126 G. H. KNIBBS. 
- Relative fluidities of distilled water, 0° to 45° C. as determined 
y, 
from Poiseuille’s experiments with glass tubes. F 
Temp. Tube 4. Tube C. Tube Di. Tube E. Mean. Compu od 
1:0000 1:0000 1:0000 1:0000 = 1-0000 4 
05 10136 1-0141 10143 1-0140 10170 © 
BS Pius Ltrer 1782" 11820 PES 11756 
10 1:3558 1:3647 1:3632 1-3674  1-3628 1:3630 ” 
15 15536 15565 1:5562 15621 1:5571 1:5621 3 
90 1:7642 1-°7716 1°7731 1:7742 17708 17m 4 
95 19876 19955 1:9903 19943 11-9919 1-956 q 
30 229297 22961 22971 2:2295 2-2264 2-2300 a 
35 24721 24803 2-4816 2-4830  2-4793 2-4762 4 
40 2°7354 2°7357 27414 27402 92-7382 2-734 4 
45 30155 3-:0069 2-9991 3-0170  3-0096 30036 4 
— 
> 
Taking out the second differences from the column of mea 
values, we find no definite law of progression, that is to say the 
third differences are irregular and variablein sign. As the second 
differences are small, a curve of the second degree will express the 
results with considerable precision. We therefore put ; 
Sf’ =1+a7r+ Br? (35) 
jf’ denoting relative fluidity, r temperature in degrees centigrade, 
and a and £ the constants to be determined. The mean of he 
second differences for the 5 degree intervals is 0-01174, s0 that | 
28x52 =0-01174 or B=0-000235! ‘ 
By subtracting from each value of the relative fluidity the corre 
ponding value Br? we eliminate the second term from the ¥ ue 
of the function, and may thus obtain that of a. This is nee 
conveniently effected by the process represented in the follo 
—— a 
1 More accurately 0:0002348. The change to 0:000235 is not wit 
advantage, for when the first term is subsequently evaluated, the limi 
number of figures used, more exactly expresses the observed values ® 
if the change had not been made. I venture to think that for P 
purposes the type of solution above indicated, together with the com 
ation of the reciprocal effect of small changes in the coéfficients, with 
view to securing a simple numerical expression that will repres* é 
observed values, is preferable to the usual method by least squares 
ns] 
