That  communication  contained  (1)  a  geometrical  construction  for  deducing
a  new  characteristic  curve  when  the  air  density  or  the  gun's  calibre  is
changed ;  (2)  the  analytical  proof  of  that  law ;  (3)  the  law  for  deducing  a
new  characteristic  curve  when  the  muzzle  velocity  is  changed ;  (4)  a  com-
parison of  range-tables  showing  how,  by  help  of  these  laws,  from  the
characteristic  curve  for  a  gun  of  any  calibre  and  muzzle  velocity,  to  deduce
the  curve  for  a  gun  of  any  other  calibre  and  muzzle  velocity;  and
(5)  empirical  formulae  enabling  a  practical  gunsight  to  be  so  constructed  that
when  set  for  true  range,  it  is  also  set  for  the  true  elevation,  whatever  the
calibi-e  of  the  gun,  the  muzzle  velocity,  the  air  density,  and  the  rate  of  change
of  range  may  be.
