size　of　the　skipper；　relative　to　its　weight；　and　the
  other　is　its　speed。　If　the　speed　is　slow　it　will
  quickly　wend　its　way　to　the　earth　in　a　gradual
  curve。　This　curved　line　is　called　its　trajectory。
  If　it　is　not　very　large　diametrically；　in　proportion
  to　its　weight；　it　will　also　make　a　gradual　curve　in
  descending；　without　〃skimming〃　up　and　down
  in　its　flight。
  SHAPE　AND　SPEED。It　has　been　observed；　also；
  that　a　round　ball；　or　an　object　not　flattened　out；
  will　make　a　regular　curved　path；　whatever　the
  speed　may　be。
  It　may　be　assumed；　therefore；　that　the　shape
  alone　does　not　account　for　this　sinuous　motion；
  but　that　speed　is　the　element　which　accounts　for
  it。　Such　being　the　case　it　may　be　well　to　inquire
  into　the　peculiar　action　which　causes　a　skipper
  to　dart　up　and　down；　and　why　the　path　thus
  formed　grows　more　and　more　accentuated　as　the
  speed　increases。
  As　will　be　more　fully　described　in　a　later　chapter；
  the　impact　of　air　against　a　moving　body　does
  not　increase　in　proportion　to　its　speed；　but　in　the
  ratio　of　the　square　of　the　speed。
  WHAT　SQUARE　OF　THE　SPEED　MEANS。In　mathematics
  a　figure　is　squared　when　it　is　multiplied
  by　itself。　Thus；　4　X　4=　16；　5　X　5　=　25；　and　so
  on；　so　that　16　is　the　square　of　4；　and　25　the　square
  of　5。　It　has　been　found　that　a　wind　moving　at　the
  speed　of　20　miles　an　hour　has　a　striking　or　pushing
  force　of　2　pounds　on　every　square　foot　of　surface。
  If　the　wind　travels　twice　as　fast；　or　40　miles
  an　hour；　the　pushing　force　is　not　4　pounds；　but
  8　pounds。　If　the　speed　is　60　miles　an　hour　the
  pushing　force　increases　to　18　pounds。
  ACTION　OF　A　SKIPPER。When　the　skipper　leaves
  the　hands　of　the　thrower　it　goes　through　the　air
  in　such　a　way　that　its　fiat　surface　is　absolutely
  on　a　line　with　the　direction　in　which　it　is　projected。
  At　first　it　moves　through　the　air　solely　by　force
  of　the　power　which　impels　it；　and　does　not　in　any
  way　depend　on　the　air　to　hold　it　up。　See　Fig。
  1；　in　which　A　represents　the　line　of　projection；
  and　B　the　disk　in　its　flight。
  _Fig。　11。　A　Skipper　in　Flight。_
  After　it　has　traveled　a　certain　distance；　and
  the　force　decreases；　it　begins　to　descend；　thus　describing
  the　line　C；　Fig。　1；　the　disk　B；　in　this　case
  descending；　without　changing　its　position；　which
  might　be　described　by　saying　that　it　merely　settles
  down　to　the　earth　without　changing　its　plane。
  The　skipper　still　remains　horizontal；　so　that　as
  it　moves　toward　the　earth　its　flat　surface；　which
  is　now　exposed　to　the　action　of　the　air；　meets
  with　a　resistance；　and　this　changes　the　angle　of
  the　disk；　so　that　it　will　not　be　horizontal。　Instead
  it　assumes　the　position　as　indicated　at　D；
  and　this　impinging　effect　against　the　air　causes
  the　skipper　to　move　upwardly　along　the　line　E；
  and　having　reached　a　certain　limit；　as　at；　say　E；
  it　automatically　again　changes　its　angle　and　moves
  downwardly　along　the　path　F；　and　thus　continues
  to　undulate；　more　or　less；　dependent　on　the　combined
  action　of　the　power　and　weight；　or　momentum；
  until　it　reaches　the　earth。
  It　is；　therefore；　clear　that　the　atmosphere　has
  an　action　on　a　plane　surface；　and　that　the　extent
  of　the　action；　to　sustain　it　in　flight；　depends　on　two
  things；　surface　and　speed。
  Furthermore；　the　greater　the　speed　the　less　the
  necessity　for　surface；　and　that　for　gliding　purposes
  speed　may　be　sacrificed；　in　a　large　measure；
  where　there　is　a　large　surface。
  This　very　action　of　the　skipper　is　utilized　by
  the　aviator　in　volplaning；that　is；　where　the
  power　of　the　engine　is　cut　off；　either　by　accident；
  or　designedly；　and　the　machine　descends　to　the
  earth；　whether　in　a　long　straight　glide；　or　in　a
  great　circle。
  As　the　machine　nears　the　earth　it　is　caused　to
  change　the　angle　of　flight　by　the　control　mechanism
  so　that　it　will　dart　upwardly　at　an　angle；　or　downwardly；
  and　thus　enable　the　pilot　to　sail　to　another
  point　beyond　where　he　may　safely　land。
  This　changing　the　course　of　the　machine　so　that
  it　will　glide　upwardly；　means　that　the　incidence
  of　the　planes　has　been　changed　to　a　positive
  angle。
  ANGLE　OF　INCIDENCE。In　aviation　this　is　a　term
  given　to　the　position　of　a　plane；　relative　to　the
  air　against　which　it　impinges。　If；　for　instance；
  an　aeroplane　is　moving　through　the　air　with　the
  front　margin　of　the　planes　higher　than　their　rear
  margins；　it　is　said　to　have　the　planes　at　a　positive
  angle　of　incidence。　If　the　rear　margins　are
  higher　than　the　front；　then　the　planes　have　a　negative
  angle　of　incidence。
  The　word　incidence　really　means；　a　falling
  upon；　or　against；　and　it　will　be　seen；　therefore；
  that　the　angle　of　incidence　means　the　tilt　of　the
  planes　in　relation　to　the　air　which　strikes　it。
  Having　in　view；　therefore；　that　the　two　qualities；
  namely；　speed　and　surface；　bear　an　intimate
  relation　with　each　other；　it　may　be　understood
  wherein　mechanical　flight　is　supposed　to　be　analogous
  to　bird　flight。
  SPEED　AND　SURFACE。Birds　which　poise　in　the
  air；　like　the　humming　bird；　do　so　because　they
  beat　their　wings　with　great　rapidity。　Those
  which　soar；　as　stated；　can　do　so　only　by　moving
  through　the　atmosphere　rapidly；　or　by　having　a
  large　wing　spread　relative　to　the　weight。　It　will
  thus　be　seen　that　speed　and　surface　become　the
  controlling　factors　in　flight；　and　that　while　the
  latter　may　be　entirely　eliminated　from　the　problem；
  speed　is　absolutely　necessary　under　any　and
  all　conditions。
  By　speed　in　this　connection　is　not　meant　high
  velocity；　but　that　a　movement；　produced　by　power
  expressed　in　some　form；　is　the　sole　and　most　necessary
  requisite　to　movement　through　the　air　with
  all　heavier…than…air　machines。
  If　sufficient　power　can　be　applied　to　an　aeroplane；
  surface　is　of　no　consequence；　shape　need
  not　be　considered；　and　any　sort　of　contrivance
  will　move　through　the　air　horizontally。
  CONTROL　OF　THE　DIRECTION　OF　FLIGHT。But　the
  control　of　such　a　body；　when　propelled　through
  space　by　force　alone；　is　a　different　matter。　To
  change　the　machine　from　a　straight　path　to　a
  curved　one；　means　that　it　must　be　acted　upon　by
  some　external　force。
  We　have　explained　that　power　is　something
  which　is　inherent　in　the　thing　itself。　Now；　in　order
  that　there　may　be　a　change　imparted　to　a
  moving　mass；　advantage　must　be　taken　of　the　medium
  through　which　it　moves；the　atmosphere。
  VERTICAL　CONTROL　PLANES。If　vertically…arranged
  planes　are　provided；　either　fore　or　aft　of
  the　machine；　or　at　both　ends；　the　angles　of　incidence
  may　be　such　as　to　cause　the　machine　to
  turn　from　its　straight　course。
  In　practice；　therefore；　since　it　is　difficult　to　supply
  sufficient　power　to　a　machine　to　keep　it　in　motion
  horizontally；　at　all　times；　aeroplanes　are　provided
  with　supporting　surfaces；　and　this　aid　in
  holding　it　up　grows　less　and　less　as　its　speed　increases。
  But；　however　strong　the　power；　or　great　the
  speed；　its　control　from　side　to　side　is　not　dependent
  on　the　power　of　the　engine；　or　the　speed
  at　which　it　travels　through　the　air。
  Here　the　size　of　the　vertical　planes；　and　their
  angles；　are　the　only　factors　to　be　considered；　and
  these　questions　will　be　considered　in　their　proper
  places。
  CHAPTER　III
  THE　FORM　OR　SHAPE　OF　FLYING　MACHINES
  EVERY　investigator；　experimenter；　and　scientist；
  who　has　given　the　subject　of　flight　study；　proceeds
  on　the　theory　that　in　order　to　fly　man　must
  copy　nature；　and　make　the　machine　similar　to　the
  type　so　provided。
  THE　THEORY　OF　COPYING　NATURE。If　such　is　the
  case　then　it　is　pertinent　to　inquire　which　bird　is
  the　proper　example　to　use　for　mechanical　flight。
  We　have　shown　that　they　differ　so　radically　in
  every　essential；　that　what　would　be　correct　in　one
  thing　would　be　entirely　wrong　in　another。
  The　bi…plane　is　certainly　not　a　true　copy。　The
  only　thing　in　the　Wright　machine　which　in　any
  way　resembles　the　bird's　wing；　is　the　rounded　end
  of　the　planes；　and　judging　from　other　machines；
  which　have　square　ends；　this　slight　similarity　does
  not　contribute　to　its　stability　or　otherwise　help
  the　structure。
  The　monoplane；　which　is　much　nearer　the　bird
  type；　has　also　sounded　wing　ends；　made　not　so
  much　for　the　purpose　of　imitating　the　wing　of　the
  bird；　as　for　structural　reasons。
  HULLS　OF　VESSELS。If　some　marine　architect
  should　come　forward　and　assert　that　he　intended
  to　follow　nature　by　making　a　boat　with　a　hull　of
  the　shape　or　outline　of　a　duck；　or　other　swimming
  fowl；　he　would　be　laughed　at；　and　justly　so；　because
  the　lines　of　vessels　which　are　most　efficient
  are　not　made　like　those　of　a　duck　or　other　swimming
  creatures。
  MAN　DOES　NOT　COPY　NATURE。Look　about　you；
  and　see　how　many　mechanical　devices　follow　the
  forms　laid　down　by　nature；　or　in　what　respect
  man　uses　the　types　which　nature　provides　in　devising
  the　many　inventions　which　ingenuity　has
  bro