At a rather later period of intellectual development, the premonitory signs of good or bad weather become formulated into short sayings, or popular prognostics. A large number of these are still current in every part of the world, but their quality and value are very varied. Some represent the astrological attitude of mind, by referring weather changes to the influence of the stars or phases of the moon; others, on the contrary, are very valuable, and, in conjunction with other aids to weather forecasting, prognostics will never be entirely superseded, especially for use on board ship. Till within a very recent period, their science and explanation had hardly advanced since they were first recorded. In many cases the prognostics came true; when they failed, no explanation could be suggested why they did so; neither could any reason be given why the same weather was not always preceded by the same signs. A halo sometimes precedes a storm; why does it not always do so? Why is rain sometimes preceded by a soft sky and sometimes by hard clouds? About one hundred and fifty years ago the barometer was invented. Very soon after that discovery, observation showed that, in a general way, the mercury fell before rain and wind, and rose for finer weather. Also that bad weather was more common when the whole level of the barometer was low, independent of its motion one way or the other, than when the level was high. But as with prognostics, so with these indications, many failures occurred. Sometimes rain would fall with a high or rising barometer, and sometimes there would be a fine day with a very low or falling glass. No reason could be given for these apparent exceptions, and the whole science of barometric readings seemed to be shrouded in mystery. The science of probabilities came into existence about the commencement of the Nineteenth Century, and developed the science of statistics. By this method the average readings of meteorological instruments, such as the height of the barometer or thermometer, or the mean direction and force of the wind, at any number of places were calculated, and the results were sometimes plotted on charts so as to show the distribution of mean pressure, temperature, etc., over the world. By this means a great advance was made. Besides giving a numerical value to many abstract quantities, the plotting of such lines as the isothermals of Dove conclusively showed that many meteorological elements hitherto considered capricious were really controlled by general causes, such as the distribution of land and sea. Still more fruitful were these charts as the parents of the more modern methods of plotting the readings of the barometer over large areas at a given moment, instead of the mean value for a month or year. Then by tabulating statistics the relative frequency of different winds at sea, many ocean voyages--notably those across the “doldrums,” or belt of calms near the equator--were materially shortened.