between the viscosity oe liquids and theih chemical nature. 575 
in attempting to deduce a suitable formula; and on the publication of Slotte’s pa])er 
he sought, by an application of the method of least squares, to employ the 'whole of 
the experimental results in arriving at the values of the constants. The improve¬ 
ment, however, was hardly commensurate with the arithmetical labour involved. 
It follows by differentiating Slotte’s formula in the shape 
that 
77 = c/(a + ty 
^ dc — rj log« (a -f t) dn ^ da, 
c cc i 
and on using the d.ifferences between the observed values of 77 and those deduced by 
Slotte’s formula as values for dr^, as many equations as there were observations were 
obtained. These were then added together into three groups, the sums being solved 
for dc, dn, and da, the corrections to be applied to the constants in the original 
formula. The results obtained by this method were again but a slight improvement 
on those given by the unmodified constants. Of course, better agreement would be 
obtained by introducing more constants into the formula. Immediately this is done, 
however, the simple character of the formula disappears, and it is rendered unwieldy, 
and indeed, unsuited for carrying out a general physico-chemical inquiry as to the 
dependence of viscosity on temperature. 
The worth of the simple formula can only be tested when some means has been 
devised for employing all the observations in deducing it. In some cases it was 
obvious that all or most of the differences between observed and calculated values 
were of the same sign, so that by slightly altering the value of C, and thus shifting the 
calculated curve, a better agreement could be obtained. When possible this was done. 
As stated before, the closeness of the agreement between the formula and obser- 
tion depends on the slope. As the difference between the slopes at 0 ° and the 
boiling point increases, the deviations increase. For many liquids calculated and 
observed numbers only give a fair agreement in the fifth decimal place, and this has 
been thought sufficiently good. In these cases, the initial slope, in general, diminishes 
to about one-tenth of its value as the curves are descended. Although, for curves in 
which the slope varies to such a large extent as this, the results giving the comparison 
of calculated and observed numbers have only been given to the fifth decimal place, 
there is every reason to believe that the observed values are just as accurate as those 
for liquids giving short straight curves and where the agreement is satisfactory as far 
as the sixth place. In the case of the alcohols the slope changes so considerably as 
temperature rises, in some cases being at the boiling-point only s^th of what it is at 0 °, 
that the observed curve has liad to be split up into two or three parts, and a separ’ate 
formula calculated for each, in order to give the required degree of agreement. It is 
significant that wdien this is done the values of l> and n vary according to the part 
of the curve chosen, a circumstance indicating that no great stress should be put 
upon the relative magnitudes of the constants in the ordinary formula. For, 
