e„  =  V(e,,-+  e,r)  =  V  (0 .  0015  +  0 .  OOK))  =  v'()  ■  00:5 1
Finally,  tlu^  mc^an  square  error  of  the  difference  of  the  readings  on


COMBINATION  OF  COMPUTED  QUANTITIES  187

the  two  objects,  which  is  that  of  the  direct  measurement  of  the
angle,  will  be,

V(eo2+6o-)  =  Vo.0062

and  that  of  the  mean  of  the  direct  and  reversed  results  will  be


,,=^^^»?  =  VOa31  =0.056"

V2

(6)  A  line  1000  feet  long  is  measured  eight  times  with  a  100-
foot  tape,  and  the  mean  square  error  of  the  mean  of  the  eight
measures  is  found  to  be  0 .  004  foot.  If  the  mean  square  error  of  the
length  of  the  tape  (resulting  from  its  standardization)  is  0.001,
what  is  the  mean  square  error  of  the  line,  due  both  to  errors  of
manipulation  and  error  in  the  tape  length?

The  mean  square  error  of  the  line  due  to  the  tape  error  is
10X0.001=0.010.  Since  the  total  error  is  the  algebraic  sum
of  both  kinds,  the  mean  square  error  due  to  both  causes  will  be  the
square  root  of  the  sum  of  the  squares  of  the  separate  mean  square
errors,  that  is,

e^  =  V{0 .  0042+0 .  010-)  =0.011

COMBINATION   OF   COMPUTED    QUANTITIES

156.  Weights  from  Mean   Square   or   Probable  Errors.     In

Art.  143,  it  was  demonstrated  that  weights  are  invcr.sely  as  the
squares  of  the  corresponding  mean  square  or  probaljle  errors.
