﻿488 
  Scientific 
  Intelligence. 
  

  

  principles 
  set 
  forth 
  in 
  these 
  publications 
  while 
  making 
  use 
  of 
  a 
  

   minimum 
  of 
  abstract 
  group 
  theory. 
  

  

  The 
  elementary 
  properties 
  of 
  linear 
  transformations 
  and 
  linear 
  

   groups 
  are 
  developed 
  in 
  the 
  first 
  chapter 
  in 
  such 
  a 
  manner 
  as 
  to 
  

   require 
  no 
  previous 
  knowledge 
  of 
  the 
  technique 
  of 
  group 
  theory. 
  

   An 
  introduction 
  to 
  the 
  theory 
  of 
  groups 
  of 
  operators 
  and 
  substitu- 
  

   tion 
  groups 
  is 
  given 
  in 
  the 
  second 
  chapter. 
  The 
  third, 
  fifth, 
  and 
  

   seventh 
  chapters 
  deal 
  with 
  linear 
  groups 
  in 
  two, 
  three, 
  and 
  four 
  

   variables, 
  respectively. 
  Chapter 
  IV 
  is 
  entitled 
  " 
  Advanced 
  Theory 
  

   of 
  Linear 
  Groups 
  " 
  and 
  it 
  prepares 
  the 
  reader 
  for 
  a 
  proper 
  apprecia- 
  

   tion 
  of 
  the 
  material 
  presented 
  in 
  the 
  later 
  chapters. 
  The 
  theory 
  

   of 
  group 
  characteristics 
  (chapter 
  vi) 
  is 
  developed 
  in 
  a 
  very 
  simple 
  

   form 
  by 
  means 
  of 
  explicit 
  definitions 
  and 
  easy 
  proofs 
  which 
  avoid 
  

   complicated 
  sigma-constructions. 
  The 
  eighth 
  and 
  last 
  chapter 
  per- 
  

   tains 
  to 
  the 
  history 
  of 
  linear 
  groups, 
  to 
  Klein's 
  extension 
  of 
  the 
  

   Galois 
  theory 
  of 
  equations, 
  and 
  to 
  the 
  connection 
  between 
  linear 
  

   groups 
  and 
  linear 
  differential 
  equations 
  having 
  algebraic 
  solutions. 
  

   The 
  value 
  of 
  the 
  text 
  is 
  enhanced 
  both 
  by 
  the 
  appendix, 
  which 
  

   contains 
  statements 
  in 
  explicit 
  form 
  of 
  certain 
  definitions 
  and 
  

   theorems 
  from 
  advanced 
  algebra 
  needed 
  throughout 
  the 
  book, 
  

   and 
  by 
  the 
  inclusion 
  of 
  115 
  exercises 
  for 
  solution 
  by 
  the 
  student. 
  

  

  h. 
  s. 
  u. 
  

  

  II. 
  Geology 
  and 
  Mineralogy. 
  

  

  1. 
  Thirty 
  -seventh 
  Annual 
  Report 
  of 
  the 
  Director 
  of 
  the 
  

   United 
  States 
  Geological 
  Survey 
  / 
  by 
  Geoege 
  Otis 
  Smith. 
  

   Director. 
  Pp. 
  185, 
  2 
  pis., 
  1916. 
  — 
  The 
  United 
  States 
  Geological 
  

   Survey 
  ranks 
  first 
  among 
  geologic 
  organizations 
  as 
  an 
  agency 
  in 
  

   developing 
  the 
  nation's 
  resources, 
  as 
  a 
  bod}^ 
  of 
  instructors 
  and 
  

   students, 
  and 
  as 
  a 
  research 
  institution. 
  The 
  Director's 
  annual 
  

   report 
  is 
  therefore 
  of 
  large 
  interest. 
  During 
  the 
  year 
  1915-1916 
  

   geologic 
  investigations 
  were 
  made 
  in 
  47 
  states, 
  Alaska, 
  the 
  Canal 
  

   Zone, 
  and 
  the 
  West 
  Indies, 
  covering 
  54,000 
  square 
  miles 
  ; 
  33,000 
  

   square 
  miles 
  were 
  mapped 
  by 
  topographers, 
  and 
  32,000,000 
  acres 
  

   of 
  land 
  were 
  classified. 
  The 
  total 
  number 
  of 
  pages 
  in 
  publica- 
  

   tions 
  for 
  the 
  year 
  was 
  19,722 
  and 
  included 
  210 
  new 
  books 
  and 
  

   pamphlets, 
  33 
  reprinted 
  books, 
  6 
  new 
  geologic 
  folios, 
  and 
  230 
  

   topographic 
  maps. 
  The 
  demand 
  for 
  the 
  Survey 
  publications 
  is 
  

   shown 
  by 
  the 
  record 
  of 
  distribution 
  for 
  the 
  year: 
  603,575 
  books, 
  

   23,534 
  folios, 
  and 
  597,149 
  maps. 
  Nearly 
  400,000 
  maps 
  were 
  sold. 
  

   In 
  addition 
  to 
  its 
  regular 
  work 
  the 
  Survey 
  prepared 
  and 
  published 
  

   maps 
  for 
  more 
  than 
  40 
  government 
  bureaus 
  and 
  departments. 
  

   The 
  widespread 
  influence 
  of 
  the 
  Survey 
  is 
  indicated 
  by 
  the 
  work 
  

   of 
  the 
  division 
  of 
  mails 
  which 
  received 
  255,504 
  letters 
  and 
  sent 
  

   out 
  436,806 
  pieces 
  of 
  mail 
  during 
  the 
  year 
  — 
  an 
  increase 
  of 
  12 
  

   per 
  cent 
  over 
  1915. 
  The 
  roll 
  of 
  secretary's 
  appointees 
  numbered 
  

   872, 
  and 
  the 
  chief 
  items 
  of 
  expenditure 
  in 
  the 
  appropriation 
  of 
  

   $1,355,000 
  were 
  geologic 
  surveys 
  and 
  geologic 
  maps, 
  $460,000 
  ; 
  

  

  