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differential

differential

```  4  definitions  found

From  Webster's  Revised  Unabridged  Dictionary  (1913)  [web1913]:

Differential  \Dif`fer*en"tial\,  a.  [Cf.  F.  diff['e]rentiel.]
1.  Relating  to  or  indicating  a  difference;  creating  a
difference;  discriminating;  special;  as  differential
characteristics;  differential  duties;  a  differential  rate.

For  whom  he  produced  differential  favors.  --Motley.

2.  (Math.)  Of  or  pertaining  to  a  differential,  or  to
differentials.

3.  (Mech.)  Relating  to  differences  of  motion  or  leverage;
producing  effects  by  such  differences;  said  of  mechanism.

{Differential  calculus}.  (Math.)  See  under  {Calculus}.

{Differential  coefficient},  the  limit  of  the  ratio  of  the
increment  of  a  function  of  a  variable  to  the  increment  of
the  variable  itself  when  these  increments  are  made
indefinitely  small

{Differential  coupling},  a  form  of  slip  coupling  used  in
light  machinery  to  regulate  at  pleasure  the  velocity  of
the  connected  shaft.

{Differential  duties}  (Polit.  Econ.),  duties  which  are  not
imposed  equally  upon  the  same  products  imported  from
different  countries.

{Differential  galvanometer}  (Elec.),  a  galvanometer  having
two  coils  or  circuits,  usually  equal,  through  which
currents  passing  in  opposite  directions  are  measured  by
the  difference  of  their  effect  upon  the  needle.

{Differential  gearing},  a  train  of  toothed  wheels,  usually  an
epicyclic  train,  so  arranged  as  to  constitute  a
{differential  motion}.

{Differential  motion},  a  mechanism  in  which  a  simple
differential  combination  produces  such  a  change  of  motion
or  force  as  would  with  ordinary  compound  arrangements,
require  a  considerable  train  of  parts  It  is  used  for
overcoming  great  resistance  or  producing  very  slow  or  very
rapid  motion.

{Differential  pulley}.  (Mach.)
a  A  portable  hoisting  apparatus,  the  same  in  principle
as  the  differential  windlass.
b  A  hoisting  pulley  to  which  power  is  applied  through  a
differential  gearing.

{Differential  screw},  a  compound  screw  by  which  a  motion  is
produced  equal  to  the  difference  of  the  motions  of  the
component  screws.

{Differential  thermometer},  a  thermometer  usually  with  a
U-shaped  tube  terminating  in  two  air  bulbs,  and  containing
a  colored  liquid,  used  for  indicating  the  difference
between  the  temperatures  to  which  the  two  bulbs  are
exposed,  by  the  change  of  position  of  the  colored  fluid,
in  consequence  of  the  different  expansions  of  the  air  in
the  bulbs.  A  graduated  scale  is  attached  to  one  leg  of  the
tube.

{Differential  windlass},  or  {Chinese  windlass},  a  windlass
whose  barrel  has  two  parts  of  different  diameters.  The
hoisting  rope  winds  upon  one  part  as  it  unwinds  from  the
other  and  a  pulley  sustaining  the  weight  to  be  lifted
hangs  in  the  bight  of  the  rope.  It  is  an  ancient  example
of  a  differential  motion.

From  Webster's  Revised  Unabridged  Dictionary  (1913)  [web1913]:

Differential  \Dif`fer*en"tial\,  n.
1.  (Math.)  An  increment,  usually  an  indefinitely  small  one
which  is  given  to  a  variable  quantity.

Note:  According  to  the  more  modern  writers  upon  the
differential  and  integral  calculus,  if  two  or  more
quantities  are  dependent  on  each  other  and  subject  to
increments  of  value,  their  differentials  need  not  be
small  but  are  any  quantities  whose  ratios  to  each
other  are  the  limits  to  which  the  ratios  of  the
increments  approximate,  as  these  increments  are  reduced
nearer  and  nearer  to  zero.

2.  A  small  difference  in  rates  which  competing  railroad
lines,  in  establishing  a  common  tariff,  allow  one  of  their
number  to  make  in  order  to  get  a  fair  share  of  the
business.  The  lower  rate  is  called  a  differential  rate.
Differentials  are  also  sometimes  granted  to  cities.

3.  (Elec.)
a  One  of  two  coils  of  conducting  wire  so  related  to  one
another  or  to  a  magnet  or  armature  common  to  both
that  one  coil  produces  polar  action  contrary  to  that
of  the  other
b  A  form  of  conductor  used  for  dividing  and  distributing
the  current  to  a  series  of  electric  lamps  so  as  to
maintain  equal  action  in  all  --Knight.

{Partial  differential}  (Math.),  the  differential  of  a
function  of  two  or  more  variables,  when  only  one  of  the

{Total  differential}  (Math.),  the  differential  of  a  function
of  two  or  more  variables,  when  each  of  the  variables
receives  an  increment.  The  total  differential  of  the
function  is  the  sum  of  all  the  {partial  differentials}.

From  WordNet  r  1.6  [wn]:

differential
adj  1:  relating  to  or  showing  a  difference;  "differential
treatment"
2:  (mathematics)  involving  or  containing  one  or  more
derivatives;  "differential  equation"
n  1:  the  result  of  mathematical  differentiation;  the
instantaneous  change  of  one  quantity  relative  to
another;  df(x)/dx  [syn:  {derived  function},  {derivative},
{differential  coefficient},  {first  derivative}]
2:  a  quality  that  differentiates  between  similar  things
3:  a  bevel  gear  that  permits  rotation  of  two  shafts  at
different  speeds;  used  on  the  rear  axle  of  automobiles  to
allow  wheels  to  rotate  at  different  speeds  on  curves  [syn:
{differential  gear}]

From  The  Free  On-line  Dictionary  of  Computing  (13  Mar  01)  [foldoc]:

differential

{differential  line}.

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