the Viscosity of Aur. 189 
If the mass of mercury filling the whole tube be M grms., 
| 1 
M=~r7p \ a? da. 
0 
Taking J/n as an element of length instead of da and replacing 
integration by summation, we have 
l 1 
M =n | ae eS oe Se 
0 n go eG 
1 be 
- Hence SS = Ne dics canna aap cate: (17) 
m n q 
In a similar way we find 
pees ye oh aze Ge EEE 
a OF Gav ne ) men 
Hence, by (17), 
WO] GN ne 
If a,’ be the mean value of the square of the radius deduced from 
the mass of mercury filling the whole tube, 
Ninseaeeeniel 1 (s IN? Sop 
| —— 27) 0 
a. = M/rpl. 
ACD) oh we lf ING 
Thus I A ROE (= 7) ge 
Hence the factor F by which //a,t must be multiplied to correct 
for the inequality of the tube is 
This factor is only very slightly greater than unity when the tube 
is nearly uniform. 
We may exhibit the correcting factor in another form. Let q, 
be the mean value of the n quantities g,, qo, ... and let 
h=t+d. Jo = Qo + ds, &e. 
Then Sa dh 46 Gh =e oo =O. 
Hence LP= =z (get 2qod + d*) = ng? + Xd. 
Also, since with a nearly uniform tube d,, d., ... are small compared 
with qQ, 
il Ht Pe ts a? fii Al 
Ss = gaan ace 
q qot+d G Ww Giga eee 
