Essays On Education And Kindred Subjects (Fiscle Part- 11) - Herbert Spencer (if you give a mouse a cookie read aloud txt) 📗
- Author: Herbert Spencer
Book online «Essays On Education And Kindred Subjects (Fiscle Part- 11) - Herbert Spencer (if you give a mouse a cookie read aloud txt) 📗». Author Herbert Spencer
Between The Sides And Angles Of Triangles--_Trigonometry_ A Subdivision
Of Pure Mathematics. Further, The Reduction Of The Doctrine Of The
Sphere To The Quantitative Form Needed For Astronomical Purposes,
Required The Formation Of A _Spherical Trigonometry_, Which Was Also
Achieved By Hipparchus. Thus Both Plane And Spherical Trigonometry,
Which Are Parts Of The Highly Abstract And Simple Science Of Extension,
Remained Undeveloped Until The Less Abstract And More Complex Science Of
The Celestial Motions Had Need Of Them. The Fact Admitted By M. Comte,
That Since Descartes The Progress Of The Abstract Division Of
Mathematics Has Been Determined By That Of The Concrete Division, Is
Paralleled By The Still More Significant Fact That Even Thus Early The
Progress Of Mathematics Was Determined By That Of Astronomy.
And Here, Indeed, We May See Exemplified The Truth, Which The Subsequent
History Of Science Frequently Illustrates, That Before Any More
Abstract Division Makes A Further Advance, Some More Concrete Division
Must Suggest The Necessity For That Advance--Must Present The New Order
Part 2 Chapter 3 (On The Genesis Of Science) Pg 114Of Questions To Be Solved. Before Astronomy Presented Hipparchus With
The Problem Of Solar Tables, There Was Nothing To Raise The Question Of
The Relations Between Lines And Angles; The Subject-Matter Of
Trigonometry Had Not Been Conceived. And As There Must Be Subject-Matter
Before There Can Be Investigation, It Follows That The Progress Of The
Concrete Divisions Is As Necessary To That Of The Abstract, As The
Progress Of The Abstract To That Of The Concrete.
Just Incidentally Noticing The Circumstance That The Epoch We Are
Describing Witnessed The Evolution Of Algebra, A Comparatively Abstract
Division Of Mathematics, By The Union Of Its Less Abstract Divisions,
Geometry And Arithmetic--A Fact Proved By The Earliest Extant Samples Of
Algebra, Which Are Half Algebraic, Half Geometric--We Go On To Observe
That During The Era In Which Mathematics And Astronomy Were Thus
Advancing, Rational Mechanics Made Its Second Step; And Something Was
Done Towards Giving A Quantitative Form To Hydrostatics, Optics, And
Harmonics. In Each Case We Shall See, As Before, How The Idea Of
Equality Underlies All Quantitative Prevision; And In What Simple Forms
This Idea Is First Applied.
As Already Shown, The First Theorem Established In Mechanics Was, That
Equal Weights Suspended From A Lever With Equal Arms Would Remain In
Equilibrium. Archimedes Discovered That A Lever With Unequal Arms Was In
Equilibrium When One Weight Was To Its Arm As The Other Arm To Its
Weight; That Is--When The Numerical Relation Between One Weight And Its
Arm Was _Equal_ To The Numerical Relation Between The Other Arm And Its
Weight.
The First Advance Made In Hydrostatics, Which We Also Owe To Archimedes,
Was The Discovery That Fluids Press _Equally_ In All Directions; And
From This Followed The Solution Of The Problem Of Floating Bodies:
Namely, That They Are In Equilibrium When The Upward And Downward
Pressures Are _Equal_.
In Optics, Again, The Greeks Found That The Angle Of Incidence Is
_Equal_ To The Angle Of Reflection; And Their Knowledge Reached No
Further Than To Such Simple Deductions From This As Their Geometry
Sufficed For. In Harmonics They Ascertained The Fact That Three Strings
Of _Equal_ Lengths Would Yield The Octave, Fifth And Fourth, When
Strained By Weights Having Certain Definite Ratios; And They Did Not
Progress Much Beyond This. In The One Of Which Cases We See Geometry
Used In Elucidation Of The Laws Of Light; And In The Other, Geometry And
Arithmetic Made To Measure The Phenomena Of Sound.
Did Space Permit, It Would Be Desirable Here To Describe The State Of
The Less Advanced Sciences--To Point Out How, While A Few Had Thus
Reached The First Stages Of Quantitative Prevision, The Rest Were
Progressing In Qualitative Prevision--How Some Small Generalisations
Were Made Respecting Evaporation, And Heat, And Electricity, And
Magnetism, Which, Empirical As They Were, Did Not In That Respect Differ
From The First Generalisations Of Every Science--How The Greek
Physicians Had Made Advances In Physiology And Pathology, Which,
Considering The Great Imperfection Of Our Present Knowledge, Are By No
Means To Be Despised--How Zoology Had Been So Far Systematised By
Aristotle, As, To Some Extent, Enabled Him From The Presence Of Certain
Organs To Predict The Presence Of Others--How In Aristotle's _Politics_
There Is Some Progress Towards A Scientific Conception Of Social
Phenomena, And Sundry Previsions Respecting Them--And How In The State
Of The Greek Societies, As Well As In The Writings Of Greek
Philosophers, We May Recognise Not Only An Increasing Clearness In That
Conception Of Equity On Which The Social Science Is Based, But Also Some
Appreciation Of The Fact That Social Stability Depends Upon The
Maintenance Of Equitable Regulations. We Might Dwell At Length Upon The
Causes Which Retarded The Development Of Some Of The Sciences, As, For
Example, Chemistry; Showing That Relative Complexity Had Nothing To Do
With It--That The Oxidation Of A Piece Of Iron Is A Simpler Phenomenon
Than The Recurrence Of Eclipses, And The Discovery Of Carbonic Acid Less
Difficult Than That Of The Precession Of The Equinoxes--But That The
Relatively Slow Advance Of Chemical Knowledge Was Due, Partly To The
Fact That Its Phenomena Were Not Daily Thrust On Men's Notice As Those
Of Astronomy Were; Partly To The Fact That Nature Does Not Habitually
Supply The Means, And Suggest The Modes Of Investigation, As In The
Sciences Dealing With Time, Extension, And Force; And Partly To The Fact
That The Great Majority Of The Materials With Which Chemistry Deals,
Instead Of Being Ready To Hand, Are Made Known Only By The Arts In Their
Slow Growth; And Partly To The Fact That Even When Known, Their Chemical
Properties Are Not Self-Exhibited, But Have To Be Sought Out By
Experiment.
Merely Indicating All These Considerations, However, Let Us Go On To
Contemplate The Progress And Mutual Influence Of The Sciences In Modern
Days; Only Parenthetically Noticing How, On The Revival Of The
Scientific Spirit, The Successive Stages Achieved Exhibit The Dominance
Of The Same Law Hitherto Traced--How The Primary Idea In Dynamics, A
Uniform Force, Was Defined By Galileo To Be A Force Which Generates
_Equal_ Velocities In _Equal_ Successive Times--How The Uniform Action
Of Gravity Was First Experimentally Determined By Showing That The Time
Elapsing Before A Body Thrown Up, Stopped, Was _Equal_ To The Time It
Took To Fall--How The First Fact In Compound Motion Which Galileo
Ascertained Was, That A Body Projected Horizontally Will Have A Uniform
Motion Onwards And A Uniformly Accelerated Motion Downwards; That Is,
Will Describe _Equal_ Horizontal Spaces In _Equal_ Times, Compounded
With _Equal_ Vertical Increments In _Equal_ Times--How His Discovery
Respecting The Pendulum Was, That Its Oscillations Occupy _Equal_
Intervals Of Time Whatever Their Length--How The Principle Of Virtual
Velocities Which He Established Is, That In Any Machine The Weights That
Balance Each Other Are Reciprocally As Their Virtual Velocities; That
Is, The Relation Of One Set Of Weights To Their Velocities _Equals_ The
Relation Of The Other Set Of Velocities To Their Weights; And How Thus
His Achievements Consisted In Showing The Equalities Of Certain
Magnitudes And Relations, Whose Equalities Had Not Been Previously
Recognised.
When Mechanics Had Reached The Point To Which Galileo Brought It--When
The Simple Laws Of Force Had Been Disentangled From The Friction And
Atmospheric Resistance By Which All Their Earthly Manifestations Are
Disguised--When Progressing Knowledge Of _Physics_ Had Given A Due
Insight Into These Disturbing Causes--When, By An Effort Of Abstraction,
It Was Perceived That All Motion Would Be Uniform And Rectilinear Unless
Part 2 Chapter 3 (On The Genesis Of Science) Pg 115Interfered With By External Forces--And When The Various Consequences Of
This Perception Had Been Worked Out; Then It Became Possible, By The
Union Of Geometry And Mechanics, To Initiate Physical Astronomy.
Geometry And Mechanics Having Diverged From A Common Root In Men's
Sensible Experiences; Having, With Occasional Inosculations, Been
Separately Developed, The One Partly In Connection With Astronomy, The
Other Solely By Analysing Terrestrial Movements; Now Join In The
Investigations Of Newton To Create A True Theory Of The Celestial
Motions. And Here, Also, We Have To Notice The Important Fact That, In
The Very Process Of Being Brought Jointly To Bear Upon Astronomical
Problems, They Are Themselves Raised To A Higher Phase Of Development.
For It Was In Dealing With The Questions Raised By Celestial Dynamics
That The Then Incipient Infinitesimal Calculus Was Unfolded By Newton
And His Continental Successors; And It Was From Inquiries Into The
Mechanics Of The Solar System That The General Theorems Of Mechanics
Contained In The _Principia_,--Many Of Them Of Purely Terrestrial
Application--Took Their Rise. Thus, As In The Case Of Hipparchus, The
Presentation Of A New Order Of Concrete Facts To Be Analysed, Led To The
Discovery Of New Abstract Facts; And These Abstract Facts Having Been
Laid Hold Of, Gave Means Of Access To Endless Groups Of Concrete Facts
Before Incapable Of Quantitative Treatment.
Meanwhile, Physics Had Been Carrying Further That Progress Without
Which, As Just Shown, Rational Mechanics Could Not Be Disentangled. In
Hydrostatics, Stevinus Had Extended And Applied The Discovery Of
Archimedes. Torricelli Had Proved Atmospheric Pressure, "By Showing That
This Pressure Sustained Different Liquids At Heights Inversely
Proportional To Their Densities;" And Pascal "Established The Necessary
Diminution Of This Pressure At Increasing Heights In The Atmosphere:"
Discoveries Which In Part Reduced This Branch Of Science To A
Quantitative Form. Something Had Been Done By Daniel Bernouilli Towards
The Dynamics Of Fluids. The Thermometer Had Been Invented; And A Number
Of Small Generalisations Reached By It. Huyghens And Newton Had Made
Considerable Progress In Optics; Newton Had Approximately Calculated The
Rate Of Transmission Of Sound; And The Continental Mathematicians Had
Succeeded In Determining Some Of The Laws Of Sonorous Vibrations.
Magnetism And Electricity Had Been Considerably Advanced By Gilbert.
Chemistry Had Got As Far As The Mutual Neutralisation Of Acids And
Alkalies. And Leonardo Da Vinci Had Advanced In Geology To The
Conception Of The Deposition Of Marine Strata As The Origin Of Fossils.
Our Present Purpose Does Not Require That We Should Give Particulars.
All That It Here Concerns Us To Do Is To Illustrate The _Consensus_
Subsisting In This Stage Of Growth, And Afterwards. Let Us Look At A Few
Cases.
The Theoretic Law Of The Velocity Of Sound Enunciated By Newton On
Purely Mechanical Considerations, Was Found Wrong By One-Sixth. The
Error Remained Unaccounted For Until The Time Of Laplace, Who,
Suspecting That The Heat Disengaged By The Compression Of The Undulating
Strata Of The Air, Gave Additional Elasticity, And So Produced The
Difference, Made The Needful Calculations And Found He Was Right. Thus
Acoustics Was Arrested Until Thermology Overtook And Aided It. When
Boyle And Marriot Had Discovered The Relation Between The Density Of
Gases And The Pressures They Are Subject To; And When It Thus Became
Possible To Calculate The Rate Of Decreasing Density In The Upper Parts
Of The Atmosphere, It Also Became Possible To Make Approximate Tables Of
The Atmospheric Refraction Of Light. Thus Optics, And With It Astronomy,
Advanced With Barology. After The Discovery Of Atmospheric Pressure Had
Led To The Invention Of The Air-Pump By Otto Guericke; And After It Had
Become Known That Evaporation Increases In Rapidity As Atmospheric
Pressure Decreases; It Became Possible For Leslie, By Evaporation In A
Vacuum, To Produce The Greatest Cold Known; And So To Extend Our
Knowledge Of Thermology By Showing That There Is No Zero Within Reach Of
Our Researches. When Fourier Had Determined The Laws Of Conduction Of
Heat, And When The
Comments (0)