From these formulae we derive two important relations, dp4 = or the function F, on the right which multiplies r, is said to be a simultaneous invariant or covariant of the system of quantics.
The reason of this appears to he that the diplococcus is frequently present in the mouth or air-passages without giving rise to any symptoms; but when the patient is exposed to chill, and the tissues of the respiratory passages are thereby weakened, the diplococcus grows, multiplies and gives rise to inflammation of the lungs.
The tree is not at present indigenous in southern Britain, but when planted in suitable ground multiplies rapidly by the wind-sown seeds; on many of the sandy moors and commons natural pine woods of large extent have been thus formed during the last fifty years.
As human intelligence and industry come into play the means of livelihood are proportionately extended; population multiplies, and with this multiplication production increases.
The report also considers it proved that the bacillus pestis multiplies in the stomach of a flea and may remain a considerable time within its host.