Equations and formulas
Today I received the April/May 2003
issue of The Industrial Physicist (my first
copy ever) and found it quite interesting,
especially the letters and the article “Curve
Fitting Made Easy,” by Marko Ledvij (p. 24).
I would like to make Mr. Ledvij aware of a little-
known detail of the English language— “formula” designates
chemical compounds (H2O is the formula for water); “equation” should
be used for all mathematical expressions that contain an equal
sign, e.g., Y = A*exp(–X/X0)].
WABCO Freight Car Products
[Copy editor replies: Thank you for your comment.
The Merriam-Webster Online dictionary
defines a formula as “a general fact,
rule, or principle expressed in usually mathematical
symbols.” The word “rule” in that
definition includes equations.]
In regard to your recent News Brief “20
watts of terahertz” (April/May, p. 9), even
though I think the topic is interesting and the
results described are important, I found the
article to be sloppy and misleading about the
terahertz field in general. A 20-W average-power
terahertz source is impressive and will
allow some nice measurements in the future.
However, using accelerators to generate
coherent terahertz radiation has been around
for a long time, for example, at the Center for
Terahertz Science and Technology at the University
of California at Santa Barbara, and
FELIX in The Netherlands.
The beginning of the second paragraph is
in some sense correct in that the average
power levels of most existing terahertz
sources tend to be low compared with this
new source, but many can exceed 1 mW.
Some techniques are just limited by scaling,
and, given the money and large enough
accelerators, many smaller sources could be
power-combined to yield 20 W as well.
There just is not a driving force to do so.
The first paragraph makes it sound like
the only gap in the spectrum is 100 to
300 µm, while the actual “gap” is much larger,
if one is thinking of commercial devices.
However, devices such as molecular gas
lasers fill in many discrete portions of this
range, and quantum cascade lasers and
many other techniques also can be used in
the terahertz range. These were not the point
of the article, but they should not be disregarded
by saying that there were no good
coherent sources until recently.
The last thing I wish to point out is that
terahertz radiation is also known as submillimeter
(not submicrometer as stated in the
first sentence). This is important because
many people are claiming that terahertz is a
new field of research, while a large amount
of literature exists dating back decades that
seems to be generally forgotten (or ignored).
The technology is improving rapidly, but the
field has been around for a long time.
Sandia National Laboratory
Albuquerque, New Mexico
[Gwyn P. Williams of Jefferson Lab responds:
Two relevant articles appeared in the November issue of Nature.
In one (Nature 2002, 420, 153), colleagues from three
national laboratories and I reported the
generation of broadband terahertz light at
average powers “several orders of magnitude
higher than any existing source.” In
the other (p. 131), Mark Sherwin of the
University of California at Santa Barbara—
commenting independently—wrote that
“such a beam has never previously been
created,” and that the work has “opened
the door to new investigations and applications
in a wide range of disciplines.” However,
we absolutely agree with Michael
Wanke that this work in no way lessens the
importance of techniques and facilities for
terahertz light having other characteristics.
As Sherwin noted, “The 20-W broadband
beam complements other sources of terahertz
[The error in the first line has now been
Thin-film solar energy
Just a note to say congratulations on the
Flms Seek a Solar Future,” by
Ineke Malsch (April/May, pp. 16–19). It
was exceptionally well researched and written.
Michael T. Eckhart
Solar International Management, Inc.
I recently helped my university build
a 25,000 sq ft energy research center in
Muskegon, Michigan. The building will be
powered (combined heat and power) by a
molten-carbonate fuel cell running nearly
85% efficient on natural gas. The building’s
roof will feature 30 kWP (kW “peak”—at
full sun with the material at 20 ºC) of building-
integrated photovoltaics. This is the first
application of United Solar’s
thin-film amorphous silicon on stainless steel, which will be
bonded to the
single-ply membrane roof. The peel-andstick
film features eight layers with a total
thickness of less than 1 µm and operates at
The UniSolar thin-film amorphous silicon
on stainless steel continuous deposition
process now running in Auburn Hills,
Michigan, is a nearly a football field long
and cost $67 million to build. Its annual
capacity (adding all the wattage from the
material made in one year) is about 30
MWP. This is now the least-cost option for
Grand Valley State University
Grand Rapids, Michigan
Jeers to whomever edited the article “Industry
Salaries Still Rising,” on page 13
of the April/May issue. The author and editor
apparently do not understand the difference
between plural and possessive nouns.
Throughout the article the term “Ph.D.’s”
(possessive) was used when the correct
form would be “Ph.D.s” (plural). Somebody
needs to repeat an English class!
NASA Glenn Research Center
[Copy editor replies: The use of Ph.D.’s as the
plural is widely accepted by language authorities. The Chicago Manual of Style (14th
ed., Sec. 6.17), states: “Abbreviations having
more than one period, such as M.D. and
Ph.D., often form their plurals by the addition
of an apostrophe and an s.” And The
New York Public Library Writer’s Guide to
Style and Usage (p. 397) says, “The question
of how to form plurals of abbreviations is
largely stylistic, and authorities differ over
whether to use an apostrophe before the s.
This book recommends using only s to form
plurals of abbreviations, initialisms, and
acronyms—HMOs, YMCAs, WASPs—but
with the following exceptions to ensure clarity:
abbreviations with periods (M.A.’s) and
abbreviations that are single letters (A’s) or
all lowercase letters (rpm’s).” Thank you for
your interest in this fine point.]