Passage adapted from The Extermination of the American Bison, by William Hornaday (1889).

The history of the buffalo’s daily life and habits should begin with the “running season.” This period occupied the months of August and September, and was characterized by a degree of excitement and activity throughout the entire herd quite foreign to the ease-loving and even slothful nature which was so noticeable a feature of the bison’s character at all other times.

The mating season occurred when the herd was on its summer range. The spring calves were from two to four months old. Through continued feasting on the new crop of buffalo-grass and bunch-grass—the most nutritious in the world, perhaps—every buffalo in the herd had grown round-sided, fat, and vigorous. The faded and weather-beaten suit of winter hair had by that time fallen off and given place to the new coat of dark gray and black, and, excepting for the shortness of his hair, the buffalo was in prime condition.

During the “running season,” as it was called by the plainsmen, the whole nature of the herd was completely changed. Instead of being broken up into countless small groups and dispersed over a vast extent of territory, the herd came together in a dense and confused mass of many thousand individuals, so closely congregated as to actually blacken the face of the landscape. As if by a general and irresistible impulse, every straggler would be drawn to the common center, and for miles on every side of the great herd the country would be found entirely deserted.

At this time the herd itself became a seething mass of activity and excitement. As usual under such conditions, the bulls were half the time chasing the cows, and fighting each other during the other half. These actual combats, which were always of short duration and over in a few seconds after the actual collision took place, were preceded by the usual threatening demonstrations, in which the bull lowers his head until his nose almost touches the ground, roars like a fog-horn until the earth seems to fairly tremble with the vibration, glares madly upon his adversary with half-white eyeballs, and with his forefeet paws up the dry earth and throws it upward in a great cloud of dust high above his back. At such times the mingled roaring—it can not truthfully be described as lowing or bellowing—of a number of huge bulls unite and form a great volume of sound like distant thunder, which has often been heard at a distance of from 1 to 3 miles. I have even been assured by old plainsmen that under favorable atmospheric conditions such sounds have been heard five miles.

Given the information provided by the passage, what is the maximum distance at which a bison's bellow be heard?