User's Manual

Discover Density Set 012–07192A
12
As an alternative to calculating the logarithms of all of the data, the data may
be plotted on log-log graph paper, also called full logarithmic paper. The
spacing between the lines on this paper is adjusted so that the appearance is
the same as plotting the logarithms of the data on ordinary paper. The result
is a straight line with a slope of 3. (Since the numbers on the paper are the
same as the original data, calculating the slope requires first calculating the
logarithms of the coordinates of two points.)
Note: As remarked before, while computer programs such as DataStudio
provide rapid methods of data analysis, logarithmic graphs such as that
above are a common and effective way to visually show this type of
relationship. For this reason it is valuable to understand the method and gain
familiarity with logarithmic graphs.
Analysis Verification
Often, data analysis of this sort is done in the hope of confirming some
hypothesis that has been proposed. In any case, some sort of check or
comparison is in order. Frequently, this check first involves algebraic
manipulation of either the equation developed, or the hypothesized
equation, to put them in the same terms.
In this example, we know that
mass = (density)(volume),
a math reference gives, for the octahedron,
volume = (1/3) a
3
(2
0.5
), where a is the length of an edge,
and another reference gives
density of fluorite = 3.18 g/cm
3
.
Combining these equations, we get
mass = (3.18 g/cm
3
)(1/3)a
3
(2
0.5
),
and simplifying results in
mass = 1.499 g/cm
3
a
3
.
This result is in agreement with the results obtained by analysis of the
experimental data.