1. Does it vary in brightness? 2. Is the brightness increasing or decreasing? 3. Is the variation uniform? 4. If not, according to what law does it vary? In a majority of cases the change will probably be found to have a periodic character, in which case several other questions will arise, such as-- 5. What is the length of the period? 6. Are there minor periods? 7. What is the law of variation within the period? 8. Is there any change in the amount of variation? 9. If so, is it a secular, *i.e.* a continually growing change, or does it give evidence of a greater period? Already the periodic changes of a certain number of stars have been determined with accuracy, and the lengths of the periods vary from less than three days up to intervals of time at least 250 times as great. Periods within periods have also been detected. There is, perhaps, no subject in which more complicated quantitative conditions have to be determined than terrestrial magnetism. Since the time when the declination of the compass was first noticed, as some suppose by Columbus, we have had successive discoveries from time to time of the progressive change of declination from century to century; of the periodic character of this change; of the difference of the declination in various parts of the earth’s surface; of the varying laws of the change of declination; of the dip or inclination of the needle, and the corresponding laws of its periodic changes; the horizontal and perpendicular intensities have also been the subject of exact measurement, and have been found to vary with place and time, like the directions of the needle; daily and yearly periodic changes have also been detected, and all the elements are found to be subject to occasional storms or abnormal perturbations, in which the eleven year period, now known to be common to many planetary relations, is apparent. The complete solution of these motions of the compass needle involves nothing less than a determination of its position and oscillations in every part of the world at any epoch, the like determination for another epoch, and so on, time after time, until the periods of all changes are ascertained. This one subject offers to men of science an almost inexhaustible field for interesting quantitative research, in which we shall doubtless at some future time discover the operation of causes now most mysterious and unaccountable. *The Methods of Accurate Measurement.* In studying the modes by which physicists have accomplished very exact measurements, we find that they are very various, but that they may perhaps be reduced under the following three classes:-- 1. The increase or decrease, in some determinate ratio, of the quantity to be measured, so as to bring it within the scope of our senses, and to equate it with the standard unit, or some determinate multiple or sub-multiple of this unit.