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In order to determine the retardation due to the resistance 
of any substance, an impulse is given to the disc, with the 
cylinder immersed in the liquid, and the reading of the 
scale at each successive turning point noted. Any length 
of are may be taken, but the initial impulse should be the 
same in all cases and should correspond to that for which 
the instrument is calibrated. An arc of large amplitude 
has an advantage, as it reduces the influence which errors 
of scale reading have upon the result. In the tests already 
made, the initial impulse has been given by turning the disc, 
in the direction which causes the numbers on the scale to di- 
minish, through one complete revolution or 360° the starting 
point is then 0 and the first reading gives the length of are 
of the first oscillation. In order to start the disc exactly at 
the zero point without vibration. it is necessary to have a 
clamp by which it may be held in the proper position and 
instantly released. The difference in the scale reading at 
adjacent turning points, gives the length of the arc of oscil- 
lation. The ratios of damping with different solutions may 
be best compared by the logarithmic decrements of these 
arcs. Representing the amplitude of the mth swing by a, 
and that of the nth swing by b, the logarithmic decrement 
will be 
logta == loz. b 
n—m 
The number corresponding to this logarithm will be the 
ratio of damping. Five or six swings are sufficient fur this 
determination. 
It is possible, by determining the necessary constants of 
the apparatus, to calculate from the diminution of the arcs 
of oscillation the amount of energy required to overcome 
the resistance which any liquid offers, but the mathematical 
considerations involved are too complicated for general use, 
and would lead to confusion in the results, if this were 
taken directly as a measure of viscosity. To avoid the ne- 
cessity for this calculation the viscosity imparted to distilled 
water by pure cane sugar is taken for astandard of com- 
parison, the apparatus being calibrated as follows: A num- 
ber of solutions, each containing a known quantity of sugar, 
are prepared and the amount of damping which each of 
these produces is determined. A curve is then constructed 
in which ordinates represent the number of grams of sugar 
per litre, and abscissas the amount of damping. This curve 
is quite regular, so that few points are required for its con- 
struction, and when once made furnishes a simple means 
for expressing the viscosity of any liquid within its range. 
The amount of damping may be expressed in several 
ways, two or three of which are indicated below. Thesum 
