[_An advantageous change of Centres._] This is the most minutely as well as circumstantially noted of all the Marquis’s inventions; yet we have no evidence of his ever afterwards recurring to it. The mention of Sir William Balfour makes it probable that the exhibition of this great weighted wheel took place between 1638 and 1641. [See Life, Times, &c., page 25.] Dr. John Dee, in his celebrated preface to Sir Henry Billingsley’s first English edition of Euclid, published in folio, 1570, speaks of such a machine, as not only possible, but as having been actually constructed, and “a thing most incredible if not seen;” this, compared with the language used by the Marquis, would lead to the supposition that he had not only read but copied the passage. It is difficult to reconcile the statement he has here made, with the declaration on the title page, of his inventions having been “tried and perfected.” In this single instance, he leaves the reader to “Be pleased to judge the consequence.” [Illustration: A weighted wheel] Dr. Desaguliers, in a memoir, published by the Royal Society, vol. 31, 1720–21, quoting the foregoing article, ventures the reply: “Now the consequence of this, and such like machines [assuming them to be as above described,] is nothing less than a perpetual motion.” Of course he does not admit even the possibility of such an arrangements of parts, he only allows that if _that_ could be executed, the other would follow. But Desaguliers admitted too much, for it may easily be demonstrated that the conditions stated may be mechanically produced, without any resulting motion. Let the annexed diagram represent a wheel of 14 feet in diameter, having 40 spokes, seven feet each, and with an inner rim coinciding with the periphery, at one foot distance, all round. Next provide 40 balls or weights, hanging in the centre of cords or chains two feet long. Now fasten one end of this cord at the top of the centre spoke C, and the other end of the cord to the next right hand spoke one foot below the upper end, or on the inner ring; proceed in like manner with every other spoke in succession; and it will be found, that, at A, the cord will have the position shown outside the wheel; while at B, C, and D, it will also take the respective positions, as shown on the outside. The result in this case will be, that, all the weights on the side A, C, D, hang to the great, or outer circle, while on the side B, C, D, all the weights are suspended from the lesser or inner circle. And if we reverse the motion of the wheel, turning it from the right hand to the left hand, we shall reverse these positions also, (the lower end of the cord sliding in a groove towards a left hand spoke) but without the wheel having any tendency to move of itself.