writes the sum, 301,095, to the right of the line. Under this number he places the third number of the series (975,642), and adds that in just as he did the first two; and so on till the process is completed. The process is longer than ours, but gives more opportunity for deliberation and the detection of errors. Where whole numbers and fractions are both involved, two series of additions are gone through. In subtraction, they write the lesser number over the larger, and begin at the left; thus, to subtract 657,869 from 786,422, they write
|786,422||and proceed, 6|
from 10 (a fictitious number which they use for convenience) leaves 4; adding 7 (the first figure of the minuend), gives 11, and 11 10 leaves 1, the first figure of the remainder. For the next digits, 5 from 10 leaves 5; adding 8 gives 13; this less 1 gives 1 2, the first two figures of the remainder. Then, 7 from 10 leaves 3, adding 6 to which gives 9, which less 1 = 8; 10 - 8 = 2 + 4 = 6 - 1 = 5; 10 - 6 = 4 + 2 = 6 - 1 = 5; 10 - 9 = 1 - 1 - 2 = 3. Whence, if the numbers are set down as they are found, the remainder appears correctly as 128,553. In multiplication they place the multiplier over the multiplicand and multiply successively each of the figures of the multiplicand by each figure of the multiplier, obtaining a large number of partial products which they have painfully to add together. The process of division is likewise absurdly complicated.
The Utilitarian Side of Botany.—Botanists, said Prof. I. B. Balfour, in his British Association address, do not seem to have realized, except in the case of medicine, that modern botany has an outlet. Chemists and physicists seek practical aims. Zoologists help the fishing industry. But where is the practical outcome of modern botany? The work of Marshall Ward is full of purpose to many large industries, and that of Oliver has bearings on horticulture; but the trend of botanical work in England has not been utilitarian. It was, however, its utilitarian side that gave the first impetus to the scientific study of botany. The plant world, as the source of products of economic value and drugs, attracted attention, and out of this grew by natural development the systematic study of plants. The point of view was that botany was an essential branch of medical study. A practical outcome was the establishment of botanic gardens, now in many instances appendages of teaching establishments, or mere pleasure grounds. But the gardens at Kew still maintain the old tradition of botanic gardens as a center through which botany renders scientific service to national progress. Under the Darwinian influence the biological features of the plant world replaced technical diagnosis and description as the aim of teachers and workers. Pharmacy is removed from the functions of the physician; but botanical study on the lines of modern teaching is part of the university training essential to medical students. There is still danger of modern teaching being strangled by its terminology, of narrowing the field of vision and mistaking the name for the thing, of elaborating the minute details of a part at the expense of its relation to the whole organism. This mechanical attitude is a consequence of specialization. But it must be counteracted if botany is to be aught else than a mechanical study. Modern botany has not yet found its full application. It has not rendered the service due to the state. In horticulture and agriculture it should find a sphere of application by which it may contribute to the national well-being. Botanists must be the apostles of forestry; and forestry in turn will react upon their treatment of botany. Botany can not thrive in a purely introspective atmosphere; it can live only by keeping in touch with the national life.
The Uses of Illuminating Gas.—Many are the advantages of gas for household purposes, says William Paul Gerhardt, and its disadvantages are comparatively few, and for this reason it is probably more used in houses at the present day than any other form of artificial illumination. Gaslight is relatively cheap, although kerosene oil, per se, is probably cheaper. It is convenient, and saves domestic labor by being always ready for lighting. It is superior in point of cleanliness to oil lamps and candles. It is brilliant, easily controlled, and not difficult to manage by persons of ordinary intelligence. It is much safer than candles or lamps in which