﻿268 
  JOURNAL 
  OF 
  THE 
  WASHINGTON 
  ACADEMY 
  OF 
  SCIENCES 
  VOL. 
  12, 
  NO. 
  11 
  

  

  particularly 
  the 
  thermal 
  electro-motive 
  force 
  and 
  thermal 
  coefficient 
  of 
  elec- 
  

   trical 
  resistance, 
  are 
  sensitive 
  even 
  to 
  spectroscopic 
  traces 
  of 
  impurities. 
  The 
  

   spectograph 
  showed 
  that 
  when 
  the 
  purest 
  platinum 
  sponge 
  was 
  fused 
  on 
  

   lime 
  or 
  magnesia 
  it 
  was 
  usually 
  contaminated 
  with 
  traces 
  of 
  calcium 
  and 
  mag- 
  

   nesium 
  but 
  when 
  fused 
  on 
  thoria 
  no 
  impurities 
  could 
  be 
  detected. 
  With 
  the 
  

   aid 
  of 
  this 
  method 
  of 
  spectrographic 
  analysis 
  platinum 
  metal 
  has 
  been 
  pre- 
  

   pared 
  which 
  is 
  positively 
  99.9999 
  per 
  cent 
  pure. 
  

  

  Discussion 
  of 
  the 
  three 
  papers 
  was 
  participated 
  in 
  by 
  Messrs. 
  Burgess, 
  

   White, 
  Foote, 
  L. 
  H. 
  Adams, 
  Harper, 
  and 
  Humphreys. 
  

  

  862d 
  meeting 
  

  

  The 
  862d 
  meeting 
  of 
  the 
  Philosophical 
  Society 
  was 
  held 
  in 
  the 
  Cosmos 
  

   Club 
  auditorium, 
  February 
  25, 
  1922, 
  with 
  President 
  Crittenden 
  in 
  the 
  

   chair 
  and 
  54 
  persons 
  present. 
  The 
  program 
  was 
  as 
  follows 
  : 
  

  

  R. 
  S. 
  Woodward: 
  The 
  calculus 
  of 
  harmonics 
  and 
  preharmonics 
  and 
  their 
  

   application 
  in 
  hydromechanics. 
  It 
  was 
  discussed 
  by 
  Mr. 
  L. 
  A. 
  Bauer. 
  

  

  (Author's 
  abstract.) 
  A 
  harmonic 
  function, 
  H, 
  is 
  defined 
  to 
  be 
  any 
  homo- 
  

   geneous 
  function 
  of 
  x, 
  y, 
  z, 
  which 
  satisfies 
  Laplace's 
  equation. 
  That 
  is, 
  

   H 
  is 
  a 
  harmonic 
  if 
  

  

  dW 
  dW 
  dW 
  ^ 
  

   'dx^ 
  by"^ 
  bz^ 
  

   This 
  equation 
  is 
  now, 
  for 
  brevity, 
  commonly 
  written 
  

  

  ^m 
  = 
  0, 
  or 
  ^H 
  = 
  o. 
  

  

  and 
  the 
  operation 
  thus 
  symbolized 
  is 
  called 
  the 
  Laplacian 
  of 
  H. 
  

  

  Conformable 
  to 
  these 
  definitions, 
  a 
  preharmonic 
  function, 
  P, 
  is 
  defined 
  to 
  

   be 
  any 
  homogeneous 
  function 
  of 
  x, 
  y, 
  z 
  which 
  satisfies 
  the 
  equations 
  

  

  A^P 
  = 
  H, 
  AWP 
  = 
  AW 
  = 
  0. 
  

  

  Corresponding 
  to 
  every 
  harmonic 
  function, 
  therefore, 
  there 
  is 
  a 
  prehar- 
  

   monic 
  function 
  determined 
  by 
  the 
  integral 
  of 
  the 
  first 
  of 
  the 
  last 
  two 
  equa- 
  

   tions; 
  and 
  since 
  there 
  is 
  an 
  extensive 
  range 
  of 
  harmonic 
  functions, 
  of 
  which 
  

   the 
  degrees 
  may 
  be 
  positive 
  or 
  negative 
  integers, 
  or 
  fractional 
  or 
  imaginary 
  

   numbers, 
  there 
  is 
  a 
  coextensive 
  range 
  of 
  preharmonic 
  functions. 
  

  

  While 
  harmonic 
  functions 
  have 
  been 
  investigated 
  in 
  elaborate 
  detail, 
  it 
  

   does 
  not 
  appear 
  that 
  much 
  attention 
  has 
  been 
  given 
  to 
  the 
  intimately 
  re- 
  

   lated 
  functions 
  here 
  called 
  preharmonics. 
  It 
  was 
  the 
  object 
  of 
  the 
  paper 
  to 
  

   outline 
  the 
  characteristics 
  of 
  these 
  functions 
  and 
  the 
  calculus 
  to 
  which 
  they 
  

   lead, 
  as 
  well 
  as 
  to 
  indicate 
  some 
  of 
  their 
  more 
  important 
  applications. 
  Gen- 
  

   eral 
  formulas 
  for 
  all 
  of 
  the 
  preharmonics 
  corresponding 
  to 
  all 
  the 
  harmonics 
  

   of 
  positive 
  and 
  negative 
  integral 
  degrees 
  were 
  given. 
  

  

  L. 
  A. 
  Bauer: 
  Some 
  results 
  of 
  recent 
  earth-current 
  observations 
  (illus- 
  

   trated) 
  . 
  

  

  (Author's 
  abstract.) 
  Renewed 
  interest 
  was 
  aroused 
  by 
  the 
  remarkable 
  

   earth-current 
  disturbances 
  of 
  May 
  14 
  to 
  May 
  ,30, 
  1921, 
  which, 
  as 
  will 
  be 
  re- 
  

   called, 
  occurred 
  simultaneously 
  with 
  brilliant 
  displays 
  of 
  polar 
  lights 
  and 
  

   severe 
  magnetic 
  storms, 
  the 
  sun 
  at 
  the 
  time 
  showing 
  remarkable 
  spot 
  ac- 
  

   tivity. 
  These 
  disturbances 
  and 
  accompanying 
  phenomena 
  occurred 
  over 
  

   the 
  entire 
  earth. 
  Northern 
  lights 
  were 
  observed 
  in 
  lower 
  northerly 
  lati- 
  

   tudes 
  than 
  usual 
  and 
  southern 
  lights 
  were 
  observed 
  as 
  far 
  north 
  in 
  the 
  South- 
  

   ern 
  hemisphere 
  as 
  Apia, 
  Samoa 
  — 
  a 
  very 
  unusual 
  occurence. 
  In 
  many 
  re- 
  

   spects 
  the 
  disturbances 
  during 
  the 
  period. 
  May 
  14 
  to 
  20, 
  1921 
  were 
  similar 
  to 
  

  

  