158  Mr.  A.  B.  Porter  on  the 
the  shading  will  approximate  that  indicated  in  fig.  3,  which 
represents  the  transparency  curve   of  a  grating  formed  by 
Fio-.  3. 
superposing  a  simple  grating  on  an  imperfectly  transparent 
surface.  Such  a  grating  should  evidently  give  a  central  image 
and  spectra  of  the  first  order  only.  This  point  was  tested  in 
the  following  manner.  A  glass  grating  by  Max  Levy,  with 
•400  very  sharply  ruled  black  lines  to  the  inch,  was  held  against 
a  photographic  dry  plate  so  that  one  edge  of  the  grating  was 
in  contact  with  the  film,  while  the  opposite  edge  was  separated 
from  the  film  by  interposing  a  strip  of  thick  paper.  During 
exposure  to  the  light  of  an  incandescent  lamp,  the  grating  and 
plate  were  kept  oscillating  about  an  axis  parallel  to  the  lines 
of  the  grating.  When  examined  under  a  microscope,  the  lines 
near  one  edge  of  the  developed  plate  are  seen  to  be  only 
moderately  blurred,  while  there  is  much  more  blurring 
toward  the  other  edge  of  the  plate.  On  looking  at  an  incan- 
descent lamp  through  that  part  of  the  plate  wdiere  the  lines 
are  sharpest,  the  spectra  of  the  first  three  orders  are  seen. 
As  the  plate  is  moved  across  the  eye  the  second  and  third 
order  spectra  rapidly  fade  away,  so  that  only  the  first  order 
spectrum  is  seen  where  the  lines  are  most  blurred.  The 
original  Levy  grating  gives  many  spectra,  the  first  thirty- 
five  orders  being  plainly  visible  when  a  sodium  flame  is  used 
as  the  source. 
6.  When  a  lens  forms  a  real  image  of  a  grating,  it  does 
so  by  adding  together  in  the  focal  plane  the  harmonic 
components  of  the  diffracted  light.  If  the  illumination  is 
central  and  the  aperture  of  the  lens  is  so  narrow  that  it  cannot 
pass  the  light  represented  by  the  second  and  succeeding  terms 
of  equation  (2),  i.  e.  if  it  passes  only  the  non-periodic  first 
