﻿100 
  PROCEEDINGS 
  OF 
  THE 
  CALIFORNIA 
  

  

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  _ 
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  {n-\- 
  p) 
  hl—nb' 
  I' 
  

   n-1 
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  XVI. 
  Having 
  subdivided 
  the 
  hollow 
  rectangle, 
  as 
  in 
  problem 
  

   XIV., 
  determine, 
  in 
  terms 
  of 
  the 
  given 
  sides 
  thereof, 
  the 
  sides 
  of 
  a 
  

   consecutive 
  series 
  of 
  similar 
  hollow 
  rectangles, 
  outside 
  the 
  given 
  

   rectangle, 
  and 
  having 
  areas 
  equal 
  with 
  those 
  of 
  the 
  prescribed 
  sub- 
  

   divisions. 
  

  

  Suppose 
  the 
  given 
  hollow 
  rectangle 
  is 
  subdivided 
  into 
  p 
  hollow 
  

   rectangles, 
  and 
  there 
  are 
  required 
  n 
  outer 
  hollow 
  rectangles 
  of 
  

   equal 
  areas 
  ; 
  let 
  l', 
  I, 
  b', 
  b, 
  x, 
  ?/, 
  z, 
  etc., 
  x', 
  y\ 
  z\ 
  etc., 
  represent 
  

   quantities 
  as 
  before; 
  and 
  o\ 
  o", 
  o'", 
  etc., 
  the 
  consecutive 
  lengths, 
  

   reckoning 
  from 
  I 
  outward 
  ; 
  o', 
  o", 
  o'", 
  etc., 
  the 
  corresponding 
  con- 
  

   secutive 
  breadths 
  ; 
  then 
  

  

  ( 
  {n 
  + 
  'p)b'l'—nbl 
  \ 
  

  

  {n 
  + 
  p) 
  h' 
  I'—nbl 
  

  

  Descriptions 
  of 
  a 
  New 
  Genus, 
  and 
  two 
  new 
  species 
  of 
  Plants 
  

   from 
  the 
  Pacific 
  Coast 
  of 
  America. 
  

  

  BY 
  A. 
  KELLOGG, 
  M. 
  D. 
  

  

  The 
  following 
  plant 
  has 
  somewhat 
  the 
  appearance 
  of 
  a 
  very 
  branching 
  speci- 
  

   men 
  of 
  Helianthus 
  giganteus, 
  and 
  is 
  closely 
  allied 
  to 
  Parthenice 
  of 
  Gray. 
  

  

  Generic 
  Description. 
  • 
  

  

  Parthenopsis, 
  Kellogg. 
  

  

  Heads 
  broadly 
  campanulate, 
  with 
  loosely 
  sub-imbricated 
  foliaceous 
  and 
  mem- 
  

   branaceous 
  involucral 
  scales, 
  many-flowered, 
  elongated 
  pistillate 
  ray 
  flowers, 
  

   about 
  11 
  or 
  12 
  from 
  the 
  axils 
  of 
  each 
  of 
  the 
  inner 
  hyaline 
  involucral 
  scales, 
  but 
  

   entirely 
  free 
  ; 
  those 
  of 
  the 
  disk 
  tubular 
  and 
  perfect, 
  about 
  60. 
  Involucre 
  in 
  

   somewhat 
  several 
  merging 
  series, 
  outer 
  more 
  loosely 
  spreading 
  ; 
  the 
  two 
  outer 
  

   sub-series 
  leafy 
  ; 
  and 
  about 
  2 
  to 
  3 
  inner 
  membranaceous 
  series 
  slightly 
  colored 
  

   (greenish 
  yellow), 
  the 
  two 
  outmost 
  marrow 
  scales 
  short, 
  distinct, 
  lanceolate 
  

   acute 
  (3-nerved), 
  the 
  other 
  3 
  or 
  4 
  of 
  this 
  foliaceous 
  series 
  larger, 
  very 
  broadly 
  

   ovate 
  sub-imbricated 
  and 
  coherent 
  into 
  the 
  broad 
  united 
  or 
  entire 
  base 
  of 
  the 
  

   common 
  involucre 
  (5 
  to 
  7-nerved). 
  The 
  more 
  or 
  less 
  membranous 
  colored 
  

   (greenish 
  yellow) 
  series 
  consists 
  of 
  about 
  5 
  very 
  broadly 
  ovate 
  obtuse 
  mem- 
  

   brano-coriaceous 
  serrate 
  scales 
  narrowing 
  into 
  about 
  5 
  or 
  6 
  oval-oblong 
  sub- 
  

   obtuse 
  serrate 
  and 
  more 
  scarious 
  3<^les 
  ; 
  and 
  successively 
  into 
  final 
  hyaline 
  acut- 
  

  

  