E. T. Whittaker

On a New Method of Graduation

Suppose that as a result of observation or experience of some kind we have obtained a set of values of a variable u corresponding to equidistant values of its argument; let these be denoted by u 1 , u 2 , … u n If they have been derived from observations of some natural phenomenon, they will be affected by errors of observation; if they are statistical data derived from the examination of a comparatively small field, they will be affected by irregularities arising from the accidental peculiarities of the field; that is to say, if we examine another field and derive a set of values of u from it, the sets of values of u derived from the two fields will not in general agree with each other In any case, if we form a table of the differences δ u 1 = u 2 – u 1 , δ u 2 = u 3 – u 2 , …, δ 2 u 1 = δ u 2 − δ u 1 , etc., it will generally be found that these differences are so irregular that the difference-table cannot be used for the purposes to which a difference-table is usually put, viz., finding interpolated values of u , or differential coefficients of u with respect to its argument, or definite integrals involving u ; before we can use the difference-tables we must perform a process of “smoothing,” that is to say, we must find another sequence u 1 ′, u 2 ′, u 3 ′, …, u n ′, whose terms differ as little as possible from the terms of the sequence u 1 , u 2 , … u n , but which has regular differences. This smoothing process, leading to the formation of u 1 ′, u 2 ′ … u n ′, is called the graduation or adjustment of the observations.

A Treatise on the Analytical Dynamics of Particles and Rigid Bodies: Contents

Thu, 13 Dec 2018 05:59:00 GMT a treatise on the analytical pdf In classical mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system.This contrasts with synthetic geometry.. Analytic geometry is widely used in physics and engineering, and also in aviation, rocketry, space science, and spaceflight.It is the foundation of most modern fields of geometry, including algebraic ... Sun, 09 Dec 2018 00:20:00 GMT Analytic geometry Wikipedia The Sciencemadness library currently holds 50426 pages of reading and reference material in 107 volumes. Shorter articles from the old Sciencemadness library remain available. Thanks go to BromicAcid for providing hosting for these old books during our time of lean bandwidth. Thanks also go to S.C. Wack for providing many of the books found here. Most of these books are provided as PDF with ... Sat, 15 Dec 2018 05:21:00 GMT Scientific and technical books of yesteryear Sciencemadness 01 ANALYTICAL PROCEDURES Laboratory Manual 01-1/

A Treatise on the Analytical Dynamics of Particles and Rigid Bodies: INDEX OF TERMS EMPLOYED

Thu, 13 Dec 2018 05:59:00 GMT a treatise on the analytical pdf In classical mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system.This contrasts with synthetic geometry.. Analytic geometry is widely used in physics and engineering, and also in aviation, rocketry, space science, and spaceflight.It is the foundation of most modern fields of geometry, including algebraic ... Sun, 09 Dec 2018 00:20:00 GMT Analytic geometry Wikipedia The Sciencemadness library currently holds 50426 pages of reading and reference material in 107 volumes. Shorter articles from the old Sciencemadness library remain available. Thanks go to BromicAcid for providing hosting for these old books during our time of lean bandwidth. Thanks also go to S.C. Wack for providing many of the books found here. Most of these books are provided as PDF with ... Sat, 15 Dec 2018 05:21:00 GMT Scientific and technical books of yesteryear Sciencemadness 01 ANALYTICAL PROCEDURES Laboratory Manual 01-1/

On a class of Differential Equations whose solutions satisfy Integral Equations

The science of the solution of Differential Equations has been in great measure systematized by the aid of ideas borrowed from the Theory of Functions, the equations being classified according to the singularities possessed by their solutions. In the case of linear Differential Equations of the second order the solutions can have no singularities except at the singularities of the functions q ( x ) and r ( x ) (and possibly also at x = ∞ ): these equations may therefore be classified simply according to the number and nature of these singularities .

On the Connexion of Algebraic Functions with Automorphic Functions.

If u and z are variables connected by an algebraic equation, they are, in general, multiform functions of each other; the multiformity can be represented by a Riemann surface, to each point of which corresponds a pair of values of u and z. Poincaré and Klein have proved that a variable t exists, of which u and z are uniform automorphic functions; the existence-theorem, however, does not connect t analytically with u and z. When the genus (genre, Geschlecht) of the algebraic relation is zero oi unity, t can be found by known methods; the automorphic functions required are rational functions, and doubly periodic functions, in the two case respectively.

Albert Einstein, 1879-1955

Albert Einstein was born on 14 March 1879, at Ulm in Wurttemberg, Germany, the son of Hermann Einstein and his wife, Pauline, née Koch. Hermann Einstein was in partnership with his brother, an engineer, in a small factory producing electrical supplies. From an autobiographical fragment* we learn that the Einstein parents were Jewish, but non-observant of their religion; at a very early age the boy’s religious nature became dissatisfied with the spiritual emptiness of his surroundings: seeking for something deeper, he attached himself ardently for a time to the faith of his fathers; but further reading led him to the opinion that fact cannot easily be separated from legend in the framework of Jewish history, and he ceased to accept Judaism as a transcendental religion, while retaining its humanitarian principles. In later life he was a keen Zionist and a Governor of the Hebrew University of Jerusalem. Meanwhile, his education was somewhat irregular, owing chiefly to changes in domicile brought about by unsatisfactory circumstances in his father’s business. Between the ages of 10 and 15 he attended the Luitpold Gymnasium at Munich. Later for a year he became a pupil of the cantonal school at Aarau in Switzerland, and at the age of 17 he entered the Technische Hochschule at Zurich, each successive move involving some discontinuity in the curriculum.

A Formula for the Solution of Algebraic or Transcendental Equations

Statement of the formula and numerical examples of it. The object of the present note is to communicate the following formula for the solution of algebraic or transcendental equations: The root of the equation

Note on the law that light-rays are the null geodesics of a gravitational field

In the “special” or “restricted” theory of relativity, for which the line-element ds of the “world” of space-time is given by , the geodesics of the world are straight lines, and the null geodesics (i.e. the geodesics for which ds vanishes) are the tracks of rays of light. When Einstein discovered the “general“ theory of relativity, in which the effects of gravitation are taken into account, he carried over this principle by analogy, and asserted its truth for gravitational fields; it was, in fact, the basis of his famous calculation of the deviation of light at the sun. The law was, however, not proved at the time: and indeed there is the obvious difficulty in proving it, that strictly speaking there are no “rays” of light—that is, electromagnetic disturbances which are filiform, or drawn out like a thread—except in the limit when the frequency of the light is infinitely great: in all other cases, diffraction causes the “ray” to spread out over a three-dimensional region.

Vito Volterra, 1860 - 1940

Vito Volterra was born at Ancona on 3 May 1860, the only child of Abramo Volterra and Angelica Almagià. When he was three months old the town was besieged by the Italian army and the infant had a narrow escape from death, his cradle being actually destroyed by a bomb which fell near it. When he was barely two years old his father died, leaving the mother, now almost penniless, to the care of her brother Alfonso Almagia, an employee of the Banca Nazionale, who took his sister into his house and was like a father to her child. They lived for some time in Terni, then in Turin, and after that in Florence, where Vito passed the greater part of his youth and came to regard himself as a Florentine. At the age of eleven he began to study Bertrand’s Arithmetic and Legendre’s Geometry, and from this time on his inclination to mathematics and physics became very pronounced. At thirteen, after reading Jules Verne’s scientific novel Around the Moon, he tried to solve the problem of determining the trajectory of a projectile in the combined gravitational field of the earth and moon: this is essentially the ‘restricted Problem of Three Bodies’, and has been the subject of extensive memoirs by eminent mathematicians both before and after the youthful Volterra’s effort: his method was to partition the time into short intervals, in each of which the force could be regarded as constant, so that the trajectory was obtained as a succession of small parabolic arcs. Forty years later, in 1912, he demonstrated this solution in a course of lectures given at the Sorbonne.

On Determinants whose elements are Determinants

The present paper is concerned with determinants whose elements are themselves determinants. The best-known determinants of this kind are those whose elements are minors of a given determinant; these are called the “adjugate” and the “compounds” of the given determinant. Determinants whose elements are themselves determinants also occur frequently in Muirs theory of Extensionals. The determinants considered in the present paper are of a somewhat more general type than adjugates, compounds, and extensionals; the principal result obtained is “Theorem A” (at the end of § 2), which relates to determinants whose elements are formed from any number of arrays. It is shown in § 3 that many other formulae, both new and old, may be obtained by specialising the arrays in “Theorem A.”