In the above series the sum of the first two terms is 20, which is 4 times the first term. The sum of the first three terms, i. e., 5 + 15 + 25 = 45-nine times the first term. The sum of the first four terms, i. e., 5 + 15 + 25 + 35 = 80, sixteen times the first term, and so on. It will thus be seen that Momentum and Energy are entirely different, although co-related; that momentum relates to velocity, which includes the element of time, whereas energy relates to the amount of work done, and may be represented by a force operating against a certain resistance, through a certain distance, entirely irrespective of time. The energy is the same with the same force operating against the same resistance, through the same distance whether the time consumed be great or small. It takes as much energy in the aggregate to wind up a bucket from the bottom of the well if done slowly as if done quickly. It would seem hardly necessary to do so, and yet it is worth while remarking that the amount of energy necessary to impart a given motion is exactly the amount of Energy that will be required to arrest that motion, and represents the amount of Energy possessed by the moving body by virtue of its motion. Work done, i. e., Energy applied in giving motion is there in that motion, ready to be returned in exactly an equal quantity--no more--no less. In all the considerations in this chapter no notice is taken of loss by friction or atmospheric resistance. We are considering pure mechanics and the laws governing them only. In actual mechanical devices it is always necessary to make allowance for atmospheric, frictional and other unavoidable resistances. CHAPTER X The Alleged Inventions of Edward Sommerset, Sixth Earl and Second Marquis of Worcester, and of Jean Ernest Eli-Bessler (Councillor) Orffyreus More interest has been taken, and more has been said and written concerning the claimed inventions of the men forming the subject of this chapter than of all other Perpetual Motion devices known to history. The reason is not difficult to explain. It was the rank and eminence of the inventors and of others whom they induced to take an interest in their inventions, and to proclaim them to the world. Intrinsically, neither their claims nor their devices are entitled to any more notice than are those of the humblest mechanic that ever labored to attain Perpetual Motion. However, so much has been said and written concerning them that they have an historical value and interest. Then, too, the interest taken in their inventions brought forth some splendid discussions which necessarily involve in a general way, at least, the entire question of Self-Motive Power. The historical interest attaching to their inventions and the discussions concerning them, entitles them to more than a passing notice in this book.