1898 



INDEX TO VOL. I. 



[MATBKJIATIC8 VCCHAKIC& 



/ 



Railway. cutting, to find the solid content* 



of ., 6S3. 



Ratio and proportion in algebra. 476. 

 Ratio*, inverse irigooomt uical, explained, 



Ml 



Ratioi of angle*, 614, ff teg. 



Ratio*, trigunomrtrical, 613, */ trq. 



Rectangle, to find the area of a, 644. 



Reduction of fraction!, 413, 467. 



Redaction, rale of; iti rise and appli- 

 cation, 440. 



Right-angled triangle*, *olution of, 641. 



Roou in algebra, 464 ; extraction of, 465 ; 

 rule* for ; exercise* in, 466. 



RooU, square and cube, table* of. 540. 



Role-of-Uiree, double, illustration* of, 

 447. 



Rule.of-thrre, principle* and practice of, 

 446. 



Ruler* uaed in geometry, 600. 



SAGITTAL length* of, 540. 



Secant*, 613. 



Section*, conic, 608. 



Sector and segment of a circle, to find the 



area of, 646. 



Semicircle, ratio of arc of to radio*, 630. 

 Series. 511, et tej. .- what i meant bj a 



convergent and divergent *erie*, 513. 

 Serie*, logarithmic, 517. 

 Serie*, trigonometrical, 627, tt teg. 

 Side* and angle* of triangle*, 623. 

 Sides and area of a triangle, 625. 

 Sign* of operation in algebra; practical 



illustrations of, 452. 

 Sine*, logarithmic, table* of, 666 688. 

 Sine*, natural. 636 ; table* of, 665. 

 Sine* of angles, 613 ; numerical Talue of, 



619; how to calculate the Talue of, 



635. 



Sine* of small angle*, 639. 

 Solid*, mensuration of. 649, ft teg. 

 Solution of right-angled triangle*, 641. 

 Solutions to algebraical exercise*, 486 



511. 

 Sphere, to find the area of a portion of a, 



648 ; the volume of a portion of a, 654. 

 Spherical geometry, 596 (See Geometry). 

 Spherical triangle*; sines of the angle* 



proportional, 657 ; solution of the, 660 ; 



Napier'* rule for solving, 660. 

 Spherical trigonometry, 657 (See Trigo- 

 nometry). 



Spheroid, to find the volume of a, 655. 

 Square measure, tables of, 439. 

 Square-root, exUactiuu of the* 44.8, 449, 



482. 



Square-root of a binomial, 48S. 



Square-root of a polynomial, 481. 



Squ ire-root, table* of, 540. 



Square. root, various algebraic exercise* 



for extracting the, 482. 

 Squares, tables of, 539. 

 Squaring the circle, problem of, 577. 

 Sul>M.liary angle*, use of, 623. 

 Subtraction of algebra, *ign of, 451 ; 



illustrations of, 454 ; exercise* in, 455. 

 Subtraction of compound quantities, 441 ; 



of fraction*, 444 ; of decimnls, 418. 

 Subtraction of fraction* in algebra : 



exercise* in, 468. 

 Subtraction, simple, we and application 



of, 434 ; various workings in, 435. 

 Surds in algebra, illustrations of, 4G4, 



483. 

 Surveying a country, operation* of, 663, 



tt teg. 



Symbolical algebra, 512. 

 Symbols of quantity in algebra, 452. 

 Symmetrical quadratic*, 476. 



TABLES, logarithmic, of natural numbers, 



525539. 



Tables of circular arcs, 540. 

 Table* of cubes, 539. 

 Table* of cube-root*, 540. 

 Tables of logarithmic tine*, tangents, &c., 



666 6H8. 

 Tables of money, time, weights, and 



measure*, 439. 



Table* of Napierian logarithms, 539. 

 Tables of natural sines and cosines, 665. 

 Table* of sagittas, 540. 

 Tables of squares, 539. 

 Tables of square-roots, 540. 

 Tangents, 613, et teg. t the calculation 



of the numerical value of, 637 ; tables 



of, and cotangents, 666 6H8. 

 Term, meaning of the word in algebra, 



452. 



Theorem, binomial (See Binomial). 

 Theorem, De Moivre's, 628. 

 Theorems of Euclid (See Propositions). 

 Time, tables of, 439. 

 Tower,, how to determine the height of a, 



643. 

 Trapezjum and trapezoid, to find the area 



of, 645. 



Triangle, to find the area of, 645. 

 Triangles, relation* between the sides and 



the angles of, 623. 

 Triangles, right-angled, numerical solution 



of, 641, et tea.; spherical, solution of. 



660. 



Triangles, spherical oblique-angled, solu- 

 tion of, 661. 



Trigonometry, calculation of tables, 635. 



Trigonometry, Drlambre'i method for 

 mall angles, 640. 



Trigonometry, De Moivre'i theorem, 

 628. 



Trigonometry, formula* connecting inverte 

 ratios, 622. 



Trigonometry, geodetic*! operation*, 662, 

 tt teg. 



Trigonometry, line* and ratio* of, 613, 

 el teg. 



Trigonometry, logarithmic formulas, 624, 

 637, el teg. 



Trigonometry, logarithmic line*, 637 ; 

 tables of, 666. 



Trigonometry, method of checking the 

 calculations in, 636. 



Trigonometry, method of proving different 

 formulas; principles of proof ; the fun- 

 damental formulas of ; various formulas 

 and expressions, 614, el teg.: " ambi- 

 guities" arising from their use, 619. 



Trigonometry, natural sines and cosines, 

 637 ; tables of, 665. 



Trigonometry, numerical solution of right- 

 angled triangles, 641, et teq. 



Trigonometry, plane, treatise on, 612, 

 el teg. 



Trigonometry, ratio of a semicircle to 

 a radius, 630. 



Trigonometry, right-angled spherical tri- 

 angles, 660 i Napier's rule for solution 

 of spherical triangles, 60 ; oblique- 

 angled triangles, 6ul. 



Trigonometry, roots of a binomial, 631. 



Trigonometry, science of defined, 612. 



Trigonometry, series, 627, et eg. 



Trigonometry, sides and angles ol triangles, 

 623. 



Trigonometry, spherical, 657, tt teg. 



Trigonometry, spherical, sines and angles, 

 657. 



Trigonometry, subsidiary angles, 623. 



Trigonometry, tables of logarithmic sines, 

 cosines, tangents, and cotangents, 666 

 688. 



Trigonometry, tangents, and cotangents, 

 637 ; bibles of, 666. 



Trigonometry, value of the sines, Ac, of 

 multiples of angles, 619, et teg. 



Troy weight, 439. 



VKBSED sines, 613. 

 WEIGHTS, tables of, 439. 



SECTIONS VIII. AND IX. MECHANICAL PHILOSOPHY APPLIED MECHANICS. 



ACTION and reaction, 693. 



Aerodynamics, or Pneumatics, 689. 



Aerostatic*, 689. 



Aerostation, 777. 



Agricultural steam-engine* described, 



8(50. 



Air a source of power, SI 9. 

 Air an elastic fluid, 748. 

 Air, apparatus for exhibiting the flow of, 



838. 



Air, condensation of, 775. 

 Air-bla*t in iron manufactories, 879. 

 Air-bubble* in cast-iron, 809. 

 Air ha* weight, 768. 

 Air, bright of, above the sea-level, 770. 

 Air is rarer the higher we ascend, 770. 

 Air. its volume inversely proportional to 



the pressure, 769. 

 Air lose* beat by rarefaction, 771. 

 Air, machinery for blowing, 783. 

 Air, movement of the, 768, 819. 



Air, pressure of, 768, 843. 



Air-pump, Smeaton's, 776. 



Air-pump described, 775. 



Air-pump, formula for computing the 

 action of an, 776. 



Air-pump in the steam-engine, its action, 

 872. 



Air-pump, Tale's, 776. 



Air retards the velocities of falling bodies, 

 838. 



Air, weight of a volume of, 769. 



Alcohol rise* in vapour at a low tem- 

 perature, 842. 



Altitude* determined by barometer, 771. 



Altitude*, formula for computing, 771. 



America, ancient architecture of, 778. 



Angle-iron tor jointing the plate* of 

 leam-boilcrs, 050. 



Animal muscular force a* a source ol 

 power, 780. 



Animal muscular power, 817. 



Animal products, machinery for treating, 



783. 



Animals employed as a moving force, 818. 

 Animals, how they walk, 715. 

 Apparatus for cutting, piercing, moulding, 



bending, crushing, ore., 783. 

 Apparatus, hydraulic, 783. 

 Arch, none in Egyptian architecture, 778. 

 Archimedes' problem on ipecific gravity, 



755. 

 Architectural drawings, what scale* are 



most convenient, 7'.M. 

 Architecture of antiquity, 778. 

 Arctic voyager* propelling their (ledge* 



by means of kites, 821. 

 Area of a circle, 908. 

 Area of an ellipse, 909. 

 Area of a sector, 909. 

 Area of a triangle, 908. 

 Area of a parallelogram, 908. 

 Area of a trapezoid, 908. 



