224.
THEORY AND PRACTICE
TRACT 37*
PROBLEM I.
25. To determine the Resistance of the Medium against a
Ball of any other size, moving with any of the Velocities
contained in the foregoing table.
The experiments, that have been so amply detailed, suf-ficiently prove that the resistances increase in a rather higherratio than the surfaces of different bodies, with the same ve-locity. Yet the ratios of the resistances, and of the surfaces,or of the squares of the diameters, which is the same thing,are so nearly alike, that they may generally be considered asequal to each other, in most calculations relating to artillery,or other practice. For example, to compare some of theexperiments which we have made with the three differentsizes of balls, viz, of 2 inches, and 2-78 inches, and 3-55inches diameter; of which the table of resistances for thefirst -was given in art. 17 preceding, and also in art. 145 oftract 34, as far as to 2000 feet velocity; that for the 2ndsize in art. 167 of that tract, from 900 to 1700 feet velocity;and that for the 3rd size, in art. 193 of the same tract, from1200 to 1800 feet velocity. Now the three diameters being2, and 2‘78, and 3 ' 55 , the squares of which are proportionalto the three numbers 1, and 1*93 1, and 3 - 15, which are alsothe ratios of the three surfaces. Now taking any one of thevelocities that is common to all the three tables, as supposethat of 1200 feet per second, v f e find the three resistances,'corresponding to this velocity, are 564'5, and 1133, and1840, which three numbers are in the ratios of 1, and 2’01,and 3’26, where the two latter numbers exceed the corre-sponding two of the former, the one by the 25th part, andthe other by the 35th part. Again, let us compare the re-sistances for the 1700 feet velocity, which are 1228‘4, and2472, and 4010, which vre find are in the ratios of 1, and2-013, and 3'26, which are again nearly in the same ratios asthe former. So that it appears, that the resistances in gene-ral may be considered as increasing above the ratio of the 'surfaces, by about the 30th part only. For example, sup-