MEASUREMENT OF HEIGHTS. 545 



TT 



log P = log i - log 337-008-^ . 0-000070095 - 37^0^' 



We obtain thus 



, P , . , 7./ H'- H 



I0gp=l0gi;-l0g6; + ^yg^^7, 



where log b, and log bj are substituted for brevity for 

 log b—t . 0-00007 and log ^>' — /'.O-OOOO7. Further, we obtain, 

 without sensible error, 



V K^-^) - 337-008 

 If we introduce log b^ and log bj in (ll.)? and put -— for /', 

 this equation becomes 



r ni + kT) 0-863 ^Q.T-cT'-l 



V-(^). 3760707 '^ V{b'bl) ^ /• 



If we change [g) in the denominator of the second member 

 into 1 , which has no sensible influence, and if we take for a. 

 the half sum of its values at the two points of observation 

 = -^^ (a + a'), then the quantity within brackets is 



_ 33 9-17 -/:T / 1 _ / ^ 172-67 10'''^"-'^' 1 



~ 400-17 1 ^''■^"V(6,6/) • 399-17-/tT J 



If we designate thenceforward 



^(^ + ^^) 399T-Vr • • • • ^^^' 



172-67.10"'^-'''^' 



399-17 -A;T 

 the equation gives 



H' - H = log b, - log b< 



by W, 



1 - 



{9) 1 ^ (« + «') w 



and as 



^^{b,b}] 



H' — H = — — -n- r = h' — 7i -\ , 



a + h! a + n a a 



II h ''" 4. '*' - ^^s^/-^"g^ / V .,, s 



