A discussion has commenced in regard to the asserted gain in the application of power by the use of the velocipede. One party states there is a decided gain by its use. The negative argument may be fairly put as follows: Equal bodies moving with different velocities require different powers to maintain their motion, that moving with the greater velocity requiring the greater power. If moving at equal velocities the powers required to move them will be equal. The amount of power necessary to transport a man say ten miles, will bs the same, no matter how it may be applied, hence it takes the same muscular exertion to propel him ten miles on a velocipede as it would to walk the same distance. Now, so far as the gain in the application of power in the US3 of the velocipede is concerned, there can be no doubt of its existence on level and descending grades. The facts prove it indubitably. It may not be amiss however to reconcile facts and theory, and thus show how the gain is made. Those who take the negative side in the argument, and whose position we have fairly stated above, are right in their views so far as premises are concerned, but wrong in their conclusions. If all the power exerted in walking were expended in propelling the body forward, and friction were the same in both cases, there would be no gain in the use of the velocipede. But only a small portion of the power expended in the act of walking or running is applied to forward propulsion, as will be seen upon a review of the mechanics of walking. In walking the heel is first placed on the ground; the weight is next thrown on the ball of the foot, and the body is raised so as to permit the free limb to swing by the'one upon which the body rests. As soon as the free limb has passed the center of gravity, the body is allowed to descend, until the heel on that side receives the weight, when the body is again raised. This alternate rising and falling of the body causes the center of gravity to pass through an undulating curve. We have pertormed a series of experiments to graphically determine the amount of this undulation, and find it to average about three inches in adults of different hights, and varying lengths of the lower limbs. Now, allowing the rate of speed attained in walking to average three miles per hour, and the length of step to average three feet, we find that the body is raised in walking 5,280 times during a walk of one hour or three miles. Reckoning the average weight of men to be 140 lbs. we have for the work expended in raising the body during an hours walk 5280X 3 XU0_s=184800 foot.pound8 perhour) or 3j060 foot. pounds per minute. According to Silliman, the power of a man when applied to the best advantage (the treadmill) is equal to 2,000,000 footpounds for eight hours or 4,166'6 foot-pounds per minute. We see then that fully three-fourths of the entire muscular power of the lower limbs is expended in raising the body during the act of walking, less some deductions to be noticed hereafter. It is not to be inferred on this account, that the apparatus for locomotion provided for us by Nature is defective. On the contrary we shall find when we examine it, that it is a mar- vel of perfection. Nature's is " nae journey wark " in any of her constructions. Direct forward propulsion is only one of the requirements of the feet and legs. They are adapted to climbing steep ascents, stairs, ladders, etc.; for descending abrupt declivities, for leaping, turning, and a variety of other movements, which wheels are incapable ot performing. They possess great elasticity to save the body from injurious shocks. Their joints are self-lubricating and their weight is the smallest possible relatively to the work they are required to perform. No art would be able to fulfill all these conditions as nature has done, but art, has in the velocipede been able to apply power to direct forward propulsion better than Nature has done, hampered as she is by all the other requirements of the case. It is undoubtedly true that a small portion of the power expended in raising the body while walking is converted into forward motion when it descends, and is thus utilized. It is also true that the elasticity of the limbs, stores up a portion of the power acquired in the descent of th"e body and applies it to the ascent of the body in each succeeding step. The loss of power is thus somewhat diminished, but making these deductions there must remain a large loss, when walking upon level ground. In walking up a grade there would be less loss in proportion to the steepness of the ascent. In going up hill, where the grade is over one inch to the foot, the power loat in walking upon level ground will be entirely utilized. In any steeper grade than this, the unassisted legs would be able to accomplish a greater distance than the velocipede, provided the latter utilized all the power of the lower limbs, which, of course it does not. There are losses from friction, and other causes, so that the legs would be found to have an advantage over the velocipede in ascending grades of considerably less than one inch to the foot; our opinion is that they would be found by experiment to be about on an equality in ascending gradients of one-third of an inch to the foot. On the contrary in going down a grade the velocipede has an increasing advantage with the steepness of the grade. The advantage possessed by the velocipede on level ground consists in the more economical application of power to direct forward propulsion, than can be obtained in walking or running, and is another illustration that a simple rotary motion is the most economical way in which power can be applied to the production of simple effects.