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Abbe, C. 83 Browne, J. 59 Abu Rayhan 10 Brunswick, Duke of 91 Adcock, R.I. 163, 184-186 Buonaparte, N. 24, 46, 49, 196 Adrain, R 83-90, 92 Burke, E. 24n Aitken, A.C. 5, 96, 139, 162,241 AI-Biruni 10 Allen, G.C. 76 , N.R 236-237 Alt, F. 52 Carroll, L. 102 Anderson, N. 237 Casella, G. 80 Anderson, T.W. 241 , J. 15 Anne, Queen 9, 11 Cassini, J.D. 49 Appa, G. 46 Cassini de Thury, D.F. 49, Cauchy, A.L. 4, 5, 7, 39-42, 46, 1100, 1180, 1610,162,173,179,184,196-202,225,230, Babb, M.J. 83, 90 238-241 Bartlett, M.S. 237 Cayley, A. 162, 240 Bassett, G.W. 800 Charnes, A. 230 Bayes, T. 24, 69, 241 Charles X, King 197 Beaufort, F. 217 Charles Edward Stuart, Prince 90 Benedict XIV, Pope 16-17 Chebyshev, P.L. 330, 1830, 202, 240 Benoit, E. 151-152, 156 Cholesky, A.L. 156, 162, 240-241 Ben-Tal, A. 180 Christian VIII, King 207 Berger, RL. 80 Clapeyron, B.P.E. 520 Bernoulli, D. 69-71, 740, 75-77, 79, 131 Clarke, D. 490 Bernoulli, J. 23, 69-70, 74 , Marquis de 24 Bertrand, J.L.F. 61,94, 1200, 131-132, 139 Coolidge, J.L. 84 Bessel, F.W. 118, 122, 131 Cooper, W.W. 230 Bienayme, U. 1830,200-204,2250,240 Cotes, R. 52-57, 59-60, 126 Bjorck, A. 237 Cowden, D.J. 235 BooIe, G. 170 Cramer, G. 3, 4, Borsch, A. 94 Creedy, J. 217-218 Borgondio, O. 17 Croxton, F.E. 235 Boscovich, RJ. 2, 16-28, 31, 33, 44, 51, 60-61, Cubranic, N. 16 69, 218, 227, 2290, 241 Czuber, E. 80, 139, 184 Bose, S.S. 237 Bowditch, N. 31, 61, 83-86,90 Bowley, A.L. 218, 227-231 Dahlquist, G. 237 Bradley, J. 11 Dale, A.I. 69 Bravais, A. 163, 179-184, 1880 d' Alembert, J.le R 24 Brentjes, S. 47, 2300, 231 Davis, C.H. 93, 95-97, 99 264 Name Index

Davis, H.A. 184 Gauss, C.F. 4, 5, 13, 33n, 52-55, 58, 60-62, 67, , I-B. 38, 62-64, 66 69,71, 77-81, 91-104, 107n, 115-120, 129, Dedron, P. 102 131-149,151-162, 165n, 173,179,188,201 de la Vallee Poussin, C.J. 4, 35, 41-43, 44n, 46, -203,208-209,217,233-235,240-241 240 Geary, R.C. 74 De L'Isle, I.N. 9 George I, King 9 de Moivre, A. 24n, 80 George II, King 9, 10 de Prony, G.C.F.M. 44-46 George III, King IOn , R. 6 George Louis, Elector 9 Dixon, J.J. 17 Glaisher, J.W.L. 18n, 21, 74n, 157, 163,170, Dodgson, C.L. 102 239 Dolby, I.L. 35, 38 Goedseels, P.I.E. 41, 44n, 127,201-202 Donkin, W.F. lOin, 163-179, 183-189,203,240 Gram, J.P. 202-203, 207, 234n Doolittle, M.H. 155n, 156 Grattan-Guinness, 1.4, 33, 46, 47, 52n, 162, 230n Duffin, R.I. 41n Graybill, F.A. 238 Durbin, J. 237 Grossmann, W. 238 Dwyer, P.S. 102 Guest, P.G. 236, 238 Gummere, J. 90

Eddington, A.S. 237 Edgeworth de Firmont, H.E. 24n, 41 Haar, A. 4 Edgeworth, F.Y. 24n, 49n, 83n, 128-129, 217- Hald, A. 1, 3, 29, 207, 212, 216, 234n 231,239 Hampel, F.R. 122n Edgeworth, L. 49n Hansen, L.P. 31, 238 Edgeworth, R.L. 5, 83n, 129 Hardy, G.F. 234 Eisenhart, C. 1, 52 Harris, T. 230 Eisenstein, G. 162 Harrison, J. 11 Ellis, R.L. 80, 115, 130 Harter, H.L. 80, 163 , J. 80 Hawkins, T.W. 162 Euler, L. 10, 12-13, 51n, 59, 70, 75-77 HeImerl, F.R. 123n, 139, 173, 184,208 Ezekiel, M. 156n Hermite, C. 162 Herschel, J.F.W. 86 Heyde, C.C. 199, 205 Farebrother, R.W. 5,17,21, 34n, 37, 38, 41, Hill, E. 17 45n, 52n, 102, 147, 162, 170, 173n, 174, 189, Hoem, J.M. 207, 234n 230 Hogan, E.R. 84, 90 Farkas, J. 4 Horak:, Z. 237 Ferguson, R. 230 Hotelling, H. 188 Fermat, P. 52n Huntington, E.V. 234 Fisher, R.A. 74n, 238 Fisher, W.D. 230 Forbes, E.G. 10, 13n, Isserlis, L. 202 Forsythe, G.E. 3, 160 Itard, J. 102 Fourier, J.B.I. 5,40-41,46-47,217,225,231 Ivory, J. 54. 56-58, 67, 158, 164 Fox, L. 3, 156n , J.von 199 Franksen, O.I. 47, 52n Jacobi, C.GJ. 18n, 79n, 162, 181n, 184n, 215 Frere, B. 184 James I, King 9n Frobenius, EG. 162 James VI, King 9n Jensen, H. 156n Johnson, N.L. 74 Galilei, G. 1n, 3n, 29n Galton, E 79, 182n, 238, 239 Name Index 265

Kass, S. 187 Mitchell, R.B. 24n Karst, 0.1. 229n Morduchow, M. 237 Kelvin, Baron 170 Morgan, W. 24 Kendall, M.G. 76, 218, 241 Muir, T. 6, 179, 197n Kepler, I. 1, 28 Keynes, I.M. 74n, 80, 218 King, G. 234 Nair, K.R. 237 Krenig, I. 21 Napoleon, Emperor 25, 46, 49, 197 Kruskal, W. 184 Nekrasov, P.A. 160 Kuhn, H.W. 52n, 53 Newcomb, S. 67, 71, 74, 163, 168-170, 184,189 Kummell, C.H. 163, 184-186 Newton, I. 17n, Kveton, K. 237

albers, H.W.M. 131-132n Laboucheix, H. 24n Oppennann, L.H.F. 207, 208, 234n Lagrange, J.L. 70, 85, 96n, 103, 140, 153, 162, Owen, D.B. 45n 179, 196, 240 Lalande, I.I.le F. lIn, 59 Lambert, J.H. 69-70, 75 Paoli, G. 17 Lame, G. 52n Patterson, P. 84n Laplace, P.S. 2, 5-7, 17n, 18n, 21-31, 39-42, 45- Pearl, R. 235 47,54,58-68,69-75,77,79-81,89-90,92, Pearson, K. 31, 80, 163, 182n, 184-188,233- lOIn, 102, 105-129, 139, 165, 174, 182, 191- 235, 238-239 196,202-205,217,224,226,239-240 Pitman, E.J.G. 71,74 Lauritzen, S.L. 207 Pizzetti, P. 80, 117, 173, 184 Lavoisier, A 24 Plackett, R.L. 1,60, 61n, 70n, 79n, 90 131, 139, Ledennann, W.W. 162 147, 179n, 184,238,241 Legendre, AM. 2, 49-52, 60, 64-67, 79n, 89-90, Porter, I.G. 156 92, 105n, 165, 240, 241 Price, R. 24n Leszczynski, S. 22n Ptolemy, C. In Livingstone, D. 184 Louis XV, King lIn Louis XVI, King lIn, 197n Rainsford, H.F. 238 Louis XVIII, King 24, 197 Rao, c.R. 238, 241 Louis-Philippe, King 197 Reamur, R.A.F. de 21 Reed, L.I. 235 Reiersol, O. 238 MacIear, T. 184 Rhodes, E.C. 227-231 Maire, C. 16-20, 23, 69 Robinson, D.W. 137 Marchant, R. 238 Robinson, G 4n, 80, 127n Markov, A.A 140 Rousseeuw, P.I. 46, 47,49, 221n Markovic, Z. 17 Maria Theresa, Empress lIn Marie-Antoinette, Queen IOn 24 Scheffe, H. 238 Mason, C. 17 Schiaparelli, G.V. 80 Maxwell, J.C. 170 Schols, C.M. 184 Mayer, J.T. 2, 3, 5,9-15,22-23, 31, 41n, 59, Schmidt, E. 202-203, 208, 240 910, 102-103, 127,238-239 Schultz, H. 235 Mechain, P-F. 38, 51, 62-64, 66 Schur, I. 117n, 196 Metakides, T. 203 Seal, H.L. 70n, 93n, 178, 238 Merriman, M. 52n, 80, 83, 84, 118n, 163, 184 Segner, I.A 10 Mikami, Y. 102 Seidel, L. 160 Mills, F.C. 235 Seneta, E. 34n, 160, 162, 173n, 199,205 266 Name Index

Sheynin, G.B. 1, 13, 18n, 61n, 70n, 75-76, 80, Thackeray, W.G. 221, 225 118n, 139, 184 Thiele, T.N. 22, 207-216, 238, 239, 241 Shiau, J.J.H. 45n Thomson, W. 170 Shrivastava, M.P. 237 Thucydides In Siegel, D.M. 170 Tienstra, J.M. 238 Simon, P. 94 Trenkier, G. 13 Simpson, T. 52-53, 70n, 234 Todhunter, I. 16, 22, 23, 49, 91n, 240 Singleton, R.R. 230 Tolley, H.R. 156n Sjoberg, B. 237 Turnbull, H.W. 96, 162,241 Smart, W.M. 238 Turner, H.H. 218, 221, 224, 225 Smith, c. 46 Tycho Brahe 28 Smith, D.E. 105n Sobel, D. 11 Somerville, M. 31, 126 Victoria, Queen 9n Stanley, W.M. 184 von Schmettau, Field Marshal 9, 16 Stay, B. 17, 19,21 Steiger, W.J. 34n, 173n Stewart, G.W. 150n Wald, A. 237 Stiefel, E.L. 44, 46, 170n, 221n Wagner, H.M. 230 Stigler, S.M. 3-4, 13, 19n, 30-31, 38n, 47n, 50n, Waterhouse, W.C. 61n 51n, 52n, 53, 60, 61, 66n, 69-71, 74-75, 80, Weierstrass, K. 162 84, 85n, 90, 127, 135n, 156n, 182n, 218, 238, Whittaker, E.T. 4n, 80, 127n 240,241 Williams, E.J. 238 Stone, J. 80 Williams, H.P. 41n Sturm, C. 162, 184 Williams, J.D. 38 Subrahmanyam, K. 18n Wilson, EJ.P. 90 Svanberg, J. 125-126 Wishart, J. 203 Svenssen, P. 237 Wright, T.W. 156n

Teboulle, M. 18n Yule, G.U. 203, 235, 238-239 SUBJECT INDEX

acre (area) 84 Cauchy's inequality liOn, 196n actuarial science 24n, 207 (lunar crater) 15 adjustment centesimal degrees 28, 62, 63 canonical 208-209 centre of gravity 52, 53n, 54, 86, 165, 185-188 by correlates 152-154, 209-211 characteristic function 204 by elements 152,211-214 College de France 197 of simple triangulation 122-125 College Mazarin 49 arithmetic mean 75-77, 80, 86, 129 Collegium Carolinum 91 axiomatic characterisation 80 Collegium Ragusinum 17 principle of 77-80, 92, 163-165 Collegium Romanum 17 astronomy 9,11-12,29-30,59,100 computational considerations 100, 201, 230, 236 asymptotic theory 105-122, 127-128 availability of equipment 3, 235, 237 atmospheric pressure 64 computational cost 103n, 129, 156,201,229 Copenhagen Observatory 207 Copenhagen University 207 Basel University 75 correlates 152, 209-211 Bayesian methods, see inverse probability correlation 182n, 188, 203, 208, 238 Bees, cells of 21 Cotes's rule 52-53, 59-60, 126 Berlin Academy of Science 10 Cramer's rule 3, 103n, 115 Bernoulli's optimality criterion, see maximum probability Bernoulli's procedure 75-77 dead reckoning 86-87, 90 Biometric School 238 71, 109, 132 Boscovich's method, 17-19,25-28,60-61,218, determinant 4,6-7, 115-117,196 226 see also matrix theory adding-up constraint 18, 50, 61 (lunar crater) 15 Boscovich's geometrical solution 19-21 distances Bowditch's generalisation 61 sum of absolute 53 elemental set characterisation 60 sum of squared 51-53, 86-87, 185 Laplace's analytical solution 25-27 disturbances, see errors of observation Laplace's weighted variant 27-28 double median method see also method of situation Bowley's variant 227 Bound functions 207-208 Edgeworth's variant 218-227 British Parliament 11 duals linear programming 46 projective geometry 45n, 46 calculus (algebraic) 44, 58, 209 Dublin University 217 calculus of inequalities 40, 46, 47 calculus of probabilities 58, 61, 71, 163 cartography 9, 10, 17 268 Subject Index

Earth, see figure of the Earth geometrical description 19-21, 40, 44-45, 182, Ecole Central du Pantheon 196 224-225 Ecole Militaire 24 geometrical mean 80 Ecole Normale 24 Georg-August Academy 10, 91 Ecole des Ponts et Chaussees 196 Gottingen Observatory 9, 10 Ecole Poly technique 196, 197 Gottingen Scientific Society 10, 11 element, see unknown constant Gottingen University 91 elemental set, see linear algebra, method of graphical solution 35-38, 170n, 218-230 selected points. Greenwich Observatory 9 elementary fitting procedures, see method of averages, method of least squares (transformed), method of normal places, method Hanoverian government 9 of selected points harmonic mean 80 element of probability 70, 71, 112, 180-183 Helmstedt University 91 ellipsoid of residuals 187, 188 Homann Cartographic Bureau 9, 10 elimination procedures hypothesis tests 2, 29n, 38, 63, 209-211, 214 ancient 98-100 Fourier's 40-41 Gauss's 100-103, 195-196,200,212 independence Gauss-Jordan 103n algebraic 94n, 95, 135, 172-173,208 Mayer's 12-13,33-34 linear 93, 135 equations statistical 57, 58, 204 of condition 29, 58 influence 54, 55, 169 final 59, 66, 98, 126 lnstitut de France 50 normal 6, 50-51, 135n, 212, 218 instrumental variable methods 238 solution of, see elimination procedures, iterative inverse probability, 69-75, 118-119, 131, 179 procedures optimality criteria 70-71 equilibrium, 165 see also maximum probability relative, 166-168 iterative procedures (linear) errors Gauss-Seidel 159-160 in departure 87-88 incomplete adjustment 159-160 law of, see law of errors Jacobi's 205 limits of 52 observed, see observed errors of observation 5, 122, 173, 183 Jesuit Order 16-17, 70n see also mean absolute error, mean positive Jupiter (planet) 13 error, mean squared error, probable error Euler's method 13 Kuhn-Tucker theorem 47 facility function see law of errors figure of the Earth 19,38,62-64, 89, 225-226 Lagrange's method of multipliers 85, 153 fluxions 85 law of eponymy 240 force 164-171, 177 law of errors free or unbound functions 207-208 chi-squared 182-183 French National Assembly 61 double exponential 72-74 general 70,105,128,129, 131,180 normal, see normal law of errors Gauss-Markov Theorem 114-115, 139-140 semicircular 75 Gauss-Newton procedure 94, 205 symmetric stable 204 geodesy 9, 88, 122-125 least median of squares procedure 46, 221n see also survey (trigonometrical) least squares procedure, see method of least squares Subject Index 269 least sum of absolute errors procedure, see also mean positive error constrained, see Boscovich's method mean positive error 109-111. 116 unconstrained, see method of situation see also most advantageous least sum of even powers 53-54 mean squared error 129. 132. 208 least sum of squared errors, see method of least see also most plausible value squares measure of precision 92. 94-98. 117-122. 133, leverage, see influence 170, 171,214,226 levers, see mechanical models for least squares measurement error model 237 likelihood function 166n mechanical models for least squares see also element of probability, maximum Cotes's 54, 55 likelihood Donkin's 163-168, 170 limit distribution 105-121, Ivory's 54-59 linear algebra Newcomb's 168-171 convex hull 45, 46n median 80, 121-122 elemental set 18n, 45, 60, 61 meridian arc measurements 27, 28, 34, 37, 50, orthogonal complement 173,204,208,211 61,63,65 see also matrix theory method of averages linear equation systems, see elimination Laplace's first variant 29-31, 107 procedures, iterative procedures Laplace's second variant 125-127, 197 linear inequalities, see calculus of inequalities Mayer's variant 13-15, 221, 234, 238 linear programming 4-5,46-47, 230-231 modern variant 237 logistic function 235 method of elemental sets, London, Royal Society of, 17 see method of selected points London University 217 method of interpolation 197-202, 238 lunar tables 12, 59 method of least squares 47, Benoit's illustrative example 151-152 Bienayme's derivation 200-202 Makeham's formula 233 Cauchy's derivation 203-204 Manilius (lunar crater) 15 computational procedures, see elimination Markov chain theory 162n procedures, iterative procedures Mars (planet) 28 constrained 152, 157-158,209 matrix games 38 Donkin's derivation 164-165 matrix theory elemental set characterisation 18n Binet-Cauchy theorem lIOn Fourier's contribution 47 Cholesky decomposition 156, 240 Gauss's first derivation 91-94 generalised inverse 137 Gauss's second derivation 131-132, 134-140 in verse of a symmetric matrix 160-161 generalised 5, 241 inverse of a triangular matrix 141-143 indirect, see method of averages, method of latent root decomposition 174-179 interpolation LDL' decomposition 96, 141-142, 179,240 Laplace's derivation 107-117,128 LL' decomposition 156,240 Legendre's derivation 50-52 linear dependence 93, 136 Legendre's illustrative example 64-66 notation 104, 161n, 194, 196 mechanical models, see mechanical models for origins 162 least squares orthogonal complement 173. 204. 208. 211 nonlinear 94, 233-235 Vandermonde decomposition 215n Thiele's derivation 208-214 see also determinant. linear algebra transformed 233-235 maximum absolute error 198, 204 two-stage, see method of normal places maximum likelihood. see maximum probability updating formulas 144-148 maximum probability 52. 75-76, 91-94. 131 method of medians, see double median method see also most probable value method of moments 31, 234 mean absolute error 132 generalised 31, 238 270 Subject Index

method of normal places 126n, 214-216,236,238 Nuremberg Cosmographical Society 10 method of selected points 6, 12,61 230, 234 method of situation Edgeworth's double median method 218, 225- observations 227 adding 144-146 Edgeworth's first variant 218 deleting 51, 148 Edgeworth's geometrical analogy 224-225 precision of, see measure of precision Edgeworth's illustrative example 219, 226 observatory Edgeworth's second variant 221-225 see Copenhagen, GOttingen, Greenwich, Paris elemental set characterisation 60 observed errors 5, 41, 173 Fourier's description 41 see also residuals Laplace's variant 127-128 optimality criterion, see inverse probability, Rhodes's algorithm 227-230 maximum absolute error, maximum likelihood, Turner's graphical solution 218-221 maximum probability, mean absolute error, see also Boscovich's method mean positive error, mean squared error, metre (length) 50, 61, 64, 66 variance, weight midrange 13, 71 orthogonalleast squares 184-188 minimax method 5, 54 orthogonal polynomials 203, 236 Cauchy'S generalisation 39, 40-41 orthogonalisation procedures characterisation 34, 35, 45 Cauchy-Bienayme 200, 202 de la Vallee Poussin's solution 41-43 Gram-Schmidt 202-203, 240 de Prony's geometrical solution 44-46 Laplace's 191-196 Fourier's geometrical solution 40 Oxford University 163,217 Laplace's first solution, 33-35 Laplace's second solution, 35-37 Laplace's third solution, 38-39 Pallas (asteroid) 100 Laplace's illustrative example 63 parallel rules 46 Stiefel's classification 46 Paris Observatory 9 mode 80 parameter, see unknown constant module (length) 62 pendulum measurements 66, 89, 225 moment of inertia 131-132, 179, 187 perch (length) 84 Moon (satellite) II, 15, 22 perpendicular least squares 184-188 libration of 59 plausibility function 171 see also lunar tables potential energy function 166 most advantageous values 57, 107 principal componant analysis 3, 188 of the unknown constants 111-114 probability most plausible value 148-149, 155, 165 curve, see element of probability constrained 151-157 density, see law of error of the mean squared error 133-134 inverse, see inverse probability of the unknown constants 134-140, 166 maximum, see maximum probability most probable value 59, 78, 85, 91-98, 106, probable error 117-122 117-118,164,186 pyramids at Memphis 46-47

Newton-Raphson procedure 94 quadratic programming 47 nonlinear programming 47, 52n quadrature 234 nonlinear relationships 2, 230, 233-235 Queen's College 83 normal law of errors 5, 107-108, 111, 128, 149, 164,208 Adrain's derivations 85-86 regie (length) 28, 64 bivariate 86, 90, 238 regression analysis 238 Gauss's derivation 77-80, 86 residuals 194 notation 6-7, 12On, 152, 166n, 180n Subject Index 271

linear unbiased scalar 171-174 Taylor series expansion 2 recursive 149, 157, 174 thermometer 64 see also observed errors taise (length) 18, 28, 62, 64 rood (area) 84 robust procedures 22, 54n, 122,231 Rutgers University 83 unknown constant 5 University, see Basel, Copenhagen, Dublin, G6ttingen, Helmstedt, London, Oxford, Saturn (planet) 13, 29-30 Rutgers, Sorbonne. scale parameter, see measure of precision Updating formulas, least squares, 144-148 score vector 166n Simpson's rule 234 simultaneous linear equations, see elimination variance, see weight procedures, iterative procedures Venus (planet) 220, 225 slope parameter, see unknown constant versed sine 17n, 18 Society of Jesus 16, 17, 70n Sorbonne 197 St. Petersburg Academy of Science 10 weight 27, 28, 52, 54, 55, 115, 139, 153, 164- Stiefel's exchange method 44 165, 169, 170,220 subset selection method, see method of selected changing 137-138, 147-148 points maximum 115, 135, 137 Sun 11, 22, 30 of determination 154, 166, 177, 193-194 surveying, land of observation, see measure of precision Bowditch's method of correction 84 see also mean squared error, most plausible surveying, trigonometrical 9, 17, 88, 151 value Benoit's illustrative example 151-152 Laplace's adjustment 122-125 Springer Series in Statistics

(continued from p. ii)

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