AND ITS APPLICATION TO MR. B. TOWER’S EXPERIMENTS. 
221 
From equations (119) and (130) 
f'— ^ ■_ ^0 _g-'044i{Z'T B -T o )4-T m } 
3'46 « 0 + mL 
whence 
lo g /=--0443fZ(T B -T 0 ) + T.!log,+ log( 3 i-q rL ). . . (137) 
In Table IX. (Tower) the values of f are given for the same values of N' and L' 
corresponding to different values of T B . 
Substituting corresponding values of f and T B in equation (137), and subtracting 
the resulting equations, we have an equation in which the only unknown quantities 
are Z and the differences of T m . 
The values of f being known, the values of T m are obtained from equations (120), 
(134), and (125), and substituting these, the equations resulting from (137) give the 
values of Z. Thus from Table IX. (Tower) 
L '=100 
■ U=100 
T b =60 /=• 59 T ? „=5"9 
Tb—- 70 /=• 48 T ot =4*8 
From (137) 
„ , 5'9—4 - 8 log’59—log‘48 
10 = -0443 x 10 x log e 
Therefore 
Z= 35 .(138) 
From this value of Z the values of f corresponding to those in Tower’s Table IX. 
have been calculated and agree well with the experimental values. 
The smallest temperature of the oil bath recorded in Tower’s Table IX. is G0° Fahr., 
therefore it is assumed that this was the normal temperature, whence 
T*=-35(T b -60) + 60 (139) 
Hence it is concluded that the actual temperature of the oil film in all the expeii- 
ments with the bath, at a temperature of 90° Fahr., is given by 
T=70*5+T„.(140) 
By the formula for p. since T. r =70’5 
p. r =-00004737<T' 0(m * 7o ‘ 5 
= "000009974 (141) 
= ’00001 (approximately) 
