Author Index

Albenga, G., 508 Alberti, L.B., 311, 350 Aldrich, D.H., 327 d'Alembert, J. Lerond, 445-447, 452,

472, 492 Alexander of Aphrodisia, 312 Alfieri, B., 400 Amici, V., 432 Ammannati, B., 328 Antiphon, 309 Apollonius, 311 Archimedes, 322, 460 Atwood, G., 429 Audoy, 429-430

Barilari, P., 463 Barsotti, G., 457, 471, 490 Belanger, J.B., 479 Belgrado, J., 400-401 Belidor, B. Forest de, 315, 336-338,

342,372,403,431 Benedict XIV, Pope, 352 Benjamin, W., 543 Benvenuto, E., 437fn, 514fn Bernardi, 450 Bernoulli, Jakob, 329, 331, 401 Bernoulli, Johann, 326-328,358,364-

365 Bertelli, F., 463 Bertot, H., 485-486, 492, 494 Bertrand, J.L.F., 477, 490-491, 508 Betti, E., 503 Blondel, F., 311 Boistard, L.C., 399fn Bompaire, F., 471 Boncompagni, Prince of, 514 Bonnycastle, C., 461 Bordoni, A., 414, 422 Borelli, A., 358, 364 Borgnis, J.A., 332 Borra, G.B., 315, 400 Boscovich, R.G., 352, 356, 371-374,

468

Bossut, C., 344, 375-386, 407, 412, 413,426,428,447-449,451

Bouguer, P., 344-348, 360, 374, 384, 413, 420-423

Bresse, J.A.C., 485fn Brunelleschi, F., 313, 350 Bryan, G.H., 529 Buti, A., 315fn, 334fn

Caizzi, B., 472 Callot, E., 471 Capriz, G., 473 Castigliano, A., 436, 442, 447, 452,

453,469,470,473,475,476, 487,491,508,509,512,513-523, 529, 531, 542-543

Cauchy, A., 468, 469, 471, 516 Cavina, V., 451fn Cecchini, A., 350 Cerruti, V., 503, 513 Cesaro, E., 503 Charlton, T.M., 508fn Chasles, M., 526 Chezy, M., 399fn Clairaut, A., 358 Clapeyron, B.P.E., 357fn, 430, 479-

488,492,494,499,508,509, 517

Clark, E., 483 Clebsch, A., 492-498, 517 Colbert, J.B., 322 Colonnetti, G., 508, 521-523 Corradi, M., 334fn, 437fn Cosimo Medici, Grand Duke, 351 Cotterill, J.H., 508-512, 517, 542 Coulomb, C., 342, 375, 386-399, 413,

418, 428-431 Couplet, C.A., 309, 338-344, 353, 359,

398, 403, 413 Cournot, A., 447, 471-476, 478,489,

508,514 Cremona, L., 491, 526, 534, 539 Croce, F., 371

Crotti, F., 508, 523-530, 543 Culmann, K., 436, 526, 534 Curioni, G., 437fn, 515

Danyzy, A.A.H., 399fn Darbon, A., 471 Delanges, P., 406, 448-450, 455-456 Derand, F., 313-315, 336 Descartes, R., 472, 473 Donati, L., 508, 510 Dorna, A., 477-479, 489, 508 Dugas, R., 467fn, 471 Dulacq, 358

Elkana, Y., 471 Engesser, F., 508 Euler, J.A., 375 Euler, L., 388, 441-444, 447, 448,

451,455,465,475,480,529

Fabri, H., 316-320 Faguol!, G., 444, 463-466 FairbaIrn, W., 480 Faraday, M., 468 Favre, F.P.G., 357-358 Fedi, R., 471 Fermat, P. de, 460 Ferussac, Baron de, 471 Foce, F., 437fn Foggini, G.B., 350 Fontana, C., 311, 350, 352, 353 Fontana, G., 457 Fontana, M., 407-411, 453-455, 466 Fourier, J., 447 Franceschinis, F.M., 404 Frezier, A.F., 358, 399fn Frisi, P., 401-404, 413 Frost, R., 447 Fusinieri, A., 463

Galilei, G., 312, 316, 324, 358, 397, 442

Galilei, V., 312 Gaudi, A., 346 Gauthey, E.M., 399fn Gebbia, M., 503 Genocchi, A., 508, 513 Gergonne, J.D., 462, 526 Gerstner, A., 432fn, 433

Author Index 545

Gerstner, F.J., 432 Grandi, G., 313 Gratognini, G., 414, 422 Green, G., 468-470, 480, 517 Gregory, D., 326-331, 358, 401 Grioli, G., 473 Guarini, G., 311 Guerrini, G.G., 350 Gunther, R.W.T., 329fn

Hann, J., 434fn Harpe, F. de la, 471 Hartsocker, N., 357 Hegel, G.W.F., 442 Heidegger, M., 442, 543 Heppel, J .M., 483 Hertwig, A., 508 Hesse, M.B., 471 Heyman, J., 342, 343fn, 386 Hire,P. de la, 315-316,321-326,331-

336,342,353,357,358,376, 384, 403, 416, 418, 448fn

Hodgkinson, E., 483 Hooke, R., 328-329fn Huygens, C., 427

Intieri, B., 352

Jacquier, F., 352, 356fn Jammer, M.F., 471 Jourawsky, D.J., 483

Krafft, G.W., 309fn, 331

Labey, J.B., 461 Lagrange, L., 451, 457, 460, 466, 469,

474,510 Lame, G., 430, 487, 510, 511 Lana Terzi, F., 358 Landi, F., 412fn Lauricella, G., 503 Legendre, A.M., 529 Leibniz, G.W., 326, 328, 358, 472,

473 Leonardo da Vinci, 316fn, 320, 342 Lesage, M., 399fn Lorgna, A.M., 404-407, 413, 449, 452-

453

Mach, E., 471

546 Author Index

Malfatti, G.F., 457-460, 514, 527 Manfredi, G., 352 Mansart, J.H., 405 Marcolongo, R., 309fn Martinez, F., 372 Martino, P. Di, 352 Marzano, S., 473 Mascheroni, L., 344, 375, 393-394,

399, 412-425, 428, 457 Masetti, G.B., 414, 419, 457 Maupertuis, P.L. Moreau de, 460 Maxwell, J.C., 492, 499-507, 542 Mazini, G.B., 358 McLean, L., 512, 516, 529 Mead, R., 358 Mehrtens, G.C., 542 Melan, J., 542-543fn Menabrea, L.F., 434, 436, 452, 469,

471,476,477,488-491,508, 510fn, 512, 514-516, 529

Mentre, F., 471 Mersenne, M., 358 Mery, E., 428, 434 Milhaud, G., 471 Mohr, 0., 487, 530-543 Molinos, L. de, 479 Monge, G., 313 Moseley, H., 432, 434, 476, 508, 511fn Mossotti, O.F., 432, 457, 468, 469,

471,478,489,508,514 Miiller-Breslau, H.F., 542-543 Musschenbroek,P.van, 357,358,362-

364

Naderi, A., 315fn Napoleon 1,455 Nasce, V., 514fn Nava, A., 371fn Navier, L., 409, 431-432, 479, 497,

516 ' Nelli, G.B.C., 350 Nelli, G.F., 350 Newton, I., 473 Nicol, W., 499

Oersted, H.C., 474 Oravas, G.Ae., 512, 513, 516, 529 Orlandi, D.G., 352

Pagani, G.M., 477, 478, 489, 508

Paoli, P., 451-452, 455, 457, 460 Pappus, 311 Parent, A., 325fn, 331, 358 Parodi, A., 490 Pasquale, S. Di, 313fn, 457fn Pearson, K., 441, 466, 467, 470 Perrodil, J.R. de, 436 Perronet, J.R., 399fn Picard, G., 358 Piola, G., 432, 457, 466-467 Pitot, H., 342 Pliny, 312 Pluecker, J., 526 Podio Guidugli, P., 473 Poinsot, L., 461, 472 Poisson, D.S., 461, 463, 468, 469, 516 Pole, W., 483 Poleni, G., 327, 352, 358-371, 372fn Poncelet, J.V., 375, 426-429, 526 Pronnier, C., 479 Prony, R., 399fn

Regi, F. de, 372 Riccati, G., 411fn Riccati, J., 411fn Riccati, V., 411fn, 451 Richer, 358 Ritter, A., 534 Rocchi, E., 471 Romano,450 Rombaux, G.B., 515 Rondelet, J., 315 Rostand, J., 471 Ruyer, R., 471

Sabbia, E.F., 490, 508 Saint-Venant, A. Barre de, 467, 516 Salimbeni, L., 331, 342, 344, 375, 406,

425-428, 449 Santini, D.S., 357 Scamozzi, V., 312, 350 Scheffler, H., 434 Schwedler, J. W., 534 Sclopis, F., 471 Second, J., 471 Seneca, 309fn Sengher, G.F., 350 Seur, T. Ie, 352, 356fn Sganzin, M.S., 399fn

Siacci, F., 508 Signorini, A., 473fn Somigliana, C., 503 Sorel, G., 472 Souflot, J.G., 376 Staudt, G.K.C. von, 526 Stefano, R. Di, 352fn, 353fn Stephenson, R., 480, 483 Stevin, S., 442, 443 Stirling, J., 358, 359 Swedenburg, E., 358

Tate, T., 483 Taviani, P., 471 Thomson, W. (Lord Kelvin), 470, 512 Timoshenko, S.P., 375, 432, 516 Todhunter, I., 441, 466fn, 470fn Torricelli, E., 349 Truesdell, C., 328-330

Author Index 547

Vanvitelli, L., 353 Vene, A.A., 474, 476, 508, 514, 529 Venturoli, G., 344, 397, 399, 414, 420-

422, 457 Villarceau, Y., 428, 490 Viollet Ie Due, E., 315 Vitruvius, Pollio, 310 Vittone, B.A., 311, 315, 400 Viviani, V., 311-313, 349, 350

Waller, R., 328 Weingarten, J.L., 508 Weyrauch, J.J., 508, 542, 543fn William of Ockham, 460 Winkler, E., 436, 437, 443, 530 Wolff, C., 315 Wood, R., 400

Subject Index

Abutments (piers) empirical evaluation of the thrust

on-, Leonardo's intimations, 309-310; Lorgna's experi­ments, 404-405; ancient ge­ometrical rules for deter­mining the thickness of-, according to Deran, 313-315; according to medieval Arabian builders, 315fn; stat­ical calculation of the width (or thickness of)-, de la Hire's method, 331-336; Belidor's improvement, 336-338; Bossut's contribution, 384; Mascheroni's solution, 416-420

Adherence between voussoirs de la Hire's hypothesis, 332; Cou­

plet's approach, 342; Favre's remarks, 357-358; Coulomb's theory, 394-399; Mascheroni's and Venturoli's analysis, 414-420

Alberti's prejudice on the best figure of an arch, 311

Amici's general equations for a ma­sonry structure, 432

Analogy between arch and bow ac­cording to Leonardo, 317fn, and Fabri, 315-320

Analogy between the problem of the arch

and the funicolar problem: de la Hire's theorem, 322-326; Mery's method, 434-436; between arches and cate­naries: Gregory's and Jakob Bernoulli's demonstrations, 326-330; Krafft's contribu­tion, 331; Stirling's solu­tion, 359; Poleni's experi­ment, 359; Bossut's deduc­tion, 381-382; Coulomb's

demonstration, 387-388; the case of arches of finite thick­ness, according to Salim­beni, 426-428; extension of the analogy to domes, ac­cording to Poleni, 360-362, and according to BOS8ut, 384; between domes and cur­tains: Bouguer's theory, 344-348; the case of domes of finite thickness, 420-424

Analogy between the linear equation of the elastic line, the lin­ear equation of the funi­colar curve, and the equa­tion of equilibrium for beams, 530fn

Annular and spiral vaults, 412 Arabian rule for determining the thick­

ness of the walls of an arch, 315fn

Arch Leonardo's concept of-, 309; ge­

ometrical rule for the safety of an- according to Leonardo, 309, and according to Cou­plet, 342; the best figure of an-: Alberti's prejudice, 311; Gregory's and Jakob Bern­oulli's solution for very thin arches, 327-330; Stirling's contribution, 359; Bossut's general theory, 375-383; Coulomb's demonstration, 388; Lorgna's attempt, 405-406; M. Fontana's equation, 407; Salimbeni's theory for arches of finite and uniform thickness, 426-428; of vari­able thickness in the hy­pothesis of smooth and mor­tarless voussoirs: de la Hire's approach, 322-326;

Arches (cont.) Couplet's variant, 339-342; Bossut's

general formulae, 379-381; Coulomb's solution, 388-390; Lorgna's approach, 406-407; G. lliccati's and M. Fontana's solution, 408-409; Salimbeni's contribution, 426; collapse mechanisms and limit analysis: de la Hire's theory, 332-336; Belidor's variant, 336-338; Couplet's contribution, 342-344; Bossut's remark, 384-385; Coulomb's method for determining the safety conditions, 394-399; Danyzy's, Gauthey's and Boistard's experiments, 399fn; Mascheroni's and Ventur-oli's limit analysis, 414-420; Audoy's contribution, 429; Lame and Clapeyron's the­orem, 430-431; made of elas­tic material: M. Fontana's approach, 409-411; Navier's solution, 431-432; Moseley's principle of "least pressure" , 434; Mery's method, 434-436; Winkler's contribution, 436-437; Curioni's theory, 437fn

Asnieres bridge, 484

Barrel vaults, see Arch Betti's theorem of reciprocity, 503 Boscovich's studies on St. Peter's dome,

351-357, and on the Cathe­dral of Milan, 371-374

Bossut's theory of vaults, 375-386 Bouguer's theory of domes, 344-348,

420-424 Breaking tests: on iron bars, 364; on

models of vaults, 399fn Bridge of S. Trinita in Florence, 328 Bridges built over the Garonne, Lot

and Tarn rivers, 484 Britannia bridge, 480-484

Subject Index 549

Castigliano's demonstration of Menabrea's

"principle of elasticity" , 517-518; theorem of work derivatives, 518-519; cal­culation of tensions in the case of self-straining, 520-522

Cathedral of Milan, 371-374 Cathedral of S. Maria del Fiore in

Florence,312-313,349-351 Center of thrust

on the weakest joints of an arch: de la Hire hypothesis, 332; Belidor's assumption, 338; Couplet's solution, 340; M. Fontana's theory, 407-411; Mascheroni's solution, 416-420; Navier's contribution, 431; Moseley's and Gerst­ner's investigations, 432; Mery's principle of the mid­dle third, 434; on the key of an arch: Couplet's as­sumption, 340; Coulomb's approach, 389-394; Mery's assumption, 434; Winkler's theory, 436-437

Centering building of domes without-, 313,

350-351; the problem of-, 340,425

Chapel of Santa Coloma, 346 Circular arch

Alberti's statement, 311; de la Hire's theorem, 332-334; Couplet's analysis of limit equilibrium, 342-344; Bossut's application of his general formula, 379; Coul­omb's calculation of the scal­ing of the width, 389-390; M. Fontana's calculation of the "convex curve" (extra­dos), 408-409

Circular planes composed of wedges having the force of domes, 412

550 Subject Index

Clapeyron's (and Lame's) theorem on the

location of the fracture joints in an arch, 430-431; three moment equation for the continuous beam, 484-485; fundamental theorem, 487-488,499,508,517

Clebsch's solution for the continuous beam,

493-495; method of defor­mations, 495-498

Coefficients of influence, 539-541 Cohesion, "produced by friction" , ac­

cording to Poleni, 364; due to tangential and normal stresses, according to Coulomb, 394-399; see also Adher­ence between voissoires

Collapse mechanisms for arches or domes; for St. Peter's dome, according to The Three Math­ematicians, 353, 356; ac­cording to Poleni, 372fn; see Arch, Dome

Colonnetti's general theory of self­straining, 522-523

Commissum denticulata, 318 Compatibility conditions, 505-507,

539-541 Complementary energy, 524-529 Composed arches and vaults, 412 Concept of force (or pressure), 442-

444, 466, 467, 473-474 Constitutive equation for elasticity,

470 Continuous beam

Clapeyron's solution, 479-485; Bertot's contribution, 485-486; Clebsch's solution, 493-495

Convex curve (extrados of an arch), see Arch of variable thick­ness

Conway bridge, 480-483 Corncob or pomegranate model for

the rupture of domes, 372-374

Cotterill's extension of the principle of least

action (or pressure), 508-509; discovery of the the­orem of work derivatives, 509-512

Coulomb's theory of frictionless and mor­

tarless vaults, 386-394; gen­eral equation of the figure of a vault acted upon any load, 388; calculation of the width of any vault under its own weight,' 388-390; the problem of the plat­band in masonry, 391-393; theory of vaults endowed with friction and cohesion, 394-399; collapse mecha­nisms, 395, 398-399; safety conditions, 396-397

Couplet's theory of arch, 338-344 Cournot's minimum principle, 475-

476 Crotti's

concept of reciprocal deforma­tion work (or complemen­tary energy), 524, 529; pos­tulate of concordant move­ment, 526-527; seven "dou­ble theorems" for the the­ory of elastic systems, 525-529

D'Alembert's approach to the prob­lem of supports, 445-447; general principle, 472

De la Hire's analogy between the problem

of the arch and the funico­lar problem, 322-326; col­lapse mechanism of an arch, 332,336,342,353,399,416, 418; calculation of the width of the abutments of an arch, 334-336

Deflections in a frame Clebsch's approach, 495-498;

Deflections in a frame (cont.) Maxwell's method, 501-503; Cas­

tigliano's solution, 518-519; Mohr's solution, 533-534

Deformation work (or energy of elas­tic deformation), 487-489, 508-509,514-515,517-522, 524-529, 543

Delange'S hypothesis for the prob­lem of supports, 456

Deran's rule for determining the thick­ness of the walls of an arch, 314-315

Dome building of-, without using props,

scaffolds and centering, 313, 350-351; geometrical con­structions for the figure of domes and the dimensions of their supports, 311, 353; the best profile of a-: Bouguer's solution for domes of min­imum thickness, 344-347; Poleni's contribution, 360-362; Bossut's general equa­tion, 384; Mascheroni's the-ory for domes of finite thick­ness, 420-424; -of variable thickness in the hypothe-sis of smooth and mortar-less voussoirs: Bouguer's and Mascheroni's theory, 422-424; the case of uniform thickness, 424; collapse mech­anisms: according to The Three Mathematicians, 353, 356; according to Poleni's and Boscovich's model of corncob or pomegranate, 372; -with a polygonal and oval base, 412

Door hinges, the problem, 457 Dorna's minimum principle, 479 Duality, law of- in geometry, 526; in

elastomechanics, 524-529 Dynamique latente, 474

Egg, the problem, 312, 321 Elastic potential energy, 436, 469-

Subject Index 551

470, 487-488; see also De­formation work

Elastic systems, 441, 488-491, 513-522

Elasticity principle (or equation), see Menabrea's principle of elasticity

Elastoplastic analysis of structures, 520-523

Empirical evaluation of the thrust on abutment piers, 309 '

Energetical principles, see Minimum principles

Equilibrium curve in converging directions of

loads, 412; for an arch, see arch, the best figure of; for a dome, see dome, the best profile of

Ether, 468 Euler's

principle for the problem of sup­ports, 444, 465, 477; solu­tion of the tripod problem, 444-445,447-448,451,455, 513-514

Extrados, calculation of the- when the intrados is given, 408-409, 411fn, 426; see Arch or Dome, of variable thick­ness

Fabri's analogy between arches and bows, 316-320

Florentine rib-and-panel vault, 312 Flying buttresses, 315, 335, 412 Fontana's, C., geometrical rules for

domes, 311, 353 Fontana's, M., calculation of the "con­

vex curve" of an arch, 408-409; discovery of ''the mid­dle third rule", 409-411; attempts at finding a "new synthesis" for the problem of supports, 453-455

Fracture joints location of- in an arch: de la

Hire's hypothesis, 332; Be­lidor's assumption, 436;

552 Subject Index

Fracture joints (cant.) Couplet's theory, 342 Bossut's

remark, 384-385; Coulomb's method, 394-399; Mascheroni's and Venturoli's method, 416-420; Lame and Clapeyron's theorem, 430-431; Gerst­ner's remark, 432; Mery's assumption, 434; location of- in a dome: the case of St. Peter's, according to the three mathematicians, 353-356; Boscovich's remark, 374

Friction, Cohesion de la Hire's remark, 326; Cou­

plet's remark, 342; Poleni's law, 364; Boscovich's re­mark, 372; Coulomb's laws of- and their application to the analysis of vaults, 390, 394-397; Venturoli's contribution, 414-420; Am­ici's treatment, 432; Mose­ley's and Gerstner's remarks, 432; coefficient (or angle) of friction, 396, 414, 432, 520; in elastic structures, 520; see also Adherence be­tween voussoirs

Frictionless (or smooth) and mor­tarless voussoirs (or joints), see Arch, Dome

Funicular equilibrium, 322-324, 342 Funicular polygon of forces, 435

Galileo's explanation of the strength of the egg, 312

Geometrical rules for determining the width of the

abutments of a vault, 314-315; for the figure of domes, 311, 353; for the safety of an arch, 309, 342

Geometrie der Lage (geometry of po­sition), 526

Green's approach to the theory of elasticity, 468-470, 517

Horror vacui, 312

Impact between two rigid bodies, 472-473

Joints direction of-, when both the in­

trados and the extrados of a vault are given, 391-394; see also Fracture joints

Key of an arch, see Center Of thrust on the-

Lagrangean methods, 451, 460, 466-467,469,510-511,517-518

Law of weights (or forces), given the figure of a vault, see Arch, Dome, of variable thickness

Leonardo's empirical evaluation of the thrust of an arch, 309; rule for the safety of an arch, 309, 342

Limit analysis of arches, see Arch Line of influence, 530-531 Line of pressure, 432, 435 Line of resistance, 432, 435 Lorgna's approach to the theory of

arch, 404-407; postulate for the problem of supports, 452-453

Malfatti's "physical axiom" for the problem of supports, 458; teleonomic principle, 460

Mascheroni's contribution to the the­ory of vaults, 412-425

Maxwell's concept of frame, 492, 507; cal­

culation of deflections in a simply stiff framework, 501-502; theorem of reci­procity, 503; calculations of tensions in statically inde­terminate frame- works, 504-507

Mechanisms of collapse for arches and domes, see Arch, Dome

Menabrea's principle of elasticity, 433, 436,476,479,488-491,512, 513-518, 520

Method of deformations, 492-498, 517-518

Method offorces, 499, 504-507, 537-542

Method of Lagrange multipliers, see Lagrangean methods

Method (or rules) of maxima and minima, 374, 386-387, 396-398,433,436-437

Middle third, rule of the-, 409-411, 431, 434

Minimum principles Vene's memoir, 474; Cournot's

solution, 475-476; Moseley's new principle of least pres­sure, 434, 476; Pagani's and Mossotti's contribution, 477-478; Dorna's solution, 478-479; Menabrea's principle of elasticity, 489-490; Bertrand's demonstration, 491; Cot­terill's extension of Mose-ley's principle, 508-509; Cas­tigliano's demonstration of Menabrea's principle, 517-518; Colonnetti's contribu-tion, 522-524; Crotti's "double theorem No. two", 525, and "dou­ble theorem No. seven" , 529

Model of smooth spheres for deter­mining the best figure of an arch or of a dome, 359-362

Mohr's analogy between the linear equa­

tion of elastic line, the lin­ear equation of the funi­colar curve, and the equa­tion of equilibrium for beams, 530fn; solution for deflec­tions in statically determi­nate trusses, 530-534;

. solution for non-canonical trusses, 534-537; solution

Subject Index 553

for statically indeterminate trusses, 537-542

Molecular theory of elasticity, 432, 467-469, 516-517

Moseley's principle of least pressure (or action), 434, 436, 476, 508-509

Mossotti's minimum principle, 477-478

Muscles Borelli's interpretation of their

action, 364; Johann Bernoulli's improvement of Borelli's mechanical model, 364-368; Poleni's experiments on Bernoulli's results, 368

Natural state of a frame, 522-523 Naval architecture, 344, 375 Non-canonical trusses, 534-537 Notched joints, 318

Pagani's minimum principle, 477 Paradox of statics, 461-462 Piesimetro, 463 Planes composed of wedges having

the force of arches, 412 Platbands in masonry, 391-394, 412-

413 Poleni's studies on St. Peter's dome,

358-371 Polygonal roofs

Leonardo's model of two bars, 309; Fabri's treatment, 316-320; Borra's approach, 400; Belgrado's solution, 400-401; Lorgna's investigation, 405; Mascheroni's analysis of the quadrangular and pen­tagonal roof, 414-416

Principle of elasticity, see Menabrea's

Principle of least pressure (or action), see Moseley's -

Principle of virtual work (or of vir­tual velocities), 356-357, 451, 456,466,475,478,488,491, 523, 531-541, 542

554 Subject Index

Pyrometer, 364

R,eciprocal deformation work, 524, 529

Reinforced beam, 318 Relative elasticity coefficients, 490 Retaining wall, 339, 405 Rigid bodies, 407, 433-434, 443-444,

461, 463-466, 472-473 Roman hull-shaped vault, 312 Roof, see Polygonal roofs Round dome of variable or constant

thickness, 424-425 Rupture joints, see Fracture joints

Safety conditions for a vault, see Arch, Dome

Scale of voussoir sizes, see Arch, Dome, of variable thickness

Second fundamental law of the dy­namical theory of heat, 470

Semicircular arch, see Circular arch Smooth, frictionless voussoirs, see Arch,

Dome Stability of equilibrium, 480, 512, 520,

529 Statically determinate systems, cal­

culation of deflections in-, see Deflections in a frame

Statically indeterminate systems, 407, 428,433-434,443,445,448, 451,455,457,458,460,463, 465,466-467,489,504-507, 537-542

Supports problem, 441-460, 461-466, 474-476,477-479,487,492

Tetrapod problem, according to M. Fontana, 454-455; accord­ing to Malfatti, 458-459

Theorem of minimum work, 489-491, 509,512,514-515,517-518, 529

Theorem of reciprocity, 503, 525-526, 541

Theorem of work derivatives, 442, 470, 509-512, 515-516,

518-519, 524-525, 542 Thermal effects on elastic structures,

521, 532-533, 538-539 Three Mathematicians'

studies on St. Peter's dome, 351-357; theorem on the strength of a ring, 356-357; Poleni's experiment on- theorem, 364-368

Three moment equation, 479, 484-487

Thrust of earth, 339, 405 Thrust of the arch on its abutments,

see Abutments, Center of thrust

Trabs armata, 318 Tripod problem, 444-445, 447-448,

459, 514 Tubular bridges for the London-Chester­

Holyhead railway, 480-484

Underwater arch, 382-383 Unilateral constraints, 445-447, 452-

453, 456, 463

Vaults, see Arch, Dome VEme's minimum or maximum prin­

ciple,474 Viviani's rules for squaring vaulted

ceilings, 311-312 Voussoirs, see Arch, Dome, of vari­

able thickness in the hy­pothesis of smooth and mor­tarless voussoirs; see also Adherence between vous­soirs

Walls of an arch, see Abutments Wedge (and lever) models for the

static behavior of an arch, 325-326,332,339-340,353-356

Winker's minimum principle, 436-437