MEM
577
MEN
i rectangle of tlie two unequal segments, that is, in the
| | reciprocal ratio of their products, ii. 145.
j j Having the length and weight of a beam that can just
| support a given weight in the middle ; to find the
j length of another beam of the same scantling, that
: shall just break with its own weight, ii. 146.
i Having the weight of a beam that can just supporta given weight in the middle ; to find the depth ofanother beam similar to the former, so that it shalljust support its own weight, ii. 146.
The weight and length of a piece of timber being given,and the additional weight that will break it ; to findthe length of a piece of timber similar to the former,so that this last piece of timber shall be the strongestpossible, ii. 147.
j Belidor ’s Experiments, ii. 148.
I M. de Buffon’s do., ii. 149.j M. du Hamel, do., ii. 150.
! Further experiments, ii. 150.
Of the absolute strength of timber, ii. 150.
Table showing the strength of a square inch in differentkinds of timber, ii. 150.
Practical observations, ii. 150.
To cut the strongest beam possible out of a round tree,whose section is a given circle, ii. 151.
To support a piece of timber by means of two propsi resting on the ground, so that it shall have no ten-
dency to go to either side, ii. 151.
To ascertain the proportions between the weight of thepiece of timber, and the compression of the props,ii. 151.
If a heavy body, A, b, C, d, be supported by two obliquestrings, d b, and cf, in a vertical plane, a straightline drawn through the intersection will pass throughthe centre of gravity of the body, ii. 151.
Given the position in which a body should be placed,and the position of a plane supporting the body atone end ; to find the position of another plane to sup-port it at another given point, and to find the pressureon the planes, the weight of the body being given,ii. 151.
Lever, ii. 97.
; Actual experiments on composition of forces, ii. 152.
I To distinguish ties from struts, ii. 153.
Strains acting on various points of a frame of carpentry,ii. 154.
Building up and scarfing of beams, ii. 158.
Of joints, ii. 160.
Of iron straps, ii. 161.
Of circular and polygonal roofs, ii. 162.
Of trusses and centres, ii. 162.
Stone Bridge, ii. 462.
Mechanical Powers, ii. 164.
The proportion the power and weight ought to have toeach other, ii. 164.
The proportion of the power and weight to each otherin a given machine, that it may produce the greatesteffect possible in a given time, ii. 164.
Lever,
ii. 97.
Plane, (inclined),
Pulley,
ii. 345.
JFedt/e,
ii. 522.
Wheel,
ii. 525.
Medallion,
ii. 164.
Medieval Architecture ii. 164.Media^as, ii. 164.
Member, ii. 164.
VOL. II.
Origin of, ii. 164.
Progress of, ii. 165.
Spiral, ii. 440.
Mensuration of lines, ii. 166.
Any two sides of a right-angled triangle being given,to find the third, ii. 166.
To find the length of a cylindrical helix, ii. 167. i
The chord and versed sine of an arc of a circle beinggiven, to find the diameter, ii. 167. 1
In the segment of a circle are given the chord and its idistance from the centre, to find the radius of thecircle, ii. 167.
The radius of a circle being given, and the chord of asegment of that circle, to find the versed sine of thelesser segment, ii. 168.
Given the distance between the two parallel sides of atrapezoid, and the breadth of the lesser end ; to findthe breadth of the greater end, so that the sides maytend to a point at any given distance, ii. 168.
To find any point in the arc of the segment of a circle,at the extremity of an ordinate, the radius of thecircle, the chord of the arc, and the distance of theordinate from the middle of the chord, being given,ii. 169.
Given the chord of a very large segment of a circle, theradius of the circle, to find any number of points inthe arc, and thence to describe it, ii. 169.
Geometry, i. 445. !
In a parabola having two abscissas and an ordinate ;to one of them, to find the ordinate of the other,ii. 169.
To find any point in the curve of a parabola by meansof an abscissal parallel, or transverse ordinate ; theheight or abscissa, the ordinate, and the distance ofthe transverse ordinate from the abscissa, beinggiven, ii. 170.
Given the abscissa and ordinate of a parabola, to findany number of equidistant diameters or abscissal•parallels, and consequently points in the curve at theextremities, ii. 170.
Synopsis of the principal rules in Mensuration , ii. 170.
The rectification, or development of curves, ii. 170.
Areas of plain surfaces, ii. 171.
“ curved do., ii. 172.
Solidities of bodies, ii. 172. j
Rectification of curves, ii. 173. j
Areas of plane figures, ii. 175.
“ curved surfaces, ii. 176.
Notes on the solidities of bodies, ii. 178. i
Of measuring curvilinear planes and solids by approxi- imation, ii. 178.
Observations on averaging surfaces bounded on one ortwo opposite sides by a curve, ii. 179.
Mensuration of artificers’ work, ii. 180.
To measure the vacuity of a window, ii. 180.
“ any angle chimney standing equally distanteach way from the angle of the roomii. 181.
To measure an angle chimney when the plane of itsbreast intersects the two sides of the room unequallydistant from the angle, ii. 181.
To measure an angle chimney when the plane of thebreast projects out from each wall, and unequallydistant from the angle of the room, ii. 181.
To find the area of an arched aperture, ii. 181.
7 B