In Fig. 21 is shown a combination consisting also of two distinct trains, in which, however, there is but one train-arm T turning freely upon the horizontal shaft OO, to which shaft the wheels A', F, are secured; the train-arm has two studs, upon which turn the idlers B B', and also carries the bearings of the last wheel F'; the first wheel A is annular, and fixed to the frame of the machine. Let it be required to determine the results of one revolution of the crank H, the numbers of teeth being assigned as follows: A = 60, F = 30, A' = 60, F' = 10. We shall then have, for the train ABF (Eq. I.), n 60 n' - a --- = - ---- = -2 = --------, in which n' = 1, m' = 0, m 30 m' - a' 1 - a 1 whence -2 = -------, 2a = 1 - a, 3a = 1, a = ---. -a 3 And for the train A'B'F' (Eq. II.), n 60 n' 1 --- = ---- = 6 = --------, in which a = ---, m' = 1, m 10 m' - a' 3 n' whence 6 = -----------, or n' = 4. 1 - (1/3) That is, the last wheel F' turns _four_ times about the axis LL during one revolution of the crank H. But according to Profs. Willis and Goodeve, we should have for the second train: n 60 n' - a 1 --- = ---- = 6 = --------, in which a = ---, m' = 1, m 10 m' - a' 3 n' - (1/3) which gives 6 = -----------, n' - (1/3) = 4, n' = 4-1/3, 1 - (1/3) or _four and one-third_ revolutions of F' for one of H. This result, no doubt, might be near enough to the truth to serve all practical purposes in the application of this mechanism to its original object, which was that of paring apples, impaled upon the fork K; but it can hardly be regarded as entirely satisfactory in a general way; nor can the analysis which renders such a result possible. * * * * * THE PANTANEMONE. The need of irrigating prairies, inundating vines, drying marshes, and accumulating electricity cheaply has, for some time past, led to a search for some means of utilizing the forces of nature better than has ever hitherto been done. Wind, which figures in the first rank as a force, has thus far, with all the mills known to us, rendered services that are much inferior to those that we have a right to expect from it with improved apparatus; for the work produced, whatever the velocity of the wind, has never been greater than that that could be effected by wind of seven meters per second. But, thanks to the experiments of recent years, we are now obtaining an effective performance double that which we did with apparatus on the old system.