than those which are acquired at any succeeding period. Young boys are not inte- rested in narrative (indeed there is hardly any other kind of composition which can engage them ;) and I have generally found them more delighted with true history and biography, if not prolix, than with poetry or novels. The tales of love, and the minutiae of private life ; *X)4 rHE YOUNG MECHANIC. do not arrest their attention so much as the ad- ventures of heroes, and the vicissitudes of war. Now although learning be a business rather than an amusement, certainly the more accept- able it can be made to the pupils, the better. On these principles, therefore, 1 would venture to deviate a little from the common order of school books, which schoolmasters are more anxious to select for the purity of the Latin, than for any real instruction or entertainment they contain. I would not be understood to insinuate, that the acquisition of the language, in the most perfect manner, is not a primary object-, but I am of opinion "that at a time when books are read only to exemplify gram- matical rules, purity and elegance are not so much required, as when the scholar is more advanced." The initiatory books, I apprehend, have little influence in forming the taste ; before that effect can take place it is necessary to be master of the rudiments, to read the language with ease, and to be able to consider it with something of a critical eye. It may please the vanity of a parent to be told, that his boy is reading Virgil or Ovid ; and it may answer the master's own. purpose, in a pecuniary view, to encourage this absurd vanity ; b'at in the mean THE LATIN LANGUAGE. ggg time the real interest of the pupil is sacrificed, For what can be more ridiculous, than to in- volve a child, who is yet unacquainted with the literal meaning- of words, in all the obscurities of figurative and poetic diction ; and, before he has acquired any ideas on common things, to expect that he should feel and admire the high- est efforts of the human imagination ? The books which I would recommend as proper to initiate children in the learned lan- guages, should be plain prose, simple, easy to be construed,, and dispensing such knowledge as is adapted to their capacities. I would lead them by just gradations from unadorned lan- guage, and plain fact, to elegance of style, ele- vation of thought, and more abstract sentiment. After some very easy Latin, just sufficient to show them the nature of construing, I think Eutropius the most proper book. It is an abridgement of perhaps the most important series of events which the annals of the globe can produce ; it is one of the easiest books to read, and the style is clear and perspicuous. After Eutropius, the young scholar may have an excellent taste of biography in the lives of Cornelius Nepos, which, in point of difficulty is properly the next step above Eutropius, 296 THE YCt> T G MECHANIC. .Justin may be read with the greatest advantage after the other two : he is not remarkable for the beauty or elegance of his style ; but he collects so many useful facts in the history of mankind, and is, as can testify from expe- rience, so delightful a book to boys, that the advantages to be derived from the perusal of him infinitely counterbalances this objection. If the pupils cannot go through the whole of these authors, the parts which they read may be chosen so as to connect together, and afford them a general view of the progress and termi- nation of the principal states of antiquity. Let them next read the most interesting parts ot Caesar and Sallust, and some of Cicero's ora- tions. A good set of the ancient maps ought to be made use of while they are reading his- tory ; and thus Geography will be insensibly acquired, and more firmly implanted, than by any otner process. Until they can construe such Latin as Cesar's Commentaries tolerably fluently, without the aid of a dictionary, and have gone at least one through a set of the common school exercises, such as Bailey's, no other language, not even Greek, should interfere with the Latin ; other- wise the memory will be confused by the dif- THE LATIN LANGUAGE. 097 ferent grammars. But by the time they have finished the course of reading already specified, it is presumed they will be capable of under- standing the study of Greek. Their'minds also will now be matured, and sufficiently cultivated to relish the charms of poetry, of which the uEneid is the chastest and most captivating spe- cimen. To the discretion of the master it may be left, how much of the Q9 previous to the reading of any author, to over- charge his memory with a multitude of syntax rules, of the use and application of which he must be totally ignorant. The concords, and a few of the principal rules, will be quite enough for him when he begins to construe. He must afterwards continue to get off a portion of the other rules every day, and must be well exer- cised in the grammar during the whole of his progress. I agree with Mr. Knox, that to teach wholly by translations is pernicious. But I must ob- serve, that if with the first and second books which a child is put to construe, no translation be made use of, the master himself must be in place of a translation ; or the pupil must, at the expense of some of his pocket money, apply to his school-fellows. It is impossible, on the first efforts to construe, to proceed without some guide ; or to use a dictionary with that ease and dexterity which are essential to profit. To allow them the assistance of a translation at first, and before they have acquired a little stock of words, is more suitable to the progressive powers of the human mind. I grant there will be some difficulty to be surmounted when they first lay aside the translation ; but this will be 310 TIIE YOUNG MECHANIC. nothing like so discouraging as the gloomy prospect of entering on a language totally un- known, and being obliged to consult, a dic- tionary for every word.* The modern practice of teaching Greek through the medium of Latin appears to me highly erroneous. It not only retards the pro- gress of a scholar, but it renders the idioms of both languages confused ; and the beauty of the article, and some of the tenses, independent of other considerations, is thus entirely lost. The labours of literary men cannot be directed to a more useful purpose, than the compilation of * dictionaries and grammars in the Greek and vernacular tongues/)* To the objection that too much time is lost in learning the words of the sentiments which we might obtain by means of translations, this plain answer may be given, that a person can never learn a language, without adding to the stock of his ideas ; and that the better the lan- guage is, (and where shall we find any equal to the Greek and Latin ?) the more correct will be the judgment, and the more vigorous the per ceptions of the learner. The learned tonguev * Gregory's Essays. f Northmore. CLASSICAL LEARNING. g]_ j form at once, even considered merely in their structure, the best code of laws for taste, and the best models for logical reasoning and argu- ment. No one who can read the classics would exchange the fruit of the time spent upon them for any other attainment which his earlier years could have made.* The Earl of Chatham says to his nephew, " I rejoice to hear that you have begun Homer's Iliad ; and have made great progress in Virgil ; I hope you taste and love these authors parti- cularly. You cannot read them too much, they are not only the two greatest poets, but they contain the finest lessons for your age to imbibe : lessons of honour, courage, disinte- restedness, love of truth, command of temper, gentleness of behaviour, humanity, and in one word, virtue, in its true signification. Go on, my dear nephew, and drink as deep as you can of these divine springs : the pleasure of the draught is equal at least to the prodigious ad- vantages of it to the heart and morals.f There is yet wanting in different languages, says Stevenson, initiatory books, containing * Edinburgh Review, iii. 351. j- Letters to T. Pitt, Esq., afterwards Lord Camelford, page 6. 27 312 THE YOUNG MECHANIC. physical facts, none of which would be dry and uninteresting. Natural History and Philosophy, in all their branches, even though they were superficial, would be of much greater use in every situation in life, than an intimacy with poetic flights of imagination, and all the lumber of the heathen mythology, the perusal of which affords but selfish, momentary, and insulated pleasure. Young people remember facts much more readily than sublime metaphor, or labour- ed sentiment.* Though I particularly recommend classical learning, says Dr. Knox, I do not recommend it exclusively. I think it ought to claim the earliest attention, and to form the foundation ; because no other learning contributes so much to open and to polish the mind. After this polish and expansion are acquired, and this foundation laid, f recommend an attention to the sciences, to natural history and experimental philosophy, to botany, to chemistry, to paint- ing, to architecture, to mechanical works, and in general to all the productions of human in- genuity. A capacious mind will view the uni- verse and all which it contains, as one vast * Remarks on the inferior utility of Classical Learning MATHEMATICS. volume laid before it for perusal. Philology alone is comparatively a confined, though ele- gant attainment. MATHEMATICS. Arithmetic may now be considered as having advanced to a degree of perfection which in former times could scarcely have been con- ceived, and to be one of those few sciences which have left little room for farther improve- ment. It is, however, a serious and almost general complaint, that few children, while at school, make any tolerable progress in arith- metic ; and that the generality, after having spent several years under the tuition of a mas- ter, are incapable of applying the few rules which they have learned, to the useful purposes of life. A few elementary principles are ac- quired by rote, and therefore quickly forgotten ; because the most essential particulars, namely, the reasons on which these rules are founded, and their extensive use in the various concerns of society are generally omitted,* So much of the science of numbers as is in common use, as the numeration, subtraction^ * Dom. Encyclopaedia. 314 THE YOUNG MECHANIC. multiplication, and division of money, should be learnt with accuracy ; to which should be added the rule of three and decimal fractions ; which will abundantly repay the labour of ac- quiring them by the pleasure and utility which will perpetually result from the knowledge of them through life.* The only sciences which can be denominated pure are the Mathematics. Of these, every mechanic and labourer should be made ac- quainted with Euclid, particularly the first six books ; also algebra ; the properties of the conic sections ; and the doctrine of fluxions. Owing to the very little attention which is paid to these sciences at present, it may appear to many, that their study is attended with great difficulty, and little advantage. Neither of these prejudices Dorders on the confines of truth. In order that those sciences may become capable of gra- tifying the desire which children entertain for the acquisition of truth and knowledge, L is absolutely necessary that they be rendered as clear and evident as possible, and also that their application and utility be made apparent. Nothing more seems wanting to render the study of mathematics pleasant and agreeable, * Dr. Darwin. MATHEMATICS. than to apply them to those purposes wnich must make their utility and perfection clear striking, and interesting. The time in which mathematics should be studied, must succeed that of literature. To comprehend abstract and general truth, some energy and comprehension of mind are requisite. To point out the pre- cise period when the study of mathematical science should commence, is attended with some difficulty. It must evidently vary, according to the progress which the mind may have made towards maturity and perfection.* I agree with Mr. Locke, that there is no study better fitted to exercise and strengthen the rea- soning powers, than that of the mathematical sciences, for two reasons ; first, because there is no other branch of science which gives such scope to long and accurate trains of reasoning ; and, secondly, because in mathematics there is no room for authority, nor for prejudice of any kind, which may give a false bias to the judg- ment. When a youth of moderate parts begins to study Euclid, every thing at first is new to him. His apprehension is unsteady ; his judg^ ment is feeble, and rests partly upon the evi- dence of the thing, and partly upon the authority ^ * Dr. Cowan. 31 Q THE YOUNG MECHANIC. of his teacher. But every time he goes over the definitions, the axioms, the elementary pro- positions, more light breaks in upon him : the language becomes familiar, and conveys clear and steady conceptions ; the judgment is con- firmed ; he begins to see what demonstration is ; and it is impossible to see it without being charmed with it. He perceives it to be a kind of evidence which has no need of authority to strengthen it. He finds himself emancipated from that bondage ; and exults so much in this new state of independence, that he spurns at authority, and would have demonstration for every thing ; until experience teaches him, that this is a kind of evidence which cannot be had in most things ; and that in his most important concerns, he must rest contented with probabi- lity. As he goes on in mathematics, the road of demonstration becomes smooth and easy ; he can walk in it firmly, and take wider steps : and at last he acquires the habit, not only of understanding a demonstration, but of discover- ing and demonstrating mathematical truths. Thus, a man, without rules of logic, may ac- quire a habit of reasoning justly in mathema tics ; and, I believe he may, by like means, ac- quire a nabit of reasoning justly in mechanics, LOGIC. 317 in jurisprudence, in politics, or in any other LOGIC. Good sense, good examples and assiduous exercise, may bring a man to reason justly and acutely in his own profession, without rules. But if any man think, that from this concession he may infer the inutility of logic, he betrays a great want of that art by this inference : for it is no better reasoning than this, that because a man may go from Edinburgh to London by the way of Paris, therefore any other road is use- less. There is perhaps no mechanic art which may not be acquired, in a very considerable de- gree, by example and practice, without reducing it to rules. But practice, joined with rules, may carry a man on in his art farther and more quickly, than practice without rules. Every ingenious artist knows the utility of having his art reduced to rules, and by that means made a science. He is thereby enlightened in his prac- tice, and works with more assurance. By rules, he sometimes corrects his own errors, and often detects the errors of others : he finds them of great use to confirm his judgment, to justify what is right, and to condemn what is wrong. 318 THE YOUNG MECHANIC. Is it of no use in reasoning, to be well acquainted with the various powers of the human under- standing, by which we reason ? Is it of no use. to resolve the various kinds of reasoning into their simple elements ; and to discover, as far as we are able, the rules by which these elements are combined in judging and in rea- soning ? Is it of no use, to mark the various fallacies in reasoning, by which even the most ingenious men have been led into error ? It must surely betray great want of understanding, to think these things useless or unimportant. These are the things which logicians have at- tempted, and which they have executed ; not indeed so completely as to leave no room for improvement, but in such a manner as to give very considerable aid to our reasoning powers. That the principles laid down with regard to definition and division, with regard to the con- version and opposition of propositions and the general rules of reasoning, are not without use, is sufficiently apparent from the blunders com- mitted by those who disdain any acquaintance with them.* Geometry should always form a part of a * Lord Kaimes' Sketches* LOGIC liberal course of studies. It has its direct uses and its indirect. It is of great importance for the improvement of mechanics and the arts of life. It is essential to the just mastery of as- tronomy and various other eminent sciences But its indirect uses are perhaps of more worth than its direct. It cultivates the powers of the mind, and generates the most excellent habits. It eminently conduces to the making man a rational being, accustoms him to a closeness of deduction, which is not easily made the dupe of ambiguity, and carries on an eternal war against prejudice and imposition.* But geome- try is not a competent guide to the art of rea- soning without the study of logic. It is a very great error to suppose that logic consists only in those formal debates and ver- bal disputations, in which the schoolmen and their fo lowers consumed so much time in the dark ages, previous to the revival of classical learning. It is equally a mistake to imagine, that it is merely intended to teach the method of disputing by rules, and to instruct a person to converse, not from a love of truth, but a desire of victory. As there is nothing more * God win's Enquirer. 320 THE YOUNG MECHANIC. disingenuous than such a conduct as this, no- thing more unbecoming a rationable being, than to oppose sophistry to good sense, and evasion to sound argument, the logician disclaims this abuse of the principles of his art, and vindi- cates its rights by displaying its true and proper office. It is in reality capable of affording the most important assistance to the understanding in its inquiries after truth ; it is eminently use- ful in the common affairs of life, and renders the greatest service to science, learning, virtue, and religion. Logic is the art of forming correct ideas, and of deducing right inferences from them ; or it may be said to constitute the knowledge of the human mind, inasmuch as it traces the progress of all our information, from our first and most simple conception of things, to those numerous conclusions which result from comparing them together. It teaches us in what order our thoughts succeed each other, and it instructs us in the relation which subsists between our idras, and the terms in which we express them It distinguishes their different kinds, and points out their properties ; discovers the sources of our intellectual mistakes, and shows how we may correct and prevent them. It displays LOGIC. 3 21 those principles and rules, which we follow, although imperceptibly, whenever we think in a manner conformable to truth. The faculty of reason is the pre-eminent quality, by which mankind are distinguished from all other animals ; but still we are far from finding that they possess it in the same degree. There is indeed as great an inequality in this respect in different persons, as there is in their strength and agility of body. Nor ought this disproportion to be wholly ascribed to the original constitution of the minds of men, or the difference of their natural endowments ; for, if we take a survey of the nations of the world, we shall find that some are immersed in igno- rance and barbarity, others enlightened by learning and science ; and, what is still more remarkable, the people of the same nation have been in various ages distinguished by these very opposite characters. It is, therefore, by due cultivation, and proper diligence, that we increase the vigour of our minds, and carry reason to perfection. Where this method is followed, the intellect acquires strength, and knowledge is enlarged in every direction ; where it is neglected, we remain ignorant of the value of our own powers; and those faculties, by 322 THE YOUNG MECHANIC. which we are qualified to survey the vast fabric of the world, to contemplate the whole face of nature, to investigate the causes of things and to arrive at the most important conclusions as to our welfare and happiness, remain buried in darkness and obscurity. No branc i of science therefore affords us a fairer prospect t f improve- ment, than that which relates to the understand- ing, defines its powers, and shows the method by which it acquires the stock of its ideas, and accumulates general knowledge.* COMPOSITION. When we are employed after a proper man- ner, in the study of composition, we are culti- vating reason itself. True rhetoric and sound logic are very nearly allied. The study of ar- ranging and expressing our thoughts with pro- priety, teaches us to think, as well as to speak, accurately. By putting our sentiments into words we always conceive them more distinctly. Every one who has the slightest acquaintance with composition knows, that when he ex- presses himself ill on any subject, when his arrangement is loose, and his sentences become * Mr. Kett's Element*. COMPOSITION 323 feeble, the defects of his style can, almost on every occasion, be traced back to his indistinct conception of the subject : so close is the con- nection between thoughts and the words in which they are clothed. The study of com- position, important in itself at all times, has acquired additional importance from the taste and manners of the present age ; an age wherein improvements, in every part of science, have been prosecuted with ardour. To all the libe- ral arts much attention has been paid ; and to none more than to the beauty of language, and the grace and elegance of every kind of writing. The public ear is become refined. It will not easily bear what is slovenly and incorrect. Every one who writes must aspire to some merit in expression, as well as in sentiment, if he would not incur the danger of being neglected and despised. I will not deny that the love of minute elegance, and attention to inferior orna- ments of composition, may have engrossed too great a degree of the public regard. It is in- deed my opinion, that we lean to this extreme ; often more careful of polished style, than of storing it with thought. Yet hence arises a new reason for the study of just and proper composition. If it be requisite not to be defi- 28 324 THE YOUNG MECHANIC. cient in elegance and ornament, in times when they are in such high estimation, it is still more requisite to attain the power of distinguishing false ornament from true, in order to prevent our being carried away by that torrent of false and frivolous taste, which never fails, when it is prevalent, to sweep along with it the raw and the ignorant. They who have never studied eloquence in its principles, nor have been trained to attend to the genuine and manly beauties of good writing, are always ready to be caught by the mere glare of language; and when they come to speak in public, or to compose, have no other standard on which to form themselves, except what chances to be fashionable and po- pular, how corrupted soever and erroneous that may be.* Though I have advised the pupil to exercise himself in composition, yet I will also caution him against the itch of scribbling. Let him never take the pen in hand, nor place the paper before him, till he has bestowed much time and deep thought on the subject. To the want of this previous attention we owe the numerous productions which disgrace letters, and which die almost as soon as they are brought forth ; * l)r. Blair's Lectures. IMPROVEMENT OF MEMORY. 325 which, like weeds in a garden, spring up luxu- riantly without cultivation, which are useless or noisome, and which only serve to impede the growth of salutary plants and pleasant flowers. Pretenders arise in every department, and disgrace it. Let the liberal and solid scholar attend to the circumstances of time and place, in the modest display of his attainments. It is unmanly timidity to conceal them on proper occasions ; it is ridiculous arrogance to intrude on unwilling and injudicious observers. Mo- desty is the characteristic of real merit; and firmness, of conscious dignity. The man of sense will be diffident, but at the same time will have spirit enough to repel the insolent attacks of ignorance and envy.*^ IMPROVEMENT OF THE MEMORY. The following observations, if attended to, may greatly assist those more advanced in life, in strengthening the memory. 1. Let the stu- dent never quit any branch of study till he be perfectly master of it, and can comprehend it as a whole ; as well as in parts. 2. Endeavour to link and connect the leading ideas, to class facts, and arrange them under different heads ; *Dr Knox. 326 THE YOUNG MECHANIC. so that the mind shall be able at one view to recall the outlines of the whole science, and af- terwards to pass to the inferior branches, or sub- divisions. The ancients formed their memories almost entirely by this method; and indeed memory can never be useful without svstem. 3. Never commit mere words to memory as substitutes for true knowledge. Many a young person forgets what he has been taught because he never understood it. This is the true reason why boys make so wretched a proficiency in attaining the Latin language, under masters who give them page after page of old Lilly to com- mit to memory, without the occurrence of a question or an explanation. In this manner they are also taught their catechisms, the ideas in which are infinitely above their comprehen- sion. The first thing which strikes us, in looking over Dr. Franklin's works, is the variety of his observations on different subjects. We might imagine, that a very tenacious and powerful memory was necessary to register them; but Dr. Franklin informs us, that it was his con- stant practice to note down every thing as it occurred to him : he urges his friends to do the same ; he observes, that there is scarcely a day IMPROVEMENT OF MEMORY, 327 passes without our hearing or seeing something, which, if properly attended to, might lead to useful discoveries. By thus committing his ideas to writing, his mind was left at liberty to think. No extraordinary effort of memory was, even on the greatest occasions, requisite.* On the whole, the most effectual way to ac- quire a good memory is by constant and mo- derate exercises of it ; for the memory, like other habits, is strengthened and improved by daily use. It is scarcely credible to what a de- gree both active and passive memory may be improved by long practice. Scaliger reports of himself that in his youth he could repeat above one hundred verses, having but once read them ; and Boethius declares, that he wrote his comment on Claudian without consulting the text. The extraordinary memory of Ma- gliabechi is well known. That of Jediah Bux- ton was of a peculiar kind ; so long was it habituated to numbers, that it could fix on nothing else. To hope, however, for such de- grees of memory as these, would be equally vain as to hope for the strength of Hercules, or the swiftness of Achilles. There are clergy-* * Chiefly by Miss Edgeworth. 28* 328 THE YOUNG MECHANIC. men who can get a sermon by heart in two hours, though their memory when they began to exercise it, was rather weak than strong : and pleaders, with other orators, who can speak in public extempore, often discover, in calling in- stantly to mind all the knowledge necessary on the present occasion, and every thing of im- portance which may have been advanced in the course of a long debate, such powers of reten- tion and recollection as, to the man who has never been obliged to exert himself in the same manner, are altogether astonishing. As habits, in order to be strong, must be formed in early life, the memories of children should therefore be constantly exercised ; but to oblige them to commit to memory what they do not under- stand, prevents their faculties, and gives them a dislike to learning. In a word, those who have most occasion for memory, as orators and pub- lic speakers, should not suffer it to lie idle, but constantly employ it in treasuring up and fre- quently reviving such things as may be of most importance to them ; for by these means, it will be more at their command, and they may place greater confidence in it on any emergency.* * The Idler. NATURAL PHILOSOPHY. 329 CHAPTER XL THE MECHANIC'S STUDIES CONTINUED. NATURAL PHILOSOPHY is commonly defined to be that art or science which considers the . powers and properties of natural bodies, and their mutual action on each other. Moral Philosophy relates to whatever concerns the mind and intellect ; Natural Philosophy, on the other hand, is only concerned with the material part of the creation. The moralist's business is to inquire into the nature of virtue, the causes and effects of vice, to propose remedies for it, and to point out the mode of attaining happiness. The naturalist, on the contrary, has nothing to do with spirit ; his business is confined to body or matter. The first and principal part of this science is to collect all the manifest and sensible appearances of things, and reduce them into a body of Natural History. Natural Philosophy differs from Natural History in its appropriated sense , the business of the latter is only to observe the appearance of natural bodies separately, and from these 330 THE YOUNG MECHANIC. appearances to class them with other bodies to which they are allied. Natural Philosophy goes farther, and recites the action of two or more bodies upon each other ; and though it can neither investigate nor point out the causes of those effects, whatever they be, yet from mathematical reasoning combined with expe- rience, it can be demonstrated, that in such cir- cumstances such effects must always take place Natural Philosophy, till lately, has been di- vided into four parts, commonly called the foui branches, viz. 1. Mechanics ; 2. Hydrostatics ; 3. Optics ; and 4. Astronomy ; and these again subdivided into many parts. Modem discove- ries have added, however, two more parts, viz., 1. Magnetism; 2. Electricity and Galvanism. Every one is acquainted with the benefits derived from the sciences of Mechanics, Hydrostatics, and Hydraulics, to which we are indebted for many useful inventions. Among these are wind and water mills, aqueducts, pumps, fire engines, steam engines, &c., &c. Pneumatics supply, even to a superficial en- quirer, much instruction and amusement. Sure- ly all are interested in the nature and properties of a fluid which is necessary to every moment of our existence. NATURAL PHILOSOPHY. 331 How great would have been the surprise of the ancients, could they have conceived the effects? which are now produced by the reflection and refraction of light I By a skilful management of these properties, telescopes, and various optical instruments are constructed. Objects too remote to be perceived by the naked eye, are enlarged and rendered visible. The satel- lites of Jupiter and Saturn, the mountains and cavities in the moon, and the changes which take place on the sun's disc, are thus discover- ed, and afford subject for admiration and in- quiry. Neither is the delightful scene of Optics confined to the contemplation of distant objects. Minute animals, the vessels of plants, and, in short, a new world in miniature is disclosed to our view by the microscope, and an inexhaus- tible fund of rational entertainment and know- ledge is brought within the spere of our senses. Of all the sciences to which geometry im- parts the solidity of its principles, and the clearness of its proofs, the most beautiful and the most sublime is Astronomy. This is per- haps the most exact and most definite part of natural philosophy : for it rectifies the errors of sight, with respect to the apparent motions of the planets ; explains the just dimensions. 332 THE YOUNG MECHANIC. relative distances, due order, and exact propor- tions of the spherical bodies, which compose the solar system. Nor is it even confined to these great objects of nature, since it opens the stupendous prospect of other suns, and other systems of planets, scattered over the bound- less fields of space, and moving in obedience to their respective laws. It marks out their particular places, assigns their various names, and classes all the systems of worlds in their respective constellations. The calculations of astronomy prove the certainty of the future phenomena of the heavenly bodies, when the eccentric comet will reappear, after having tra- versed the most distant regions of the heavens, or at ^hat point of time the bright luminaries of da^ and night will be immersed in the par- tial, or total darkness of an eclipse. CHEMISTRY. As soon as man begins to think, and to rea- son, the different objects which surround him on all sides naturally engage his attention. After being astonished at the wonders of the atmospheric and higher regions, he cannot fail k) be struck with the number, diversity, and beauty of those on earth, and naturally feels a CHEMISTRY 333 desire to be better acquainted with their proper- ties and uses. If he reflect also, that he him- self is altogether dependent on these objects, not merely for his pleasures and comforts, but for his very existence, this desire must become irresistible. Hence that curiosity, that eager thirst for knowledge, which animates and dis- tinguishes generous minds. As a science, chemistry is intimately con- nected with all the phenomena of nature j the causes of rain, snow, hail, dew, wind, earth- quakes ; even the changes of the seasons can never be explored with any chance of success while we are ignorant of chemistry : and the vegetation of plants, and some of the most im- portant functions of animals, have received all their illustration from the same source'. No study can give us more exalted ideas of the wisdom and goodness of the eternal cause than this. As an art, it is intimately connected with all our manufactures : the glass-blower, the potter, the smith, and every other worker in metals ; the tanner, the soap-maker, the dyer, the bleacher, are practical chemists ; and the most essential improvements have been intro- duced into all these arts by the progress which chemistry has made as a science. Agriculture 334 THE YOUNG MECHANIC. can only be improved rationally, and certainly, by calling in the assistance of chemistry ; and the advantages which medicine has derived from the same source, are too obvious to be pointed out.* NATURAL HISTORY. I am convinced, says Rousseau, that at all times of life, the study of nature abates the taste for frivolous amusements, prevents the tumult of the passions, and provides the mind with a nourishment which is salutary, by filling it with objects most worthy of its contempla tion. Of all the studies in which the minds o? youth may be employed, none, perhaps, deserve more strongly to be recommended, than thos* of natural history and physics. The object* on which they are occupied being such as com* under the Cognizance of our senses, they ar s more easily comprehended by the juvenile un derstanding, than the refinements of grammar or the abstract ideas of moral philosophy: p- the same time, they afford an inexhaustible fun^ of entertainment; and their great utility ir * Thomson's Chemistry. NATURAL HISTORY. 333 rvery situation in life is universally acknow- ledged.* It is the glorious privilege of man, while other animals are confined within the limits which instinct has prescribed, to carry his ob- servations beyond his own immediate wants, and to contemplate the universe at large. He extends his inquiries to all the objects which surround him ; exercises his judgment, and in- forms his understanding, by ascertaining their na&nre, properties, and uses. In the various branches of mathematics, in the abstract specu- lations of metaphysics, or in searching the re- cords of history, he is solely intent on the opera- tions of his own mind, or the actions of him- self and his fellow creatures : but in the study of nature, he examines every object presented to his senses, and takes a general survey of the wide and interesting prospect of the creation. The earth he treads, the ocean he crosses, the air he breathes, the starry heavens on which he gazes, the mines and caverns he explores, all present to him abundant materials for his re- searches. And, when thus employed, he is engaged in a manner peculiarly suitable to his * Preface to Pleasing Preceptor. 29 33n THE YOUNG MECHANIC. faculties, since he alone is capable of know- ledge, he alone is distinguished by the power of admiration, and exalted by the faculty of reason. The terraqueous globe presents a most glorious and most sublime prospect, equally worthy of the capacity of man to contemplate, and beautiful to his eye to behold. And the treasures of nature, which this prospect com- prehends, are so rich and inexhaustible, that they may furnish employment for his greatest di- ligence, stimulated by the most ardent curiosity and assisted by the most favourable opportuni- ties. At the same time that she solicits him to follow her, not only in her open walks, but likewise to explore her secret recesses, she fails not to reward him with the purest gratifications of the mind, because at every step he takes, new instances of beauty, variety, and perfection are unfolded to his view. The study of the works of nature is in itself capable of affording the most refined pleasure, and the most edifying instruction. All the ob- jects with which we are surrounded, the small- est as well as the greatest, teach us some useful lesson. All of them speak a language directed to man, and to man alone. Their evident ten- dency to some determined end, marks the de- NATURAL HISTORY. 337 sign of a great Creator. The volume of crea- tion contains the objects of arts, science, and philosophy, and is open to the inspection of all the inhabitants of the globe. Nature speaks by her works an universal language, the rudi- ments of which are peculiarly adapted to the inclination and capacity of the young, whose curiosity may be gratified and excited by turns ; but more profound and extensive inquiries are suitable to the contemplation of persons of every age ; and no subjects can be more worthy of their attentive observation.* A walk in the fields, after reading a little in natural history, may furnish opportunities of important instruction. The hills, the dales, and quarries afford matter of speculation on their formation, use, and beauty. And this may be rendered intelligible to a child, by a person who really understands the subject, and is not a mere pedant who has only committed techni- cal words to memory. So in all probability may every branch of real knowledge. Those branches which are now lost to common sense by calculations and mathematical processes, are not always, if they be ever understood by those * Mr. Kett's Elements. 338 THE YOUNG MECHANIC. who profess to understand them. Every thing which is not applicable to use, and the applica- tion of which cannot be made obvious to com- mon sense, is gothic jargon, and not science ; and people who glory in such acquisitions have not a clear and good idea of what constitutes real knowledge. This explains the problem, why, in the present state of learning, there are no plain, intelligible, and easy methods of teach- ing the sciences, and so few good elementary books. The reason is, that the sciences are not generally and thoroughly understood. Every man can easily teach another what he perfectly understands himself. But if half his terms be merely technical, and he can give no definitions of them which convey ideas, it is no wonder that learning is difficult, as it is always painful to commit to memory words which have no meaning ; and all the progress made upon such foundations is ever attended with that anxiety and anguish, which have so strongly marked the countenances of our philosophers. In the same manner as the general truths of natural history might be occasionally exemplified in the fields, many of the mathematic, astronomic, and particularly the mechanic problems, rnigh* be examined in a walk. This would not only XATURAL HISTORY. 6e ^esent instruction, but bring the pupil into a habit of having an object and a view in every action. He would not then experience the common unhappiness of not knowing what to do with himself; or when he has determined on a walk or a ride, be miserable for want of being able to determine where to gv or with what object to engage his thoughts * 340 THE YOUNG MECHANIC. CHAPTER XII. THE MECHANIC'S STUDIES CONTINUED HISTORY. CURIOSITY is one of the strongest and most active principles of human nature. Through- out the successive stages of life, it seeks with avidity for those gratifications, which are con- genial with the different faculties of the mind. The child, as soon as the imagination begins to open, eagerly listens to the tales of his nurse : the youth, at a time of life, when the love of what is new and uncommon is quickened by sensibility, is enchanted by the magic of ro- mances and novels : the man, whose mature judgment inclines him to the pursuit of truth, applies to genuine history, which even in old age continues to be a favourite object of his at- tention ; since his desire to be acquainted with the transactions of others has nearly an equal power over his mind with the propensity to relate what has happened to himself History, considered with respect to the nature of its subjects, may be divided kito general and HISTORY. 34] particular ; and with respect to time, into an- cient and modern. Ancient history commences with the creation, and extends to the reign of Charlemagne, in the year of our Lord 800. Modern history, beginning with that period, reaches down to the present times. General history relates to nations and public affairs, and may be subdivided into sacred, ecclesiastical, and profane. Biography, memoirs, and letters, constitute particular history. Statistics refer to the present condition of nations. Geography and Chronology are important aids, and give order, regularity and clearness to them all. To draw the line of proper distinction be- tween authentic and fabulous history, is the first object of the discerning reader. Let him not burden his memory with events which ought perhaps to pass for fables ; let him not fatigue his attention with the progress of em- pires, or the succession of kings, which are thrown back into the remotest ages. He will find that little dependence is to be placed upon the relations of those affairs in the Pagan world, which precede the invention of letters, and were built upon mere oral tradition. Let him leave the dynasties of the Egyptian kings, the expeditions of Sesostris, Bacchus, and Jason, 342 THE YOUNG MECHANIC. and the exploits of Hercules and Theseus, for poets to embellish, or chronologists to arrange. The fabulous accounts of these heroes of anti- quity may remind him of the sandy deserts, lofty mountains, and frozen oceans, which are laid down in the maps of the ancient geogra- phers, to conceal their ignorance of remote countries. Let him hasten to firm ground, where he may safely stand, and behold the striking events, and memorable actions, which the light of authentic records display to his view. They alone are amply sufficient to en- rich his memory, and to point out to him well attested examples of all that is magnanimous, as well as of ail that is vile ; of all that debases, and all that ennobles mankind.* Unfortunately the study of history is not without its dangers and inconveniences of va- rious kinds. It is a very difficult matter to place one's self in such a point of view as to be able to judge equitably of our fellow crea- tures. It is one of the common vices of his- tory to paint man in a disadvantageous rather than in a favourable light. Revolutions and fatal catastrophes being most interesting, so long as a people have continued to increase and * Mr. Kelt's Elements. HISTORY 343 prosper in the calm of a peaceable government history has remained silent ; it speaks of na- tions only when, growing insupportable to themselves, they begin to interfere with their neighbours, or to suffer their neighbours to in- terfere with them. We are favoured with very exact accounts of those nations which verge towards destruction ; but of those which have been flourishing, we have no history; they have been so wise and happy as to furnish no events worth recording. The historical rela- tions of facts which we meet with, are by no means accurate delineations ; they change their aspect in the brain of the historian, they bend to his interest, and are tinctured by his preju- dices. What historian ever brought his reader to the scene of action, and laid the event cir cumstantially as it happened ? Ignorance and partiality disguise every thing. How easy it is to give a thousand varied appearances to the same facts, merely by a difference in the repre- sentation of circumstances. Exhibit an object in different points of view, and we scarcely be- lieve it to be the same, and yet nothing is changed, except the eye of the spectator., How often has it happened that a few trees, a hill on the right or left, or a sudden cloud of dust, 344 THE YOUNG MECHANIC. have turned the scale of victory, without the cause first being perceived ? Nevertheless the historian will assign a reason for the victory or defeat with as much confidence as if he had been at the same instant in every part of the battle. The worst historians, for a young reader, are those who favour us with their judg- ment. A plain narrative of facts is all he wants : let him judge for himself, and he will learn to know mankind. If he be constantly guided by an author's opinion, he sees only with the eyes of another; and when these are taken from him he does not see at all. History is generally defective in recording only those facts which are rendered conspicuous by name, place, or date ; but the slow progressive causes of those facts, not being thus distinguished, remain for ever unknown. A madness for party having possession of them all, they never endeavour to see things as they really are, but as they best agree with their favourite hypotheses.* It is the business of history to distinguish between the miraculous and marvellous; to reject the first in all narrations merely profane and human ; to scruple the second ; and when * Rousseau, b. iv. HISTORY. 345 obliged by undoubted testimony to admit of something extraordinary, to receive as little ot it as is consistent with the known facts and circumstances.* In undertaking a course of history, it is cer- tainly of great advantage to follow the chrono- logical order of events. You have then the gradual progress of man from barbarism to refinement; from refinement to corruption, ve- nality, and slavery ; from slavery back again to darkness and ignorance ; and from this state again to knowledge, civilization, and liberty. The most ancient history, except the Bible, is Herodotus ; and no history was ever more de- lightful for its simplicity, perspicuity, the un- affected style of the narrative, and easy and harmonious flow of the language. Mr. Beloe's translation, though not elegant, partakes in some measure, of the simplicity of the original. The history of Thucydides takes not so wide a scope as that of Herodotus, but the period which he describes is interesting, and his man- ner is incomparable. Smith's translation is tolerably good, and even that of Hobbes may be read without disgust. A more connected *Hume. 346 THE YOUNG MECHANIC view of ancient history may be learnt from Rollin. The Ancient Universal History is an excellent and elaborate compilation, but it is tedious, and the style is dry and inharmonious : it is a book therefore rather for reference than study. The indefatigable Dr. Mavor has pro- duced an abridgment of this work, with addi tions, to the year 1802, in 25 volumes, 18mo Of the Roman historians there is a deplorable dearth of good translations. The order in which they may be read is Livy, Sallust, Ca3sar. The Epistles of Cicero are chiefly historical, which are admirably translated by Mr. Mel- moth. Plutarch's Lives should be read imme- diately after the Greek and Latin historians, or rather in conjunction with them : a good trans- lation has been done by the brothers Lang- horne. Of modern works, Vertot's Roman Revolutions, Montesquieu's Greatness and De- cline of the Romans, and Dr. Middleton's in- comparable Life of Cicero, may be read with the ancient historians. The last is a produc- tion of original genius, and yet comprises all which is most excellent in the writings of the great man whose life it narrates. The Anabasis of Xenophon, and the history of Polybius are most interesting and engaging books ; of the HISTORY. 347 latter there is a translation by Hampton. Of the English compilations which contain the history of the Roman commonwealth, Fergu- son's is preferable to Hook's. Suetonius's His- tory of the Twelve Caesars is an ill-written book, yet it contains facts which are not to be found in any other original author. Tacitus is a treasure, not merely on account of the his- torical matter which it contains, but for the mass of moral instruction which it conveys. Murphy's translation may be pronounced supe- rior to Gordon's. After finishing Tacitus, we must, of necessity, have recourse to compila- tion. Mr. Gibbon takes up the subject where Tacitus left it, and certainly a nobler monu- ment of genius was never erected, than the " Decline and Fall of the Roman Empire ;" a narrative which extends to so modern a period, that a few books will serve to unite the chain of history with that of our own country. Dr. Robertson's Charles the Fifth is perhaps the most perfect historical composition in the En- glish language ; and Dr. Watson's history is well connected with it ; both of which relate to some of the most important events recorded in history, the reformation of religion, and the establishment of the Batavian republic. Mr. 30 348 THE YOUNG MECHANIC Wraxall has filled up a chasm on the historical shelf, by his agreeable history of France yet the student should not satisfy himself with that author's account of the age of Henry the Great, but inspect for himself the interesting and un- blemished pages of Sully ; and there are few scholars who will not find exquisite pleasure in the general history of the correct De Thou. Vertot's Revolutions of Sweden and of Portu- gal, are both of them animated narratives of important events. Voltaire's Age of Louis the fourteenth and fifteenth, may be classed among original histories, though not of the first rank ; his Charles the Twelfth borders much on the romance. Dr. Robertson's History of Ameiica is a much admired composition. After such a course of reading, the student will not be ill prepared for the history of his own country. Hume's History is a bad compilation. Hume is, moreover, the avowed enemy of the two principles which conduce; most to ihe happiness of mankind, ^eligion ana liberty; and he who makes him t'ue fciandard of his historical faith, will embrace numerous errors, arising not merely trom design but from negligence. As a general history, Rapin's is preferable ; and if the state papers be passed over, it will not be HISTORY. 349 'bund more voluminous than Hume. Perhaps a better course of English historical reading would be to take Dr. Henry's History for the early periods ; from the conclusion of which he may proceed with Rapin to the date of Cla- rendon's History ; and, for the affairs of Scot- land, having recourse to the classical narrative of George Buchannan, and the elegant history of Queen Mary, by the accomplished Robert- son. Clarendon's History, with his life, are invaluable records ; but his statements will, in some instances, be corrected by Whitlock's Memorials, which every student of history ought to read, and by the plain and manly, but interesting Memoirs of the ill-treated Ludlow. Though Bishop Burnet's egotisms have been ridiculed by Pope, Arbuthnot and Swift, yet he will continue to be read by every one who wishes to inform himself correctly of the man- ners and circumstances of the times in which that excellent prelate and really candid writer lived. Mrs. Macaulay's history evidently fa- vours republicanism, but her narrative is pure, and she is scrupulously exact in producing evi- dence and authority for all her facts. The student of history should always read with a map of the country before him. A good 350 THE YOUNG MECHANIC. Biographical Dictionary is also an useful com- panion in the study of history. Various plans have been recommended for connecting history with chronology in the mind ; the best method is perhaps to endeavour to fix in the memory the dates of some of the most remarkable events. The intermediate transactions will generally be found to have some link of association with the great events, and it will not be difficult to decide nearly on the date of any of them. There is, however, no better aid to the memo- ry than Dr. Priestley's Historical Chart.* On English History, the late Earl of Chatham thus wrote to his nephew. tt If you have finished the abridgment of English History and of Burnet's History of the Reformation, I recommend to you next, before any other read- ing of history, Oldcas tie's Remarks on the His- tory of England, by Lord Bolingbroke. Let me apprise you of one thing before you read them, and that is, that the author has bent some passages to make them invidious parallels to the times he wrote in; therefore be aware of that, and depend, in general, on finding the truest constitutional doctrines; and that the * Mon. Mag. May, 1797. HISTORY. 351 facts of history, though warped, are no where falsified. I also recommend Nathaniel Bacon's Historical and Political Observations ; it is without exception, the best and most instruc- tive book we have on matters of that kind They are both to be read with attention, and twice over ; Oldcastle s Remarks to be studied and almost got by heart, for the inimitable beauty of the style, as well as the matter. Ba- con for the matter chiefly, the style being un- couth, but the expression forcible and striking. " I desired you sometime since to read Cla- rendon's History of the Civil Wars. I have lately read a much honester and more instruc- tive book, of the same period of history ; it is the History of the Parliament, by Thomas May, Esq. If you have not read Burnet's His- tory of his Own Times, 1 beg you will. " I suppose you are going through the bio- graphers, from Edward the Fourth downwards, nor intending to stop till you reach to the con- tinuator of honest Kapin. There is a little book which 1 never mentioned, Welwood's Me- moirs ; I recommend it. Davis's Ireland must not on any account be omitted ; it is a great performance, a masterly work, and contains much depth and extensive knowledge in state 352 THE YOUNG MECHANIC. matters, and settling of countries, in a very short compass. I have met with a scheme of chronology by Blair, showing all contemporary historical characters, through all ages : it is of great use to consult frequently, in order to fix periods, and throw collateral light upon any particular branch you are reading.^* Such is the recommendation of { Chatham, a first rate authority. Among the historical works produced in our own country, Bancroft's History of the United States, 3 vols. 8vo., is entertaining and carefully written ; but it only brings the history down to a period shortly before the commencement of the Revolution. Frost's History of the United States, written for schools, brings it down to the year 1836. Prescott's Ferdinand and Isa- bella, and Irving's Columbus are delightful to read, and of the highest authority. BIOGRAPHY. Biography* is a highly important branch of history. The biographer, by his accurate re- searches, supplies the deficiencies of the histo- rian. What the latter gives us only in outlines Letters, passim. BIOGRAPHY. 353 and sketches, the former presents in more com- plete and highly finished portraits. Their pro- vince does not merely extend to those who have acted upon the great theatre of the world, as sovereigns, statesmen, and warriors ; but to all who have improved human life by their useful discoveries, adorned it by their works of genius, and edified mankind by their exam- ples. With what pleasure do we select a Ba- con, a Boyle, a Newton, an Addison, a Locke, a Radcliffe, a Howard and a Hanway, from the multitudes which surround them, and become acquainted with their particular characters and conduct ! To contemplate such men, not in- flamed by vain ambition, or courting empty popularity, but seeking retirement, and giving dignity to the walks of private life by the efforts of genius, and the exertions of philanthropy, is a high gratification to the mind, and inspires it with an admiration and a love of those vir- tues, which come within the reach of general imitation. No species of writing gives a more perfect insight into the minds of men, than their let- ters. We observe them as they thought in their retired moments, when, withdrawn from the bustle of the world, they a ave free scope to 35 i THE YOUNG MECHANIC. their unrestrained opinions, and poured them without reserve, into the bosom of their friends. Among the numerous instances, which might hr selected of epistolary excellence, we distin- guish the letters of Cicero, which display the sentiments of a vigorous mind, and give an in- sight into the eminent characters of his event- ful times. Pliny, in letters remarkable for neat- ness and precision of thought, expresses the dictates of a cultivated and generous mind. If we turn our attention to the epistolary litera- ture of our own country, we shall find that the piety and affection of Lady Russel, the quaint- ness and pleasantry of Howel, the manliness and political sagacity of Stafford, the philoso- phical exactness and cool judgment of Locke, the simplicity of Rundle, the moralizing vein of Johnson, and the taste and elegance of Gray, mark their respective letters with the strongest characters of originality, and give us the most pleasing pictures of their minds.* Besides the names above enumerated by Mr. Kett, the following may be added, as justly celebrated letter writers, viz. : Pope, Swift, Ad dison, Steele, Arbuthnot, Gay, Shenstone, Sterne, * Mr. Kett's Elements. BIOGRAPHY. 355 Lyttleton, Lady Mary Wortley Montague, Rich- ardson, Chesterfield, Cowper, Sevigny, Mainte- non, Burns, Lord Byron, and Horace Walpole. Biography is, in general, a most pleasing as well as instructive branch of literature. When faithfully written it unveils man to man ; dis- covers the virtues and vices, the nobleness and meanness of which he is capable ; and shows how the original sameness of human nature is varied by the operation of external causes into ten thousand different shapes, and assumes as many shades and hues. Man, to be known, must be viewed in every situation ; and when- ever he is fairly exhibited, whatever may have been his rank, station, or circumstances of birth or fortune, a valuable addition is made to sci- ence. Whether the record respects the strug- gles of talents and worth through the chilling regions of obscurity and penury, up to the glittering eminences of fame and reward ; or whether it details the operations of pride and ambition on minds born to wealth and power ; it presents an useful lesson, which those who are disposed to exertion and virtue will not read in vain.* * Mon. Rev. 30* 358 THE YOUNG MECHANIC. J would begin the study of the human heart, says Rousseau, by reading the lives of particu- lar men ; for there the hero conceals not him- self for a moment. The biographer pursues him into the most secret recesses, and exposes him to the piercing eye of the spectator ; he is best known when he believes himself most concealed. I confess the genius of a people is very different from that of man considered as an individual, and that we shall be imperfectly acquainted with mankind if' we neglect the study of the multitude ; but it is also true, that we must begin by studying man in order to know mankind ; and that if we know the pro- pensities of each individual it will not be diffi- cult to foresee their effects when combined in the body of the people. The lives of kings may be written and rewritten, but we shall never see another Suetonius. Plutarch's excel- lence consists chiefly in those very minutia3 into which we dare not enter. There is an inimitable gracefulness in his manner of paint- ing great men engaged in trivial employments, and he is so happy in the choice of his inci- dents, that frequently a single word, a smile, a gesture, is- sufficient to characterize his hero. Marshal Turenne was incontestably one of the BIOGRAPHY. 357 greatest men of the age in which he lived. The writer of his life has had the resolution to ren- der it interesting by relating some minute par- ticulars which make his hero known and be- loved ; but how many was he obliged to sup- press, which would have taught us to know and love him still more! I shall instance one which I had from good authority, and which Plutarch would by no means have omitted, but which Ramsay, if he had known it, would not have dared to relate. The Marshal happened, one hot day, to be looking out at the window of his antichamber in a white waistcoat and night cap. A servant entering the room, was deceived by his dress, and mistook him for one of his under cooks. He crept softly behind him, and gave him a violent slap on the breech. The Marshal instantly turned about, and the fellow, frightened out of his senses, beheld the face of his master : down he fell on his knees. " Oh ! my lord ! I thought it was George !" " And suppose it had been George,* 5 replied the Marshal, rubbing his back, " you ought ot to have struck quite so hard." There are few people capable of conceiving the effect which reading, thus directed, would have on youoig minds. 358 TJIE YOUNG MECHANIC. The " American Biography" of Mr. Sparks, in ten volumes, is a work of great merit. Jt foims a part of Harper's School Library, in which may be found many other biographical works of our own countrymen as well as of distinguished foreigner*. ACCOMPLISHMENTS IN GENERAL. 359 CHAPTER XIII. THE MECHANIC'S STUDIES CONTINUED. ACCOMPLISHMENTS IN GENERAL. A PROPER degree of attention should always be paid to what are called the accomplishments of life, but they should never supersede for a moment more useful studies. Every occupa- tion should be estimated according to its future utility, and as those points which are deemed essential to the demeanour of a gentleman should not be neglected, and demand but a small portion of time to acquire, a pupil should be early and properly attended by the best masters in the several departments of drawing, music, horsemanship, and dancing. These ac- complishments, and the art of swimming, give a suppleness to the limbs, a grace of action, and an elegance of address and fine taste which always obtain the favourable preposses- sion of the company to whom a person may be introduced ; but talents and virtues complete the conquest of affection, and convert the pass- THE YOUNG MECHANIC. ing applause of the human race into a solid and durable esteem. A copious selection., says Mr. Yorke, from the excellent letters of Lord Chesterfield to his son, are always before my pupil, which inspire him with a laudable desire of uniting to the character of a man of knowledge, the accom- plishments of a gentleman. The object of in- struction is to make men better, not to embrute them. Whatever, therefore, is deemed auxiliary to such a disposition, should be encouraged. No evil can arise from an easy address, or from agreeable manners. Politeness is the handmaid of civilization ; perhaps it may be shown to be the attendant on virtue. Whatever means, therefore, are judged expedient to furnish the opportunity of exhibiting this amiable quality, are commendable, and ought to be adopted. I allude, in this instance, to genuine politeness, not to that false affectation of good manners^ which consists in foppery and a servile imitation of the servile manners of the great, and of men of honour, as, by a strange perversion of lan- guage, they are improperly called. The term great man, is so equivocal, says Dr. Beattie, that I will have nothing to do with it. The vilest scoundrel on earth, if possessed of a ACCOMPLISHMENTS IN GENERAL. QQ^ crown or a title, immediately commences great man, when he has with impunity perpetrated any extraordinary act of wickedness ; murder- ed fifty thousand men, robbed all the houses in half a dozen provinces, or dexterously plun- dered his own country to defray the expense of a ruinous war, formed to satiate his avarice. The term honour is also of dubious import According to the notions of the present times, a man may sell his country, murder his friend, pick the pocket of his fellow sharper, and em- ploy his whole life in seducing others to vice and perdition, and yet be accounted a man of honour ; provided he be accustomed to speak certain words, wear certain clothes, and haunt certain company. To the pernicious influence of this unnatural law of honour the just senti- ments of Archdeacon Paley may be applied. " It is a law," says he, " which, being consti- tuted by men occupied in the pursuit of plea- sure, and for the mutual convenience of such men, will be found, as might be expected from the character and design of the law makers, to be, in most instances, favourable to the licen- tious indulgence of the natural passions. Thus, it allows of fornication, adultery, drunkenness, prodigality, duelling, and revenge in the ^x- 3(32 THE YOUNG MECHANIC. treme ; and lays no stress upon the virtues op- posite to these." If any additional supports were necessary in behalf of the argument that bodily accom- plishments may be considered as a component part of the happiness and perfection of man, we might introduce the powerful authorities of Mr. Locke and Dr. Watts, who have applauded this mode of instruction, when limited to such views. The latter was a man of singular piety, modesty, and uprightness ; the former was as much distinguished for the elegance of his manners, as for his knowledge of the world, and his deep insight into the powers of the human mind. TASTE. Taste is that power, which the mind pos- sesses, of relishing the beauties found in the works of nature and art. Say what is Taste, but the internal powers, Active and strong, and feelingly alive To each fine impulse 1 a discerning sense, Of decent and sublime, with quick disgust From th : igs deform'd. It has beeu alleged that Taste is a natural taleni as independent of art as strong eyes, or a deli TASTE. 363 cate sense of smelling ; and, without all doubt^ the principal ingredient in the composition of taste is a natural sensibility, without which it cannot exist ; but it differs from the senses in this particular, that they are finished by nature ; whereas taste cannot be brought to perfection without proper cultivation : for taste pretends to judge not only of nature, but also of art; and that judgment is founded upon observation and comparison. Though nature should have done her part, by implanting the seeds of taste, great pains must be taken, and great skill exerted, in raising them to a proper pitch of vegetation. The judicious tutor must gradually and tenderly unfold the mental faculties of the youth com- mitted to his charge. He must cherish his delicate perception ; store his mind with proper ideas ; point out the different channels of ob- servation ; teach him to compare objects ; to establish the limits of right and wrong, of truth and falsehood ; to distinguish beauty from tin- sel, and grace from affectation ; in a word, to strengthen and improve by culture, experience, and instruction, those natural powers of sensi- bility and sagacity, which constitute the faculty 31 36 i THE YCUNG MECHANIC. called taste, and enable the possessor to enjoy the delights of elegant learning.* I do not call taste a species of judgment, although it be actually that part of judgment, whose objects are the sublime, beautiful and affecting ; because this kind of judgment is not the result of reason and comparison, like a mathematical inference, but is perceived instan- taneously, and obtruded on the mind, like sweet and bitter on the sense, from which analogy it has borrowed the name of taste.f Taste presides with supreme authority over all the elegant arts. There are none so low in their subserviency to the uses of mankind, as not to afford subjects for its decisions. It ex- tends its influence to dress, furniture, and equip- age ; but presides, as in its most distinguished and eminent provinces, over poetry, eloquence, painting, architecture, sculpture, and music ; because among them genius takes its unbound- ed range, ant 1 exerts its fullest power. Taste is derived from the concurrent voices of men of various ages and nations, possessed of en- larged and cultivatedfcunderstandings, who have lurveyed the works of genius with close atten- * Goldsmith. f Usher's C li o. TASTE. don, and have recorded in animated descriptions the impressions made upon their minds. This authority has stamped its approbation upon works which have obtained the general ap- plause of all ages and countries, and must still continue to produce a similar effect, so long as the intellectual powers of man remain the same; so long as his imagination and sensibility are capable of being affected by all which is beau tiful, pathethic and niblime. The advance of national taste is similar to the progress of taste from childhood to man- hood. When the attention of an unpolished people is first directed to works of art, they are captivated by mere novelty ; and the rudest paintings and most unpolished verses obtain their applause. In proportion as superior efforts of genius are made, the opinion of the judi- cious part of the public, at least, becomes more correct; and what at first delighted is finally rejected with disapprobation. As soon as comparisons are made between different pro- ductions of the same kind, true taste is brought into action, its decisions are called for, and the justness of its discriminations is universally acknowledged. The polished contemporaries of Horace blushed at the praises which their 366 THE YOUNG MECHANIC. ancestors had bestowed on the rude dialogues of Plautus, and were charmed with the polite and elegant comedies of Terence. The lower orders of society are disqualified from deciding on the merits of the fine arts ; and the department of taste is consequently confined to persons enlightened by education, and conversant with the world, whose views of nature, art, and mankind, are enlarged by an extensive range of observation, and elevated far above gross ignorance and vulgar prejudice.* The general rudiments of taste are to be ac- quired first by reading books, which treat pro- fessedly on the subject. Secondly, by select- ing and explaining beautiful passages in Shaks- peare, Johnson, Sterne, &c. And lastly, by exhi- biting and explaining prints of beautiful objects, or casts of the best antique gems and meda- lions. Authors have divided the objects of taste into the sublime, the beautiful, and the new; but another sect of inquirers into this subject have lately added the picturesque ; which is supposed to differ from the beautiful by its want of smoothness, and from the sublime, from its want of size.f * Mr. H. Kett. fSee Essay on the Picturesque, by U. Price, Esq. TASTE. 367 Others have endeavoured to make a distinc- tion between beauty and grace, and have e teemed them a kind of rivals for the possession of the human heart. By grace may be defined beauty in action ; for a sleeping beauty cannot be called graceful, in whatever attitude she may recline ; the muscles must be in action to pro- duce a gracefrl attitude, and the limbs to pro- duce a graceful motion.* Taste, says Lord Kaimes, is one of our facu 1 ties which is the slowest in its progress toward- maturity ; and yet may receive some improve- ment during the course of domestic education. Compare with your pupils two poems on the same subject, or two passages. Take the lead in pointing out beauties and blemishes, in the sim- plest manner. Aft^r so me time, let them take the lead under your correction. You cannot have a better book for that exercise than the Spectator. A pleasing vein of genteel humour runs through every one of Addison's papers, which like the sweet flavour of a hyacinth, constantly cheers, and never overpowers. Steele's papers, on the contrary, are little better than trash ; there is scarcely a thought or sentiment which is worthy * Dr. Darwin's Plan of Education. 368 THE YOUNG MECHANIC to be transferred into a common-place book. My pupil reads a few papers daily without a single observation on my part. After some time, I remark to him the difference of compo- sition, which, in the course of reading, becomes more and more apparent. The last step is to engage him in distinguishing the two authors. He at first made awkward attempts ; from fre- quent trials, he began to distinguish. Now he will almost in the first period cry, " Foh ! this is Steele, let us have no more of him." If we wish to be directed to authors, who were eminent for correctness of taste, we may select in painting Fresnoy, Vasari, and Rey- nolds ; in music, Burney ; in eloquence, Cicero and Quintilian ; and in poetry, Horace, Pope, Gray, and the Wartons. These were critics, who had the singular merit of teaching that art in which they were themselves distinguished ; and their own works are an example and an illustration of their rules.* It is no wonder that wholly uneducated people want elegance and taste. It is not from them that we are to seek the natural bias of the soul The necessaries of life, when they are to be * Mr. H. Kett's Elements. DRAWING. procured by an individual for a wife and nume- rous young children are procured by vast la- bour and hardship. Labour requires strained, forced, and violent motions. This race of men walk not for pleasure, but to perform journeys of necessity. They take advantage therefore of bending the body forward, and assisting their motion by a sling with their arms. Their low station, their wants, and their drudgeries, give them a sordidness and ungenerosity of disposi- tion, together with a coarseness and nakedness of expression ; whence their motions and ad- dress are equally rude and ungraceful. This dishonoured state of man is the offspring of his wants, and of the miseries which yoke him down a slave to the globe which he tills, and depress together his mind and his body.* DRAWING. Drawing is not only an accomplishment the -nost elegant, agreeable, and ornamental, but, at the same time that it is the foundation of paint- ing, is of the utmost utility to the sculptor,, the civil and naval architect, the engraver, the en- gineer, the mathematician, and navigator. It Clio. 370 TfIE ^*>UNG MECHANIC. also assists the gardener, the cabinet maker, thr weaver, &,c. In short, there is scarcely a branch of civil society which is not indebted to it, from the maker of the iron rails before our house, to the tea urn on our table. To it we are indebt- ed for representations of those elegant remains of antiquity which have contributed so much to the advancement of our knowledge of fine form. Volumes of verbal description will not convey so true an idea of an object, as the slightest outline. Hence the source of much of our knowledge in antiquity, of which Ian guage could convey no adequate idea. To be able on the spot to make a sketch of a fine building, beautiful prospect, or any curious pro- duction of nature or of art, is not only a very desirable and elegant accomplishment, but in the highest degree entertaining. To treasure up whatever may occur in our travels, either for future use or to illustrate conversation, to represent the deeds of former ages, to preserve the features of our most valued friends, has made this art not only one of the highest em- bellishments of our nature, but the delight of $11 ages. The greatest writers have united to praise, and empires to encourage it. It has been in the highest degree morally useful ; and DRAWING. 37j where it has flourished, conferred honour on the country.* It is impossible to judge accurate! y of the dimensions of bodies, unless we learn also to know their figures, and even to imitate those figures ; for this imitation is founded on nothing else but the rules of perspective, and we can- not estimate the extension of bodies by their appearance, unless we have some knowledge of those rules. Children, being great imitators, all attempt to design ; I will have my pupil, says Rousseau, cultivate that art ; not so much for the art itself, as for the sake of giving him a good eye and a flexible hand. I will take care that he shall rarely imitate imitations. He should have before his eyes the original itself, and not the paper representing it. Thus he should design a house from a house, a tree from a tree, a man from a man, that he may be ac- customed to observe minutely and accurately the appearance of bodies, and not take false and artificial imitations for those which are true and genuine. I would even discourage him from endeavouring to trace any tiling from memory, till by frequent and repeated observations, its * Mr. E. Dayes in Mr. Tilloch's Philosop. Mag. vol Xiv. 219. 372 THE YOUNG MECHANIC. figure should be strongly imprinted on his imagination ; lest he should otherwise, by sub- stituting some fantastic image instead of the real one, lose the knowledge of proportion, and a taste for the genuine beauties of nature. If my pupil wishes to become a painter, he does not commence his career by a dry study of lines ; he does not " imitate imitations ;" he paints from nature. At the same time, that he may not lose the advantages derived from the labours of past ages, he submits his productions to a master of the art, who may correct his errors and accelerate his improvement. So in electricity, chemistry, &c., he begins by experi- ment, under the eye of a master, and thence either deduces his own general rules, or con- firms those of others.* MUSIC. Music may be considered one of the most usefal means which we possess of improving and cultivating the mind of man, and by far the most powerful in softening the heart, and ren- dering it susceptible of every fine and more Baited sentiment. Nor can music be called * * Northmore. MUSIC. 373 merely an art calculated to please and delight he senses alone, for certainly its execution employs the mind much more than the body. To instance the many surprising effects pro- duced by music over the minds of men, even the most rude and barbarous, would be super- fluous and impertinent. The delight which music imparts to the mind, can be enjoyed in every period of life, from the earliest infancy to the total decay of all vital powers. No art affording so much felicity and happiness can be so easily cultivated and attained. The in- fluence of this part of education over the mind of the female sex, must be, and certainly is, highly beneficial. Their hearts are hence in a particular manner cultivated and refined, and those sensations are exercised and strengthened in their bosoms, which render them peculiarly lovely and amiable. Many females, however, are entirely deprived of the advantages result- ing from this part of education. It is sincerely to be lamented and regretted, that the truly respectable sect of Quakers should forbid the cultivation and practice of music in their societies; and it is wonderful that the effects which already have resulted from this prohibition, have not yet convinced them of the 374 TIIE YOUNG MECHANIC. impropriety and pernicious tendency of their unreasonable prejudice against music. Such indeed are the effects produced by the total neglect of this divine art among the society of Friends, that the tones of their voice in reading and public speaking are so harsh and discordant as scarcely to be endured by a person of a nice and delicate musical ear. The worship of the catholic church, and that of the quakers, are in this respect as opposite as possible. The catholics chant their worship, and its influence is thereby augmented. The bravery and independence of the Swiss *e universally known, and in no people, per- haps, is the influence of pathetic music so pow- erfully exerted. The inhabitants of many other mountainous countries afford striking examples of the same kind. No people are more pos- sessed of true independence of mind than the inhabitants of the Highlands of Scotland, and in no country are the softer sensibilities of the heart more cultivated and indulged. I have never yet known an instance of a person capa- ble of enjoying all the ecstacy of musical de- light whose heart was not warm, tender and benevolent.* * Dr. Cowan. DANCING. 375 DANCING. The design of this accomplishment is to ob- tain a graceful carriage, and a pleasing address on all occasions. It has been said, that " no person can either sit, stand, or walk well, un- less he dances well." This is certainly carry- ing tJie matter too far. There are some who never so much as learned a step, who both sit, stand., and walk with more grace than some professed dancing masters. This art, however, frequently teaches young people to walk with firmness and ease, to enter a room gracefully, to incline the head or body, even when sitting and conversing, without any distortion ; and removes that awkward stiffness, which in country people who have not had the advan- tages of a good education, is so apparent. To obtain great perfection in this art, though it be necessary for professional performers, would be a shameful waste of time, which might be infi- nitely better employed in mental attainments. POLITENESS. There is a fascinating manner in the address of some people, which almostly instantly con- ciliates the good- will, and even the confidence 32 376 THE YOUNG MECHANIC. of their acquaintance. Machiavel in his his- tory of Castruccio Castricani observes, that his hero could assume such openness of counte- nance, that though he was known to be a man practised in every art of fraud and treachery, yet in a few minutes he gained the confidence of all whom he conversed with; they went away satisfied of his good will towards them, and were betrayed to their ruin. This enviable address, which may be used for good purposes as well as bad ones, is difficult to analyse ; it may possibly consist simply in a countenance animated with pleasure at meeting and con- versing with our acquaintance ; and which dif- fuses cheerfulness by pleasurable contagion into the bosoms of others ; and thus interests them in our behalf. It is net the smile of flat- tery, nor the smile of self-approbation, nor the smile of habit, nor of levity ; but it is simply an expression of pleasure, which seems to arise at the sight of our acquaintance; and which persuades them, that they possess our love, for which they barter their own in return. How- ever this conciliating manner may have beer used, as above related, for bad purposes, it pro bably proceeded originally from friendliness %nd openness of heart, with cheerful benevo POLITENESS. 377 lence ; and that in those, who have in process of time become bad characters, the appearance of those virtues has remained, after the reality of them lias vanished. What then is the method by which this enchantment of countenance can be taught ? Certainly by instilling cheerfulness and benevolence into the minds of young peo- ple early in life, and at the same time an anima- tion of countenance in expressing them ; and though this pleasurable animation be at nrst only copied, it will in time have the appearance of being natural ; and will contribute to pro- duce, by association, the very cheerfulness and benevolence, which it at first only imitated. This is an observation to which those who have the care of young children should closely attend. Next to the winning manners above described, the art of pleasing in conversation seems to consist in two things ; one of them to hear well, and the other to speak well. The per- petual appearance of attention, and the varying expression of the countenance of the hearer to the sentiments or passion of the speaker, is a principal charm in conversation; to be well heard and accurately understood encourages our companions to proceed with pleasure, what- ever may be the topics of their discourse. 378 THE UNG MECHANIC. To speak agreeably, in respect to manner, consists in a voice clear, yet not loud ; soft, yet not plaintive ; with distinct articulation, and with graceful attitudes rather than with graceful actions ; as -almost every kind of gesticulation is disagreeable. In respect to the matter, it should be such as coincides with the tastes or pursuits of those to whom the conversation is addressed. Hence it will appear that to hear well, and to speak well, requires an extensive knowledge of things, as well as of the tastes and pursuits of mankind ; and must therefore ultimately be the effect of a good education in general, rather than a particular article of it. There are, however, faults to be avoided, and cautions to be observed, which should be point- ed out to young people. Of these I shall, men- tion, 1. That whenever the thirst of shining in conversation seizes on the heart, the vanity of the speaker becomes apparent ; and we are disgusted with the manner, whatever may be the matter of the discourse. 2. That it is always childish, and generally ridiculous, when young people boast of their follies, or when they accuse themselves of virtues. 3. They should be apprised, that there is danger in speaking ill even of a bad person ; both be- POLITENESS. 379 cause they may have been misinformed, and because they should judge their neighbours with charity. A friend of mine was once asked how he could distinguish whether the lady, whom he meant to address, was good temper- ed, and gave this answer : " When any dubious accusation is brought in conversation against an absent person , if she always inclines to believe the worst side of the question, she is ill tempered." There are some nice distinc- tions on this subject of good nature in Lady Pennington's Advice to her Daughters, whicb are worth the attention of young ladies. 4 Strong asseverations, or a kind of petty oaths, such as upon my honour ;" appealing to others for the truth of an affirmation ; an always wrong, because such strong expression derogate somewhat from the character of the speaker, as they intimate that a simple assertion may not be believed. 5. Loud laughter, or tittering in short shrieks, as practised by some ladies at cards, are reprehensible. Dignity of character always suffers by being violently agitated at trivial circumstances. 6. A uniform adherence to sincerity in conversation is of the first importance. No artificial polish ol man- ners can compensate for the apparent want of 32* THE YOUNG MECHANIC this virtue, nor any acquirements of knowledge for the reality of such a want. Opinions should be given with exact truth, if given at all ; hut when the characters of others are con- cerned, they should be delivered with diffidence and modesty. Lastly, a marked disapprobation should always be shown to indecency, immo- rality, or irreligion. In the softer sex, so great is their power in meliorating the characters of men, that if profligacy, infidelity, and debauchery, were universally despised, the morals of the age would be entirely reformed. To these might be added many other observations from various writers, concerning a due respect in con- versation to superiors, good temper to equals, and condescension to inferiors ; but as young people are not expected to speak with the wis- dom, or precision of philosophers ; and as the careless cheerfulness of their conversation, with simplicity of manner, and with grace, ease, and vivacity natural to youth, supplies it with its principal charms, these should be particularly encouraged, as there are few artificial accom- plishments, which could compensate for the Loss of them.* Dr. Darwin. MORALS. 3QJ CHAPTER XIV. THE MORALS OF THE MECHANIC. THE only lesson of morality proper for children, and the most important to persons of all ages, is never to do an injury to any one. Even the positive precept of doing good, if not made subordinate to this, is dangerous, false, and contradictory. Who is there who does no good ? All the world, even the vicious man, does good to one or other party : he will make one person happy at the expense of making a hundred miserable ; hence arise our calamities. The most sublime virtues are negative ; they are also the most difficult to put in practice, because they are attended with no ostentation, and are even above that pleasure so flattering to the heart of man, that of sending away others satisfied with our benevolence. Oh how much good must that man necessarily do his fellow creatures, if such a man there be, who never did any of them harm! The injunction of doing no one harm, infers that of doing the least possible harm to the community in gene- 382 TIIE YOUNG MECHANIC. ral ; for in a state of society the good of one man necessarily becomes the evil of another.* I think it might be proved, that the best pre- cepts of morality, inculcated even under the sanction of religious awe, are not of half the efficacy in the prevention of vice, as a taste for reading and science. Experience informs us how soon the principles of morality inculcated in childhood are forgotten, or accommodated to the prevailing customs of the world : but if a taste for science be acquired, the affections are then fixed upon a rational object; there is no temptation to allure them from the path of vir- tue ; at least the most powerful of all incite- ments to criminal amusements is removed, the tediousness of life during the intervals of lei- sure.! Plato has observed with great propriety, that the end of the education and instruction of youth as well as the end of government, is to make men better; and that whoever departs from this rule, however meritorious lie may otherwise appear to be in reality, deserves neither the esteem nor the approbation of the public. The greatest erudition is of no value, * Rousseau, b. 2. -J- Gregory's Essays. MORALS. gg^ if unattended with probity. It is worse, it is dangerous to the welfare and tranquillity of so- ciety Quintilian, in his admirable treatise, has laid it down as a rule in forming a perfect orator, that none but an upright man can merit that name, and therefore he asserts as a necessary qualification, that he should not only speak well, but also possess all the moral virtues. Mr. Justice Blackstone has wisely adopted a similar opinion in his introductory lecture on the study of the law, in which, after having enumerated all the qualities of the head, he adds to them those of the heart, as indispensably necessary to form a truly valuable English lawyer, a Hyde, a Hale, or a Talbot. And Dr. Blair has, with great elegance and propriety, suggested the same idea as a necessary ingredient in the character of a sublime writer. But this just sentiment is not to be restricted to any particular profession or order of men. The knowledge and prac- tice of morality is the voice of nature, which is unbounded and universal : and however ex- pedient it may be in those whose stations in life, render them objects of imitation or esteem, to perform with the most rigid punctuality every moral duty, it must not be forgotten, that the conviction of the utility of the practice, 3S4 THE YOUNG MECHANIC. should make it the common sense and common respect of all mankind. The general rules of morality are formed by a constant observation of the fitness and pro- priety of actions in other men. What is fit to be done, and what excites universal applause, not only calls forth our own approbation, but warms us into a spirit of imitation. What ought to be avoided, we discover in the general sentiment of detestation which attends the per- petration of crime. The propriety of the former and the deformity of the latter quickly excite our emulation or abhorrence. We soon esta- blish a general rule for the regulation of our conduct, which receives a full confirmation from the opinion of the rest of mankind. It is thus that the general rules of morality are formed. They are ultimately founded upon experience of what, in particular instances, our moral faculties, our natural sense of merit and pro- priety, approve or disapprove of. We do not originally approve or condemn particular ac- tions ; because, upon examination, they appear to be agreeable or inconsistent with a certain general rule. The general rule, on the contrary, is formed by finding from experience that all actions of a certain kind, or circumstanced in MORALS. certain manner, are approved or disapproved of. An amiable action, a respectable action, a horrid action, are all of them actions which naturally excite for the person who performs them, the love, the respect, or the horror of the spectator. The general rules which determine what actions are, and what are not, the objects of each of those sentiments, can be formed no other way than by observing what actions ac- tually and in fact excite them. The regard to those general rules of conduct, is what is pro- perly called a sense of duty, a principle of the greatest consequence in human life, and the only principle by which the bulk of mankind are capable of directing their actions. Without this sacred regard to general rules, there is no man whose conduct can be so much depended upon. It is this which constitutes the most essential difference between a man of principle and honour, and a worthless fellow. The one adheres on all occasions, steadily and resolutely to his maxims, and preserves through the whole of his life, one even tenor of conduct. The other acts variously and accidentally, as humour inclination, or interest chances to be uppermost. On the most scrupulous observance of these rules of conduct, depends the very existence 388 THE YOUNG MECHANIC and happiness of human society, which would crumble into nothing if mankind were not generally impressed with a reverence for them. Among the many fortuitous events which spring up daily in the world, opportunities of inculcating a moral lesson frequently present themselves ; and when the mind has habituated itself to inquiry and discrimination, it will insensibly acquire a considerable degree of acumen, which may hereafter be employed with great emolument. For as it developes its powers of reasoning, it will direct this habit to other purposes of life, and virtue will have so strengthened its seat in the understanding, that its principles will be both relished and admired when at a future period they are examined ab- stractedly. It is for this reason, we cannot too often, after having laid down a moral principle, proceed to explain it by a practical illustration. A very little industry will qualify any one for this undertaking. The same volubility of speech which is often admirably exerted to propagate the villanous reports of scandal, and to tear piecemeal the domestic happiness of others, may be diverted, by this means, to an honourable and useful end. RELIGION. ggi* RELIGION. Disbelief or distrust of the truth of Chris- tianity arises in different men from different causes. Some who have been much accustomed to foreign travel, and have beheld opposite re- ligions firmly established in different countries, on the contrary sides of the same mountain, or the neighbouring banks of the same river; and others who have learnt from the records of his- tory that various systems of faith have suc- cessively prevailed in the same country ; that they have been changed again and again within very short periods ; and that each in its day has been implicitly received, and has produced, or, if an occasion offered, could have produced its martyrs ; such persons are sometimes prone to form what they term the liberal conclusion, that all religions are alike. They assert that the Supreme Being has enabled mankind to disco- ver, by the reasoning faculty with which he has endowed them, those plain precepts of mo- rality, the observance of which is the only service required by him ; and that the object of all religions, however they may be encum- bered with fanatical rites and doctrines, which, in everv country, the wise will inwardly regard 33 388 THE YOUNG MECHANIC. with contempt is to inculcate the obligation of those precepts. Or they boldly pronounce that religion of every kind is superstition : in other words, that though certain modes of conduct ought to be followed, and others to be ex- ploded, from principles of honour, and for the good of society ; to deem men bound to act in any case with a reference to a supposed will of the Deity, if a Deity exists, is of all absurdities the grossest. Others again, who have addicted themselves to philosophical investigations, have become decided unbelievers. Not that philoso- phy is the enemy of religion. The former is the natural ally of the latter. An inquiry into the laws which God has prescribed to the hu- man mind, to organized bodies, and to inanimate matter, leads at every step to a new display of his power, wisdom and goodness. But men who pursue it without any aim or desire to apply it to its most important use, that of heightening their reverence for the great Creator by a nearer acquaintance with his glorious at- tributes, easily become absorbed in the contem- plation of second causes ; and, though they may admit the existence, learn to deny the superin- tending care of the First Cause, and his interfe- -ence with the course of the material or the RELIGION. moral world. Others seek for refuge in unbelief, on the same principle on which many of the Jews did in the days of Christ ; who " loved dark- ness rather than light, because their deeds were evil, and would not come to the light lest their deeds should be reproved." Resolved to per- sist in the vicious practices which Christianity proscribes, they take pains to convince them- selves that the gospel is the production of fraud and delusion ; they catch eagerly at every ob- jection against it of every kind, and turn from whatever seems to make in its favour ; in the language of scripture, they wink purposely with their eyes lest they should see, and shut their ears lest they should hear, and harden, their hearts lest they should believe. Others by degrees becoming altogether immersed in political, commercial, or professional business, or in a continued succession of dissipated amusements, proceed from the omission of the practices of religious duties to the disuse and disregard of religious considerations, and ulti- mately to the disbelief of revealed religion, if not of all religion. And lastly, disdain of think- ing with the vulgar, disgust at casual instances uf superstition, and difficulties as to particular 390 THE YOUNG MECHANIC. doctrines, occasionally contribute to lead me* to unbelief. Besides the confirmed unbelievers of each of these descriptions, there are many persons who from various causes, advance only part of the way on the road to infidelity, and stop short at different stages of doubt and distrust. Concerning unbelievers and doubters of every class, one observation may almost universally be made with truth ; that they are little ac- quainted with the nature of the Christian reli- gion, and still less with the evidence by which its truth is supported. Now those who question or deny the truth of Christianity will yet readily admit, that if the Supreme Being has actually made a revealed communication of his will, and has unequivocal- ly addressed it to all mankind ; and if there are facts connected with that revelation which are acknowledged even by its enemies, and which justly afford, independently of other evidence, a strong presumption of its reality ; those per- sons must be highly guilty, who, having suffi- cient abilities and opportunities for inquiry, re- fuse or neglect to examine into the validity of its pretensions; and to examine with fairness, and with the attention which the subject demands RELIGION. 391 Is it then a thing highly improbable in itself that the Creator of the world should have given a revelation to mankind, and at the period when Christianity first appeal ed ? If the present stage of existence, is but a very small part of the whole duration of a human being ; if this stage is designed for the purpose of trial and proba- tion, and is thus to fix the state of each indivi- dual for ever ; if men were in fact ignorant of the certainty of these momentous truths, and unable to ascertain it by unassisted reason ; if, for want of a knowledge of that certainty, they were become a prey to crimes and delusions, indulging themselves in every species of wick- edness, and worshipping stocks and stones, and personified vices, with absurd and abominable rites ; can it be improbable that He who had manifested his goodness in creating them, should add another proof of the same disposition by imparting to them the further light necessary to correct their wanderings, and to guide them steadily in the way to happiness ? They who are led by these or other consi- derations to regard a revelation as a thing not improbable in itself, ought from that circum- stance to feel, and naturally will feel, a greater readiness to inquire into the evidence of any 33^ 39-2 THE YOUNG MECHANIC. professed revelation which bears outward marks of reality. They who deem the existence of a revelation highly improbable cannot affirm that it is impossible ; and ought consequently in a similar case to institute a similar inquiry. For an antecedent persuasion of the improbability of the Deity's acting in any particular manner is no more a reason for refusing to examine whether he has not acted thus, if existing facts afford strong presumptive evidence that he has, than it would be for refusing to believe that he has, if conclusive evidence were produced. The question then which remains to be an- swered is this. Are there any leading circum- stances attending Christianity, circumstances genera Uy admitted, and resting on independent proofs, which seem scarcely capable of being accounted for on any supposition but on that of truth ; and consequently furnish so strong a presumption of its being a divine revelation as to render those who doubt, or deny it, not merely imprudent but criminal, if they do not seriously inquire into its evidence ? The following statement, I apprehend, will justify the answering of that questior. decidedly in the affirmative. The Christian religion, whether true or false^ RELIGION. 393 had its origin in a country and nation held in proverbial contempt in almost every part of the known world. The author of the religion was not only a Jew, but of the lowest rank among the Jews. He is universally allowed to have been uninstruc-ted in literature and philosophy. He employed, in propagating his doctrine, as- sistants who were also Jews, and of a station as obscure, and of minds as little cultivated by learning, as his own. The religion which they preached was of such a nature as to be gene- rally and unavoidably most obnoxious. It was avowedly intended to supersede and annihilate every other religion. It attacked not only the doctrines and ordinances of the Jews, which they regarded as having been appointed by God himself; but those inveterate prepossessions which were rooted no less firmly in their hearts ; pronouncing the abolition of the pecu- liar privileges of the Jewish race, and the free admission of the abhorred Samaritans and Gen- tiles to all the benefits of the new dispensation. It not only exasperated the Romans by brand- ing as impious and detestable those rites and institutions which they had received with im- plicit reverence from their remote ancestors; and deriding as vain fictions every object of 394 THE YOUNG MECHANIC. their adoration, even all the tutelary deities oi their empire ; but it also touched their jealousy in the tenderest point, by suggesting a prospect of the revolt of Judea, and holding forth to their imaginations a competitor of Ceesar, and the portentous appearance 6f the long expected sovereign, whom fate had destined to arise in the east. The founder of Christianity had neither the favourable circumstances to turn to his advantage, of which other teachers of new religions have availed themselves ; nor did he resort to those methods of proceeding to which they owed their success. He did not, like Ma- homet, pay court to a particular set of men, or a particular sect ; nor, like him, artfully conci- liate persons of all the different religious per- suasions in the country, by adopting and incor- porating into his own system some of the prin- cipal of their respective tenets ; nor, like him, permit licentious indulgences and promise licen tious rewards to his followers ; nor, like him. direct the propagation of his doctrine by the sword. He did not confine his instructions to solitudes and obscure hamlets ; but delivered them in the most public manner, in populous cities, in the most frequented parts of Jerusalem itself. He did not rest his pretensions on any RELIGION. 39/5 species of evidence of a secret nature, or in any respect not generally cognizable by his co- temporaries ; but appealed to professed miracles performed in the sight of multitudes, and of such a kind that every man could judge as to their reafcty. He was not permitted by the contempt or the supineness of his enemies to proceed unmolested in making proselytes ; but was actively opposed from the beginning by the priests and chief men of the national religion ; was repeatedly in danger of losing his life ; and after a short ministry of three years duration at the utmost, was delivered to the civil power, and crucified as a malefactor. Yet notwith- standing this event the progress of the religion continued. The disciples of Christ, though they could have no reason to expect better treatment than their master had received; though they expected, as they had been taught by him and professed to expect, nothing in the present life but troubles and persecutions, per- severed in preaching the same religion as he had taught, with this additional and extraordi- nary circumstance that their master, on the third day after his crucifixion, had arisen from the dead : and encountered the severest punish- ments, and death Uself, rather than cease from 396 THE YOUNG MECHANIC. publishing and attesting doctrines and facts, which, if false, they could not but know to be so ;- and from the preaching of which, if true, they could look for no present advantage. And from these humble beginnings, and by these unpromising methods, did Christianity make its way so successfully, that within three centuries from the first preaching of Christ, it penetrated to the remotest extremities of the Roman em- pire, and established itself on the ruins of every other religion which it found existing. When all these circumstances are considered, and they are such as unbelievers in general are ready to admit, it seems nearly impossible not to come to the following conclusion : that a religion of such an origin, and avowedly aiming at such objects; a religion thus destitute of all worldly means of credit and support, thus pro- voking and experiencing every kind of worldly opposition, could scarcely ever have obtained belif and acceptation, if its pretensions had not been founded on irresistible truth ; and con- sequently, that its establishment under all these circumstances affords so very strong a presump- tion that it is true, as necessarily to render every competent judge to whom they are known, and who doubts or disbelieves Christianity, crimi- RELIGION. 3917 nal in the sight of God, if he does not carefully examine into the specific evidence by which that religion is supported. This is the conclusion to which it has been my object to lead by fair reasoning the^canclid reader, who distrusts or denies the truth of the Christian revelation. If this conclusion appears to him well established, he will naturally seek for a detailed account of the evidence of the Christian religion in treatises written professedly on the subject ; and will make himself acquaint- ed with the many striking internal proofs which it bears of its own authenticity, by a diligent and attentive study of the Scriptures. And let him conduct the whole of his investigations with that impartial spirit which is always essen- tial to the discovery of the truth, whatever be the subject under discussion ; guarding against the influence of former prepossessions, and former practices, with a degree of caution and solicitude proportioned to the supreme import ance of the inquiry in which he is engaged. Let him be prepared " to do the will of God ;" and he will not fail, " to know concerning the doctrine whether it be of God." I would in the next place offer a few obser- vations to the consideration of those believers 398 THE YOUNG MECHANIC. in Christianity, who contend that an exact ob* servance of all its precepts is more than is now required of them. This plea for deliberate deviations from the strictness of obedience, a plea which we more frequently hear obscurely intimated than expli- citly stated, appears, when unfolded, to resolve itself into the following assertions : that if the generality of men would act in scrupulous con- formity to the precepts of Christianity, no in- dividual could be vindicated were he to conduct himself otherwise ; but that every man must take the world as it is, and consider what is practicable in the existing state of things : that if government, for example, cannot be carried on without a certain degree of deceit and cor- ruption, the politician is excusable who prac- tises it ; that if men in trade cannot maintain their station without using the same objection- able arts which are adopted by their competi- tors, the necessity of the case is a sufficient apology ; that similar reasoning is applicable to every other profession ; that extravagant and needless, latitude would certainly be unjustifi- able ; but that it is absurd to require points of morality to be pushed to extremes, and to refuse -.2-JSJi^. RELIGION. 399 to make necessary allowances for compliance with established customs. Before we examine what countenance the plea in question meets with in the Scriptures, it may be useful to inquire whether it approves itself to sober reason. Now, since they who allege this plea, pro- fessedly make the degree in which it is custo- mary for men to deviate from the rules pre- scribed in the Gospel, the standard measure of the degree of latitude in deviating from them which each individual is at liberty to use ; they must unavoidably admit, if they will reason con- sistently with their own principles, that when the general depravity is augmented in any pro- portion, exactly in the same proportion is that latitude augmented ; and consequently that a degree of latitude, which in one state of things they pronounce extravagant and unnecessary," may become highly needful and proper in another. This in fact is to affirm, that instead of the practice of men being rendered conform- able to the laws of God, the degree of obe- dience due from any man to those laws depends solely on the practice of his neighbours ; and that if it should be the general practice utterly to disregard and contemn them, no individual 400 TIIE YOUNG MECHANIC. would be under any obligations to pay to them the slightest attention whatever. If an argu- ment like this, which strikes directly at the root of all religion, cannot be maintained by those who believe in Christianity; neither can the plea which necessarily involves it. In the next place, does this plea receive more encouragement from the Scriptures ? From that quarter it experiences nothing but repulse and condemnation. Those who urge it cannot pro duce one single text authorizing an individual to relax in his obedience to the precepts of the Gospel, for the sake of escaping difficulties and losses, through fear of giving offence, through deference to custom or authority, or through any worldly motive whatever. What is the language of the Old and New Testaments on the subject ? u Thou shalt not follow a multi- tude to do evil." " Be not conformed to this world," (that is, to the evil principles and prac- tises which prevail in it,) "but be transformed by the renewing of your mind, that ye may prove what is that good, and acceptable and perfect will of God." " Love i ot the world, neither the things that are in the world. If any man love the world, the love of the Fathei is not in him Fo. r all that is in the world, the RELIGION. 40} lust of the flesh, and the lust of the eyes, and the pride of life, is not of the Father, but is of the world. And the world passeth away, and the lust thereof : but he that doeth the will of God abide th for ever." u Be ye therefore per- feet, even as your Father which is in Heaven is perfect." " The love of Christ constraineth us, because we thus judge, that if one died for all, then were all dead : and that he died for all, that they which live should henceforth not live unto themselves, but unto him which died for them and rose again." " What shall it profit a man, if he shall gain the whole world, and lose his own soul ? Or what shall a man give in exchange for his soul ? Whosoever there- fore shall be ashamed of me, and of my words, in this adulterous and sinful generation, of him also shall the Son of man be ashamed, when he cometh in the glory of his Father with the holy angels." To these passages are to be added the directions incidently given by St. Paul to persons in many different stations, exhorting them to fulfil the respective offices peculiar to those stations " for conscience sake, as unto the Lord, and not unto men ;" directions which, Dy parity of reasoning we may rest assured that the apostle would have applied to all other 402 THE YOUNG MECHANIC. situations and circumstances of life, if he had been led by his subject to notice them distinctly And lie r Jid in fact make the application univer- sal, when he delivered these general and com- prehensive precepts : " Whatsoever ye do, do all to the glory of God." " Whatever ye do, in word or in deed, do all in the name of the Lord Jesus." A serious desire to please God in all we do, rendering the manner of pursuing the business of our calling, be it what it may, one of the expressions of that desire, is the grand principle which these passages inculcate ; and it is the principle which, beyond all others, I could wish to impress on the mind of the reader, whatever be his station or profession, as being the only one which will lead him steadily to fix his attention on the duties which he has to perform, and the temptations which he must encounter. It is impossible to conceive that he who knowingly deviates from the path of moral rectitude and Christian duty, because most others in the same rank and profession with himself deviate from it, and because, by forbear- ing to deviate, he should incur embarrassment and losses, odium and disgrace, is, in that in- stance, acting consistently with the letter or the spirit of the various scriptural inj unctions which RELIGION. 403 have been quoted. Let those who find them- selves tempted to such deviations, consider whether it is not probable that the Supreme Being, on whose providence the success of every undertaking depends, will prosper those who scrupulously observe the laws which he has prescribed for their conduct, and leave the issue in his hands, rather than those who mani- fest their distrust of his care by resorting to arts and practices which he has forbidden ; whether those who are injured in their worldly prospects by their conscientious adherence to the line of rectitude, are not entitled to the full benefit of the scriptural consolation, u If ye suffer for righteousness sake, happy are ye :" and whether it is not the part of wisdom as well as of duty, whatever be the event at pre- sent, to regulate every action by that rule, ac- cording t,o which it will be judged at the last day THIS BOOK IS DUE ON THE LAST DATE STAMPED BELOW I AN INITIAL FINE OF 25 CENTS WILL BE ASSESSED FOR FAILURE TO RETURN THIS BOOK ON THE DATE DUE. THE PENALTY WILL INCREASE TO SO CENTS ON THE FOURTH DAY AND TO $1.OO ON THE SEVENTH DAY OVERDUE. OCT DUE AUG 2 5 W JUN 9 1978 m LIBRARY, COLLEGE OF AGRICULTURE, DAVIS UNIVERSITY OF CALIFORNIA 5m-4,'41 (2361s) 1 42158 Kelt. T., cbmp TJ14.fi The meghar:lc y s text- book and engineer f s practical guide - LIBRARY/COLLEGE OF AGRICULTURE, DAVIS UNIVERSITY OF CALIFORNIA