chemical elements (1867):

Lavoisier's Elements of Chemistry (1789) was the first modern list of chemical elements, with 33 including light & caloric.  By 1818 Berzelius had determined atomic weights for 45 of the then 49 accepted elements.  In the 1860s various scientists from across Europe worked on classifying the elements in table format showing their atomic weights; numerous relations & trends were noted.  In 1869 Mendeleev identified 66 elements.  he used his periodic to correct certain erroneous properties of known elements & predicted 8 elements yet to be discovered.  His predictions were corroborated a few years later.  Until the early 20th century an element was defined as a pure substance that could not be decomposed into any simpler substance; it cannot be transformed into other chemical elements by chemical processes.  Elements were distinguished by their atomic weights, a property measurable with fair accuracy by available analytical techniques.

 

chemical elements (1917):

In 1913 the English physicist H. Moseley discovered that the nuclear charge is the physical basis for an atom's atomic number, further refined when the nature of protons & neutrons became appreciated.  This led to the modern definition of an element based on atomic number, the number of protons per atomic nucleus.  The use of atomic numbers, rather than atomic weights, to distinguish elements has greater predictive value & resolves certain ambiguities in the chemistry.

 

chemical elements (volatilizing): * see Endnote<A>

Elements change through nuclear transmutation, the conversion of a chemical element or an isotope into another chemical element.  Elements are defined by the number of protons & neutrons in the atomic nucleus, transmutation occurs when the number of protons or neutrons changes.  This occurs either via a nuclear reaction (where outside particles react with a nucleus) or by radioactive decay (where no outside cause is needed).  This was first observed by Soddy & Rutherford in 1901 when they discovered radioactive thorium converting into radium, the natural transmutation as part of the radioactive decay of the alpha decay type.  In 1919 Rutherford had shown a proton was emitted from alpha bombardment experiments, though he had no information about the residual nucleus.  The 1921-1924 experiments by Blackett provided the first evidence of an artificial nuclear transmutation.  Blackett correctly identified the underlying integration process & identity of the residual nucleus.  In 1925 he & Rutherford achieved the first artificial transmutation of nitrogen into oxygen, using alpha particles directed at nitrogen

 

Physiology:

branch of biology dealing with the functions & activities of living organisms and their parts, including all physical and chemical processes.

 

acoustics, optics & heat (distinguished by bodily senses):

this would be respectively hearing, seeing & feeling

 

dynamics of matter…aether: * see EndNote<B>

in this context Spengler probably means simply space; atomic theory speculated that atoms were mostly space, tiny bits of matter surrounded by huge volumes of empty space

and see above page 418- Luminous aether, Lord Kelvin (proved mathematically no aether)

 

epistemology (latest): * see EndNote<C>

branch of philosophy concerned with knowledge, its nature, origin & scope; epistemic justification, the rationality of belief & related issues; 1 of 4 main branches of philosophy (with ethics, logic & metaphysics).

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higher analysis:

branch of mathematics dealing with limits & related theories, such as differentiation, integration, measure, infinite series, and analytic functions, usually studied in the context of real & complex numbers and functions; it evolved from calculus; although distinct from geometry it can be applied to any space of mathematical objects that has a definition of nearness (a topological space) or specific distances between objects (a metric space)

 

theoretical physics:

branch of physics that employs mathematical models & abstractions of physical objects and systems to rationalize, explain and predict natural phenomena; it is differentiated from experimental physics, which uses experimental tools to probe these phenomena.

 

theory of Relativity:

see above page 419

 

sign-language (of the emanation-theory of radioactivity): * see Endnote<D>

this is a reference to standard scientific, mathematical notation used to describe the phenomenon of radiation

 

emanation-theory of radioactivity:

theory of Rutherford & Soddy (1902) which defined radioactivity as an ‘atomic’ phenomenon accompanied by sub-atomic ‘chemical’ changes.  In 1902, Rutherford had not yet inferred from large-angle scattering experiments that the atom had a nucleus.  They posited that a chemical element was transformed into another by emitting charged particles, either α-particles or β-particles.  Rutherford already knew that radioactivity manifested itself in the form of ‘alpha rays’ or ‘beta rays’, which proved to consist of particles.  This theory called into question the immutable atom of 18th & 19th century science and proposed the transitory nature of elements (rather than Lavoisier's permanent & stable elements).

 

elements (valency):

in chemistry the quality that determines the number of atoms or groups with which any single atom or group will unite chemically; the relative combining capacity of an atom or group compared with that of the standard hydrogen atom

 

elements (weight):

aka atomic mass, the mass of an atom; in the 19th century the standard for atomic weight was hydrogen, with a value of 1, from 1900 oxygen was used as the reference standard.  Protons & neutrons of the atomic nucleus account for most of the total mass of atoms (electrons & nuclear binding energy make minor contributions).  Consequently the numeric value of the atomic mass has nearly the same value as the mass number, the sum of the protons & neutrons in a nucleus.

 

elements (affinity):

see page above 425 –chemical affinity.

 

elements (reactivity):

aka reactivity series; in Chemistry an empirical, calculated & structurally analytical progression of a series of metals, arranged by their "reactivity" from highest to lowest, used to summarize information about the reactions of metals with acids & water, single displacement reactions and the extraction of metals from their ores.

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elements…compounds:

The conventional use of the word “compound” in Chemistry refers to pure substances composed of 2 or more elements whose composition is constant.  We refer to these compounds as molecules (e.g. water, H2O, oxygen & hydrogen atoms).  However, in the context of this discussion, Spengler is using the word “compound” in a rather idiosyncratic manner.  He is not referring to molecules, but to atoms, which are “complexes of different units”, the latter being sub-atomic particles, electrons, protons & neutrons.  All 3 had been tentatively identified by 1922 (publication date for 2nd edition Decline).  This somewhat clumsy reference may reflect the newly discovered nature of sub-atomic particles, an incomplete (or sceptical) understanding or simply a weak translation.

 

lifetime of elements:

see above page 423-radioactivity (chronological number)

 

Lavoisier (his elements):

co-writer of “Method of Chemical Nomenclature” (1787) which introduced a new system which was linked to Lavoisier's new oxygen theory of chemistry.  It abandoned the Classical elements (earth, air, fire, & water) replacing them with 55 substances.  These substances were elements that could not be decomposed into simpler substances by any known chemical means.  In 1789 he published his Elementary Treatise on Chemistry, presenting a unified view of the new theories of chemistry.  Prominent were his list of “elements” which could NOT be broken down by any known method of chemical analysis; from said elements came the chemical compounds

 

Entropy:

see above page 420, 421, 422

 

aggregates:

aka set theory; branch of mathematical logic that studies sets or collections of objects; objects of any kind can be collected, but set theory is mostly concerned with those relevant to mathematics.  The study of set theory was initiated by the German mathematicians G. Cantor (considered the founder) & R. Dedekind in the 1870s.

 

square numbers:

aka perfect square; an integer that is the square of an integer; the product of some integer with itself (e.g. 9 is a square number, as it equals 3 squred & can be written as 3 × 3)

 

differential equations:

see Chapter II page 89

 

potency: * see Endnote<E>

in this context the word may refer to power sets; In set theory, the power set of a set S is the set of all subsets of S, including the empty set and S itself.  It is the set of all the subsets of a set.

 

order:

an ordered set is defined as a sequence of elements that is distinguished from the other sequences of the same elements by the order of the elements.  Thus Set Alpha {a, b} is not identical to Set Bravo {b, a}

 

equivalence:

two sets are equivalent if they have the same number of elements; equivalence relations highlight one characteristic of the objects being studied while ignoring all the others; equivalence brings the issue of size (a.k.a. cardinality) into focus while ignoring other features

an example- if Set A = {1,2,3} and Set B= {a, b, c}, then Set A and Set B are equivalent

 

countableness:

in set theory, a countable set is a non-infinite set, whose cardinal number is smaller than the set of all natural numbers; conversely an uncountable set is an infinite set that contains too many elements to be countable. The uncountability of a set is related to its cardinal number: a set is uncountable if its cardinal number is larger than that of the set of all natural numbers;