The expression "Follies of Science" does not seem a very appropriate one. Real science has no follies. Neither can these vain attempts be called _scientific_ follies because their very essence is that they are unscientific. Each one is really a veritable "Will-o'-the-Wisp" for unscientific thinkers, and there are many more of them than those that we have here named. But the expression has been adopted in literature and it is just as well to accept it. Those on the list that we have given are the ones that have become famous in history and they still engage the attention of a certain class of minds. It is only a few months since a man who claims to be a professional architect and technical writer put forth an alleged method of "squaring the circle," which he claims to be "exact"; and the results of an attempt to make liquid air a pathway to perpetual motion are still in evidence, as a minus quantity, in the pockets of many who believed that all things are possible to modern science. And indeed it is this false idea of the possibility of the impossible that leads astray the followers of these false lights. Inventive science has accomplished so much--many of her achievements being so astounding that they would certainly have seemed miracles to the most intelligent men of a few generations ago--that the ordinary mind cannot see the difference between unknown possibilities and those things which well-established science pronounces to be impossible, because they contradict fundamental laws which are thoroughly established and well understood. Thus any one who would claim that he could make a plane triangle in which the three angles would measure more than two right angles, would show by this very claim that he was entirely ignorant of the first principles of geometry. The same would be true of the man who would claim that he could give, in exact figures, the diagonal of a square of which the side is exactly one foot or one yard, and it is also true of the man who claims that he can give the exact area of a circle of which either the circumference or the diameter is known with precision. That they cannot both be known exactly is very well understood by all who have studied the subject, but that the area, the circumference, and the diameter of a circle may all be known with an exactitude which is far in excess of anything of which the human mind can form the least conception, is quite true, as we shall show when we come to consider the subject in its proper place.