angulation was extended over about 12,000 square miles. Materials were collected for a topographical map of the Yellowstone Park, on the scale of one mile to an inch. Its geology was studied minutely. A peak of the Wind River range, named Fremont's Peak, was found to be over 14,000 feet in height above the sea; no trace could be seen of the presence of man on its summit at any time. Three glaciers were discovered on the east side of the Wind River Mountains. The object of again surveying the Yellowstone Park was to bring it under the system of triangulation, which has been very successfully employed in Colorado, and to make the entire work uniform. All the old hot-spring basins were resurveyed and mapped, soundings and temperatures of several thousand hot springs were made, and the action of the geysers carefully studied. Over fifty fine photographic views were obtained of the bowls and other curious ornamental details of the Hot Springs.
The Personal Equation.—One of the principal defects of "our primary mathematical instrument," the human mind itself with its organic apparatus, is very clearly pointed out by W. Mattieu Williams. This defect makes itself apparent in certain astronomical observations, when the observer has to note the moment at which a star appears to touch the wire or wires stretched across the field of a telescope. The old way of doing this was to look at a clock as the star approaches the wire, count the beats of the clock, and then note at which beat or fraction of the beat the transit of the wire occurs. Despite the apparent simplicity of this operation there is no human being whose eye, ear, and internal nervous apparatus of perception and volition are sufficiently perfect to perform it accurately. None of us either sees, hears, or feels instantaneously. The sensation has to be transmitted from the external organ of sense to the nervous center, and the response has to be transmitted outward. These operations involve time. Nor is that all: they require a different length of time for different persons, different constitutions. Thus in the same observatory there may be three assistants. A, B, and C, and they are tested by making a number of corresponding observations. In every case it will be found that A is say a quarter of a second ahead of B, and B half a second ahead of C. What is to be done? If all erred alike—if all observers required just half a second to collect their sensations of sight and hearing, and to bring them to bear upon the same perception, then by setting the clock half a second ahead of the true time, the needed correction would be made. But, failing this, some personal standard of comparison must be taken, and the observers' rated to this standard like chronometers. This is done in observatories, and the result is called the "personal equation" of the individual observer. And not only has the personal equation of each observer to be determined on his entrance upon his duties, but it demands periodical revision, for it varies with age and constitutional conditions.
Use of the Balloon in Arctic Exploration.—In a paper read before the London Aeronautical Society, Mr. Brearey, its secretary, advocated the employment of balloons in polar exploration. Re-to the last English polar expedition, Mr. Brearey said that, instead of a seventy days' journey to accomplish about seventy miles, at a fearful cost of life and suffering, consequent on having to drag over ice hummocks sleds containing provisions, the whole of the stores could have been conveyed over the heads of the explorers, and the men holding the ropes of this floating observatory would have been assisted by the upward tendency of the balloon. The question is, Would the daily consumption of stores compensate the leakage of gas? and its answer is found in Beaumont's history of the balloon as employed in the United States war of the rebellion. He writes that "the balloon when inflated can, unless in very windy weather, be very readily carried. Twenty-five or thirty men lay hold of cords attached to the ring and march along, allowing the machine to rise only sufficiently to clear any obstacle." He had frequently seen it carried thus without the least difficulty. As for the leakage of gas, by the use of proper varnish it might be so checked that at the end of a fortnight the balloon could make an ascent without being replenished.