**Document ID**: 03_19_97_1

**Date Received**: 1997-03-19 **Date Revised**: 1997/10/20 **Date
Accepted**: 1997/10/28

**Curriculum Topic Benchmarks**: S15.3.1, M3.2.1, M3.3.1, M3.3.14,
M4.3.4, M4.3.10, M4.3.17, M1.3.10

**Grade Level**: \[6-8\] Middle School

**Subject Keywords**: pollution, landfill, law, lead, enamel,
multiplication, units, liability, expert

**Rating**: advanced

**Dr. Smith vs. The Lawyer**

**By**: Joseph L Ruby, Wiley, Rein & Fielding (law firm), 1776 K Street,
N.W.,

Washington DC 20006 e-mail: jruby@wrf.com

**From**: The PUMAS Collection http://pumas.jpl.nasa.gov

©1997, California Institute of Technology. ALL RIGHTS RESERVED. Based on
U.S. Gov\'t sponsored research.

**A lawyer\'s use of some very simple science and math**. The facts are
true, although simplified; the company names have been changed.

Acme Enameling Company operated a cast-iron foundry and enameling plant,
where it made bathtubs and sinks for twenty-seven years. It dumped
factory wastes on vacant property behind the plant. Zenith Construction
Company then bought the property and used it as a construction waste
landfill.

Years later, Zenith decided to develop the property as an office park.
In preliminary testing, Zenith discovered that the property was
contaminated with lead. The State will not allow any development until
the lead is removed to permissible levels. Zenith sues Acme, claiming
that Acme\'s factory wastes are the source of the lead, and demanding
that Acme pay \$26 million to clean up the problem. Acme says that
almost all its wastes were clean sand and foundry wastes, containing no
lead. Acme retains an expert, Dr. Smith, who submits a report saying
that the levels of lead contamination on the site could not have come
from Acme. He says that the landfill must be the source of the lead
contamination.

**As the lawyer for Zenith, I learned the following facts**:

1\) Acme manufactured about 10 tons (20,000 lb.) of enamel every working
day. All the raw materials used in the manufacture of the enamel wound
up in the finished product.

2\) The factory operated 5 days a week, 52 weeks a year, and was closed
for holidays. Because there are about 10 holidays, we can assume that
the factory ran 250 days per year.

3\) The enamel formula contained about 4% lead oxide (PbO) by weight as
a raw material. Although the lead\'s chemical form changed from lead
oxide to lead silicate in the manufacturing process, all the lead wound
up in the finished product.

4\) The plant had an \"enameling yield\" of about 90%. This means that
10% of all pieces (tubs and sinks) were defective.

5\) The defective pieces were shot-blasted to remove the enamel from the
cast iron, so that the iron could be re-enameled. The blasted-off enamel
was a fine, powdery material. It was disposed of by being dumped onsite
with the foundry sand and slag.

6\) Lead, Pb, has an atomic weight of 207. Oxygen, O, has an atomic
weight of 16. Lead oxide, PbO, has an atomic weight of 223. Lead oxide
is 207/223 = 92.8% lead by weight.

**I now take the deposition of Dr. Smith**. I take him through the facts
in through 1 - 6 above, which he agrees are true. **I then take him
through the following calculations**:

1\) Out of the 20,000 lb. of enamel made each day, 4% by weight started
out as lead oxide, so 800 lb. was lead oxide.

2\) 800 lb. x 92.8% = 742.4 lb. per day of lead used in the manufacture
of enamel.

3\) Because 10% of the finished product was defective and had to be
shot-blasted, 10% of all the enamel wound up as enameling waste from the
shot-blasting process.

4\) 10% x 742.4 lb. = 74.24 lb. of lead (rounded to 74 lb.) in the
enameling waste per day.

5\) Therefore, Acme dumped 74 lb. of lead on the property per day.
Because the plant was in operation 250 days per year, Acme dumped 74 x
250 = 18,500 lb. of lead on the property per year. Because the plant was
in operation for 27 years, Acme dumped 18,500 x 27 = 499,500 lb. or
about **half a million pounds** **of lead** on the property during its
years of operating the plant!

**At the end of this line of questioning, Dr. Smith admitted that
Acme\'s wastes caused at least some of the lead contamination at the
site. Thus he was forced to repudiate the conclusion in his report**.

**Author's note**: The important math concept is that multiplication of
even small quantities can yield large quantities. The important science
concepts are: (1) repetition of seemingly trivial events over a long
enough time can have real-world consequences, and (2) often, information
that is easily obtained allows you to calculate results that you might
have thought were unknowable.

Very simple math and science can reveal important truths, even to
non-scientists, that mere words will never uncover \-- especially if it
is someone\'s intent to hide the truth. There are people in the world
who appear quite respectable (like Dr. Smith), and yet bend the truth.
Such people may tell obvious sorts of untruths because they know that
most people are simply not equipped to detect them. But with just a
little knowledge \-- sometimes science and math, sometimes history,
sometimes something else \-- many of these lies are quite easy to
expose.

My major incentive for writing this example is to show non-science
oriented kids \-- kids who want to be lawyers, or journalists, or
business people, or whatever \-- how, if you\'re not afraid of science
and math, you\'ll do better in whatever profession you choose.