And so the week began the way many summer weeks begin in these swampy parts: Forecasters warned of an oppressive air mass pushing east, sinking into the region and lingering for days, bringing not just high temperatures but also something far more sinister: a stifling heat index.

The measure of misery reached 105 degrees yesterday and could go beyond 110 today and Wednesday, but even as Darrell Townsend sat in the thick and heavy 2 p.m. sun yesterday -- even as he has planned his Julys and Augusts around this precious, if mystical, number -- he confessed to having exactly no understanding of how it is devised.

He simply trusted it, an article of summer faith.

"How it's determined?" he asked, his forehead glistening. "I have no clue."

For those who are curious, the heat index has its modern origins in the Journal of Applied Meteorology, Vol. 18, No. 7.

A 1979 report titled "An Assessment of Sultriness: Part I: A Temperature-Humidity Index Based on Human Physiology and Clothing Science," by an Australian named R.G. Steadman, tried to express empirically the toll of heat and humidity on the human body -- specifically, on a 5-foot-7 male body weighing 147 pounds with a certain capacity for sweating and standing in a wind of eight knots. Taking into account more than a dozen factors such as rates of evaporation, the body's core temperature, salinity and clothing resistance to heat transfer, Steadman devised an elegant chart of numbers he called the "apparent temperature," and by the mid-1980s, the National Weather Service began using it, including the so-called "heat index" in regular forecasts.

But the weathermen of the world were not satisfied and began lobbying for a more precise gauge. In 1990, Lans P. Rothfusz, working in Texas, answered the call, publishing a paper subtitled, "More than you ever wanted to know about the heat index."

"Now that summer has spread its oppressive ridge over most of the Southern region, [National Weather Service] phones are ringing off their hooks with questions about the heat index," he wrote by way of introduction. "Some are satisfied with the response that it is extremely complicated. . . . But there are few who will settle for nothing less than the equation itself."

And so he gave it to them, a formula of T's (dry bulb ambient temperature) and R's (relative humidity) that tries to reduce the complexities of human physiology and thermodynamics to math:

HI or Heat Index = -42.379 + 2.04901523T + 10.14333127R

- 0.22475541TR - 6.83783x10{+-}{+3}T{+2}

- 5.481717x10{+-}{+2}R{+2}

+ 1.22874x10{+-}{+3}T{+2}R

+ 8.5282x10{+-}{+4}TR{+2} - 1.99x10{+-}{+6}T{+2}R{+2}

"It's as good as we can get in terms of a formula," said Rothfusz, who works in Peachtree City, Ga., where the heat index yesterday was pushing 107. "The caveat is it's chock full of assumptions, like wind speed, type of clothing and the clothing's resistance to moisture."

Ultimately, the heat index is a subjective matter, and as the late afternoon sun draped McPherson Square yesterday, there were as many indices as there were people having lunch, each with his own threshold of suffering.

Marc Mosby, eating a hot sandwich out of hot tinfoil without benefit of shade, said that if the outside temperature was in the 90s, his own personal heat index at the moment was somewhere in the range of "not that hot." But he is a slim man raised in Louisville.

Across the way, near a garden full of marigolds that looked like so many blazing suns, Ki-Hong Han, a heavier man visiting from the more delicate climate of Seoul, considered his own heat index at the moment. His forehead shone. He apologized for his English, then offered his assessment.

"Killing hot," he said, nodding. "K-i-l-l."

"Too hot to concentrate," he added, pointing to the book he'd stopped reading, "A Very Short Introduction to Anarchy."

Staff writer Peter Slevin and researcher Bobbye Pratt contributed to this report.

In Annapolis, Kris Sweedler encourages her dog, Jack, to join her in the Severn River, perhaps in an attempt to escape the oppressive heat index.