Essays On Education And Kindred Subjects (Fiscle Part- 11) by Herbert Spencer (best fiction novels to read TXT) 📕

Fixed, Could So Regular An Architecture Be Executed. In The   Case Of    The

Other Division Of    Concrete Mathematics--Mechanics, We Have Definite

Evidence Of    Progress. We Know That The   Lever And The   Inclined Plane Were

Employed During This Period: Implying That There Was A Qualitative

Prevision Of    Their Effects, Though Not A Quantitative One. But We Know

More. We Read Of    Weights In The   Earliest Records; And We Find Weights In

Ruins Of    The   Highest Antiquity. Weights Imply Scales, Of    Which We Have

Also Mention; And Scales Involve The   Primary Theorem Of    Mechanics In Its

Least Complicated Form--Involve Not A Qualitative But A Quantitative

Prevision Of    Mechanical Effects. And Here We May Notice How Mechanics,

In Common With The   Other Exact Sciences, Took Its Rise From The   Simplest

Application Of    The   Idea Of    _Equality_. For The   Mechanical Proposition

Which The   Scales Involve, Is, That If A Lever With _Equal_ Arms, Have

_Equal_ Weights Suspended From Them, The   Weights Will Remain At _Equal_

Altitudes. And We May Further Notice How, In This First Step Of    Rational

Mechanics, We See Illustrated That Truth Awhile Since Referred To, That

As Magnitudes Of    Linear Extension Are The   Only Ones Of    Which The

Equality Is Exactly Ascertainable, The   Equalities Of    Other Magnitudes

Have At The   Outset To Be Determined By Means Of    Them. For The   Equality

Of The   Weights Which Balance Each Other In Scales, Wholly Depends Upon

The Equality Of    The   Arms: We Can Know That The   Weights Are Equal Only By

Proving That The   Arms Are Equal. And When By This Means We Have Obtained

A System Of    Weights,--A Set Of    Equal Units Of    Force, Then Does A Science

Of Mechanics Become Possible. Whence, Indeed, It Follows, That Rational

Mechanics Could Not Possibly Have Any Other Starting-Point Than The

Scales.

Let Us Further Remember, That During This Same Period There Was A

Limited Knowledge Of    Chemistry. The   Many Arts Which We Know To Have Been

Carried On Must Have Been Impossible Without A Generalised Experience Of

The Modes In Which Certain Bodies Affect Each Other Under Special

Conditions. In Metallurgy, Which Was Extensively Practised, This Is

Abundantly Illustrated. And We Even Have Evidence That In Some Cases The

Knowledge Possessed Was, In A Sense, Quantitative. For, As We Find By

Analysis That The   Hard Alloy Of    Which The   Egyptians Made Their Cutting

Tools, Was Composed Of    Copper And Tin In Fixed Proportions, There Must

Have Been An Established Prevision That Such An Alloy Was To Be Obtained

Only By Mixing Them In These Proportions. It Is True, This Was But A

Simple Empirical Generalisation; But So Was The   Generalisation

Respecting The   Recurrence Of    Eclipses; So Are The   First Generalisations

Of Every Science.

Respecting The   Simultaneous Advance Of    The   Sciences During This Early

Epoch, It Only Remains To Remark That Even The   Most Complex Of    Them

Must Have Made Some Progress--Perhaps Even A Greater Relative Progress

Than Any Of    The   Rest. For Under What Conditions Only Were The   Foregoing

Developments Possible? There First Required An Established And Organised

Social System. A Long Continued Registry Of    Eclipses; The   Building Of

Palaces; The   Use Of    Scales; The   Practice Of    Metallurgy--Alike Imply A

Fixed And Populous Nation. The   Existence Of    Such A Nation Not Only

Presupposes Laws, And Some Administration Of    Justice, Which We Know

Existed, But It Presupposes Successful Laws--Laws Conforming In Some

Degree To The   Conditions Of    Social Stability--Laws Enacted Because It

Was Seen That The   Actions Forbidden By Them Were Dangerous To The   State.

We Do Not By Any Means Say That All, Or Even The   Greater Part, Of    The

Laws Were Of    This Nature; But We Do Say, That The   Fundamental Ones Were.

It Cannot Be Denied That The   Laws Affecting Life And Property Were Such.

It Cannot Be Denied That, However Little These Were Enforced Between

Class And Class, They Were To A Considerable Extent Enforced Between

Members Of    The   Same Class. It Can Scarcely Be Questioned, That The

Administration Of    Them Between Members Of    The   Same Class Was Seen By

Rulers To Be Necessary For Keeping Their Subjects Together. And Knowing,

As We Do, That, Other Things Equal, Nations Prosper In Proportion To The

Justness Of    Their Arrangements, We May Fairly Infer That The   Very Cause

Of The   Advance Of    These Earliest Nations Out Of    Aboriginal Barbarism Was

The Greater Recognition Among Them Of    The   Claims To Life And Property.

But Supposition Aside, It Is Clear That The   Habitual Recognition Of

These Claims In Their Laws Implied Some Prevision Of    Social Phenomena.

Even Thus Early There Was A Certain Amount Of    Social Science. Nay, It

May Even Be Shown That There Was A Vague Recognition Of    That Fundamental

Principle On Which All The   True Social Science Is Based--The Equal

Rights Of    All To The   Free Exercise Of    Their Faculties. That Same Idea Of

_Equality_ Which, As We Have Seen, Underlies All Other Science,

Underlies Also Morals And Sociology. The   Conception Of    Justice, Which Is

The Primary One In Morals; And The   Administration Of    Justice, Which Is

The Vital Condition Of    Social Existence; Are Impossible Without The

Recognition Of    A Certain Likeness In Men's Claims In Virtue Of    Their

Common Humanity. _Equity_ Literally Means _Equalness_; And If It Be

Admitted That There Were Even The   Vaguest Ideas Of    Equity In These

Primitive Eras, It Must Be Admitted That There Was Some Appreciation Of

The Equalness Of    Men's Liberties To Pursue The   Objects Of    Life--Some

Appreciation, Therefore, Of    The   Essential Principle Of    National

Equilibrium.

Thus In This Initial Stage Of    The   Positive Sciences, Before Geometry Had

Yet Done More Than Evolve A Few Empirical Rules--Before Mechanics Had

Passed Beyond Its First Theorem--Before Astronomy Had Advanced From Its

Merely Chronological Phase Into The   Geometrical; The   Most Involved Of

The Sciences Had Reached A Certain Degree Of    Development--A Development

Without Which No Progress In Other Sciences Was Possible.

Only Noting As We Pass, How, Thus Early, We May See That The   Progress Of

Exact Science Was Not Only Towards An Increasing Number Of    Previsions,

But Towards Previsions More Accurately Quantitative--How, In Astronomy,

The Recurring Period Of    The   Moon's Motions Was By And By More Correctly

Ascertained To Be Nineteen Years, Or Two Hundred And Thirty-Five

Lunations; How Callipus Further Corrected This Metonic Cycle, By Leaving

Out A Day At The   End Of    Every Seventy-Six Years; And How These

Successive Advances Implied A Longer Continued Registry Of    Observations,

And The   Co-Ordination Of    A Greater Number Of    Facts--Let Us Go On To

Inquire How Geometrical Astronomy Took Its Rise.

The First Astronomical Instrument Was The   Gnomon. This Was Not Only

Early In Use In The   East, But It Was Found Also Among The   Mexicans; The

Sole Astronomical Observations Of    The   Peruvians Were Made By It; And We

Read That 1100 B.C., The   Chinese Found That, At A Certain Place, The

Length Of    The   Sun's Shadow, At The   Summer Solstice, Was To The   Height Of

The Gnomon As One And A Half To Eight. Here Again It Is Observable, Not

Only That The   Instrument Is Found Ready Made, But That Nature Is

Perpetually Performing The   Process Of    Measurement. Any Fixed, Erect

Object--A Column, A Dead Palm, A Pole, The   Angle Of    A Building--Serves

For A Gnomon; And It Needs But To Notice The   Changing Position Of    The

Shadow It Daily Throws To Make The   First Step In Geometrical Astronomy.

How Small This First Step Was, May Be Seen In The   Fact That The   Only

Things Ascertained At The   Outset Were The   Periods Of    The   Summer And

Winter Solstices, Which Corresponded With The   Least And Greatest Lengths

Of The   Mid-Shadow; And To Fix Which, It Was Needful Merely To Mark The

Point To Which Each Day's Shadow Reached.

And Now Let It Not Be Overlooked That In The   Observing At What Time

During The   Next Year This Extreme Limit Of    The   Shadow Was Again Reached,

And In The   Inference That The   Sun Had Then Arrived At The   Same Turning

Point In His Annual Course, We Have One Of    The   Simplest Instances Of

That Combined Use Of    _Equal Magnitudes_ And _Equal Relations_, By Which

All Exact Science, All Quantitative Prevision, Is Reached. For The

Relation Observed Was Between The   Length Of    The   Sun's Shadow And His

Position In The   Heavens; And The   Inference Drawn Was That When, Next

Year, The   Extremity Of    His Shadow Came To The   Same Point, He Occupied

The Same Place. That Is, The   Ideas Involved Were, The   Equality Of    The

Shadows, And The   Equality Of    The   Relations Between Shadow And Sun In

Successive Years. As In The   Case Of    The   Scales, The   Equality Of

Relations Here Recognised Is Of    The   Simplest Order. It Is Not As Those

Habitually Dealt With In The   Higher Kinds Of    Scientific Reasoning, Which

Answer To The   General Type--The Relation Between Two And Three Equals

The Relation Between Six And Nine; But It Follows The   Type--The Relation

Between Two And Three, Equals The   Relation Between Two And Three; It Is

A Case Of    Not Simply _Equal_ Relations, But _Coinciding_ Relations. And

Here, Indeed, We May See Beautifully Illustrated How The   Idea Of    Equal

Relations Takes Its Rise After The   Same Manner That That Of    Equal

Magnitude Does. As Already Shown, The   Idea Of    Equal Magnitudes Arose

From The   Observed Coincidence Of    Two Lengths Placed Together; And In

This Case We Have Not Only Two Coincident Lengths Of    Shadows, But Two

Coincident Relations Between Sun And Shadows.

From The   Use Of    The   Gnomon There Naturally Grew Up The   Conception Of

Angular Measurements; And With The   Advance Of    Geometrical Conceptions

There Came The   Hemisphere Of    Berosus, The   Equinoctial Armil, The

Solstitial Armil, And The   Quadrant Of    Ptolemy--All Of    Them Employing

Shadows As Indices Of    The   Sun's Position, But In Combination With

Angular Divisions. It Is Obviously Out Of    The   Question For Us Here To

Trace These Details Of    Progress. It Must Suffice To Remark That In All

Of Them We May See That Notion Of    Equality Of    Relations Of    A More

Complex Kind, Which Is Best Illustrated In The   Astrolabe, An Instrument

Which Consisted "Of Circular Rims, Movable One Within The   Other, Or

About Poles, And Contained Circles Which Were To Be Brought Into The

Position Of    The   Ecliptic, And Of    A Plane Passing Through The   Sun And The

Poles Of    The   Ecliptic"--An Instrument, Therefore, Which Represented, As

By A Model, The   Relative Positions Of    Certain Imaginary Lines And Planes

In The   Heavens; Which Was Adjusted By Putting These Representative Lines

And Planes Into Parallelism And Coincidence With The   Celestial Ones; And

Which Depended For Its Use Upon The   Perception That The   Relations

Between These Representative Lines And Planes Were _Equal_ To The

Relations Between Those Represented.

Were There Space, We Might Go On To Point Out How The   Conception Of    The

Heavens As A Revolving Hollow Sphere, The   Discovery Of    The   Globular Form

Of The   Earth, The   Explanation Of    The   Moon's Phases, And Indeed All The

Successive Steps Taken, Involved This Same Mental Process. But We Must

Content Ourselves With Referring To The   Theory Of    Eccentrics And

Epicycles, As A Further Marked Illustration Of    It. As First Suggested,

And As Proved By Hipparchus To Afford An Explanation Of    The   Leading

Irregularities In The   Celestial Motions, This Theory Involved The

Perception That The   Progressions, Retrogressions, And Variations Of

Velocity Seen In The   Heavenly Bodies, Might Be Reconciled With Their

Assumed Uniform Movement In Circles, By Supposing That The   Earth Was Not

In The   Centre Of    Their Orbits; Or By Supposing That They Revolved In

Circles Whose Centres Revolved Round The   Earth; Or By Both. The

Discovery That This Would Account For The   Appearances, Was The   Discovery

That In Certain Geometrical Diagrams The   Relations Were Such, That The

Uniform Motion Of    A Point Would, When Looked At From A Particular

Position, Present Analogous Irregularities; And The   Calculations Of

Hipparchus Involved The   Belief That The   Relations Subsisting Among These

Geometrical Curves Were _Equal_ To The   Relations Subsisting Among The

Celestial Orbits.

Leaving Here These Details Of    Astronomical Progress, And The   Philosophy

Of It, Let Us Observe How The   Relatively Concrete Science Of    Geometrical

Astronomy, Having Been Thus Far Helped Forward By The   Development Of

Geometry In General, Reacted Upon Geometry, Caused It Also To Advance,

And Was Again Assisted By It. Hipparchus, Before Making His Solar And

Lunar Tables, Had To Discover