On the other hand, during a considerable portion of the time when it is varying, the light will be so much less than usual that a careful measurement is not needed to detect the change. Moreover, it will be useless to look for an increase of light, and the observation may be so planned as to detect a diminution only. If we assume that only during one tenth of the time the change in light will be sufficient to be perceptible, the chance on any given evening will be 9 out of 10 or 9/10 that the star will have its full brightness. For two evenings the chance will be (9/10)^2 for three (9/10)^3, etc. These quantities expressed decimally are .9, .81, .73, .66, .59, .53, .48, etc. Even after seven nights' observations, on which no change is noted, it will only be about an even chance that the star may not still be of the Algol type. A different method of observing is therefore recommended when the star is supposed to belong to this class. Select for comparison a star slightly fainter, so that a moment's glance will satisfy the observer that the suspected variable is the brighter. It is only necessary to repeat this observation night after night. If the star is bright enough to be visible with a field glass, a few seconds will be sufficient for this observation after the observer has become familiar with the vicinity. The fact that the light is normal, and the time to the nearest minute, should be recorded after each observation. When convenient, it is well to repeat the inspection two or more times during the night, as in determining the period all the observations will have a value, provided that they are separated by intervals of more than two or three hours. If the star is ever found below its normal brightness, comparisons should be made with the adjacent stars, and continued as long as possible, or until it has regained its usual brightness. The most complete proof that a star was not of the Algol type would be for observers in the polar regions to examine it at intervals of a few hours for several days, or for observers in different longitudes to make the same observations. If it could thus be watched for a week or fortnight by enough observers to avoid interference by clouds, it would be nearly certain that it is not an Algol star unless its period is greater than that of any such object as yet discovered. The problems to be undertaken may be defined as follows:-- 1. To observe all the long period variables once or twice every month throughout their variations according to such a system that all the observations may be reduced to the same absolute scale of magnitudes. 2. To observe the stars whose variability is suspected and prove either that they are really variable, or that in all probability they do not belong to the first, second, or fourth class. If any are thought to belong to the fifth class, to watch them until such a variation is proved, or is shown to be improbable.