﻿254 
  ANNUAL 
  REPORT 
  SMITHSONIAN 
  INSTITUTION, 
  194 
  3 
  

  

  expense 
  of 
  the 
  others, 
  or 
  to 
  achieve 
  the 
  best 
  compromise 
  among 
  them 
  

   without 
  any 
  one 
  being 
  mathematically 
  true. 
  For 
  example, 
  a 
  map 
  on 
  

   which 
  all 
  areas 
  are 
  shown 
  in 
  true 
  relative 
  size 
  (called 
  equal 
  area) 
  

   is 
  bound 
  to 
  have 
  distortions 
  in 
  shape, 
  distance, 
  and 
  direction. 
  In 
  

   some, 
  two 
  properties 
  can 
  be 
  satisfactorily 
  combined, 
  as 
  for 
  example 
  in 
  

   the 
  azimuthal 
  equidistant 
  map. 
  This 
  is 
  so 
  constructed 
  that 
  from 
  

   its 
  central 
  point 
  direction 
  and 
  distance 
  are 
  true 
  to 
  any 
  other 
  point, 
  

   but 
  a 
  nonradial 
  distance 
  is 
  more 
  or 
  less 
  seriously 
  out 
  of 
  scale. 
  (The 
  

   term 
  "azimuthal" 
  is 
  typical 
  of 
  the 
  obscure 
  terminology 
  of 
  cartog- 
  

   raphy. 
  In 
  the 
  case 
  of 
  maps 
  it 
  simply 
  means 
  radial, 
  or 
  as 
  the 
  spoke 
  

   of 
  a 
  wheel.) 
  The 
  well-known 
  Mercator 
  map 
  has 
  the 
  remarkable 
  

   property 
  of 
  showing 
  both 
  true 
  compass 
  directions 
  (but 
  not 
  the 
  great 
  

   circle 
  directions) 
  and 
  true 
  shape. 
  The 
  size 
  of 
  areas 
  and 
  distances, 
  

   however, 
  are 
  highly 
  misleading. 
  

  

  Perhaps 
  the 
  question 
  most 
  frequently 
  asked 
  of 
  cartographers 
  is, 
  

   "What 
  is 
  the 
  best 
  world 
  map?" 
  The 
  question 
  goes 
  to 
  the 
  heart 
  of 
  

   the 
  cartographer's 
  problem 
  for 
  the 
  answer 
  is 
  "There 
  is 
  no 
  such 
  thing 
  

   as 
  the 
  perfect 
  map." 
  One 
  can 
  pick 
  out 
  a 
  "best" 
  map 
  for 
  a 
  given 
  

   purpose, 
  but 
  that 
  map 
  will 
  not 
  satisfy 
  other 
  requirements. 
  For 
  ex- 
  

   ample, 
  the 
  density 
  of 
  population 
  is 
  measured 
  by 
  the 
  number 
  of 
  people 
  

   inhabiting 
  a 
  specific 
  area 
  and 
  should 
  be 
  shown 
  on 
  an 
  equal 
  area 
  map, 
  

   for 
  to 
  show 
  it 
  on 
  a 
  map 
  where 
  unit 
  areas 
  differ 
  would 
  introduce 
  

   another 
  variable 
  making 
  the 
  study 
  of 
  relative 
  density 
  valueless. 
  

   Where 
  true 
  compass 
  direction 
  between 
  points 
  is 
  required 
  (as 
  in 
  navi- 
  

   gation), 
  we 
  must 
  use 
  Mercator; 
  where 
  great 
  circles 
  (the 
  shortest 
  dis- 
  

   tance 
  between 
  two 
  points 
  on 
  the 
  globe) 
  is 
  the 
  object 
  of 
  study, 
  we 
  

   must 
  use 
  the 
  gnomonic 
  projection 
  which 
  is 
  unfortunately 
  limited 
  in 
  

   scope 
  to 
  less 
  than 
  a 
  hemisphere. 
  To 
  measure 
  distances 
  accurately 
  we 
  

   must 
  have 
  recourse 
  to 
  the 
  globe 
  or 
  use 
  cumbersome 
  methods 
  for 
  trans- 
  

   lating 
  these 
  distances 
  from 
  different 
  projections. 
  In 
  fact, 
  all 
  these 
  

   questions 
  can 
  best 
  be 
  studied 
  on 
  a 
  scale 
  model 
  of 
  the 
  earth. 
  Only 
  

   a 
  scale 
  model 
  is 
  proportionately 
  accurate 
  in 
  all 
  respects 
  — 
  provided 
  it 
  

   is 
  accurately 
  made. 
  Unfortunately 
  the 
  globe 
  has 
  disadvantages 
  too. 
  

   One 
  can 
  see 
  less 
  than 
  half 
  of 
  it 
  at 
  a 
  given 
  moment 
  ; 
  it 
  is 
  bulky 
  ; 
  it 
  is 
  

   expensive. 
  A 
  fine 
  collection 
  of 
  good 
  detailed 
  maps 
  or 
  a 
  first-class 
  

   atlas 
  can 
  be 
  purchased 
  for 
  the 
  price 
  of 
  an 
  18-inch 
  globe. 
  But 
  a 
  

   globe 
  is 
  the 
  one 
  and 
  only 
  corrective 
  for 
  the 
  distortion 
  present 
  in 
  all 
  

   maps. 
  

  

  Selecting 
  a 
  world 
  map 
  on 
  which 
  to 
  study 
  strategy 
  or 
  the 
  geography 
  

   of 
  war 
  is 
  practically 
  an 
  insuperable 
  problem. 
  For 
  strategy 
  demands 
  

   geographical 
  truth 
  — 
  distances, 
  directions, 
  and 
  areas 
  must 
  be 
  pretty 
  

   close 
  to 
  scale 
  because 
  when 
  they 
  are 
  true 
  it 
  follows 
  that 
  geographical 
  

   relationships 
  in 
  general 
  are 
  true. 
  This 
  is, 
  however, 
  impossible 
  in 
  any 
  

   kind 
  of 
  world 
  map. 
  

  

  