“Botany Square is an ellipsis,” replied the matter-of-fact sweeper; “but if the transverse, conjugate, and abscissa are known, it is easy to find the ordinate. To proceed to it from this point requires a right line to where the next street appears at a right angle with it, whence, going along any part of its superficies, you will approach where the sides of three streets form an isosceles triangle; take the one side nearest to you in its whole extent, which having found, describe the area of a trapezium, whose diagonal is equal to twice its perpendiculars; and from the centre continue a right line till you approach a trapezoid whose sides are parallel; and from this, diverging in such a manner as to construct a hyperbola, if straight lines be drawn from the centre through the extremities of its conjugate axis, these will lead direct to the ellipsis you are desirous of finding.”
“Can you direct me to Botany Square?” again asked Oriel Porphyry, puzzled to think whether the man was mad or did not understand his question.
“Botany Square is an ellipsis, I tell you again,” said the geometrician rather sharply; “and Euclid himself could not have described to you a more accurate method of finding it than that you have just heard from me. Work the problem properly, and the result must be what you require. All the parts are equal to the whole; the greater includes the less; and of several equal parts all are alike: and these propositions are not more true than is the answer I have given to your query; therefore allow me to hope that you will, in consideration of the accuracy of my analysis, find the perpendicular of your pocket, subtract from its base any circle whose circumference is a known quantity, and place it within the superficies of my hand.”
“He’s mad!” exclaimed Oriel, walking on.
“He’s minus!” cried the beggar, and returned to his geometry.
The two pedestrians continued on their way, wondering not a little at meeting with the strange character with whom they had just parted, when, upon entering the next street, they observed a confused mass of people running to and fro, shouting and making a most discordant uproar.
“Can you tell me the cause of this disturbance?” inquired Oriel Porphyry, addressing a respectable looking mechanic who was hurrying past him.
“The cause?” replied the stranger, immediately stopping in his career. “The cause is always the phenomenon which precedes the effect. Philosophers have disputed about the most appropriate definition of the term; but in any system of transcendental ideas there must always be an antecedency and a subsequency; and although they have been considered synchronous in their existence, in my opinion the effect is to the cause what the shadow is to the light—the shadow is not in the light, but is produced by the operation of the light upon an object; so the effect is not in the cause, but is produced by the action of the cause upon an agent. Some metaphysicians conceive that the relation of cause and effect should be considered as a synthetical judgment à priori—a postulate of pure reason. In my opinion, this idea is open to many objections; but I will avoid all argument on that point for the present, and merely go into an analysis of the nature of causation. There are three indispensable conditions to any philosophical theory of causation. In the first place, there are two objects—the agent and the patient. Secondly, there are three changes, which are—that of the agent, reason of the effect; that of the patient, effect of the action; that which is produced by the patient on the agent, and the effect of re-action. And, thirdly, there are four distinct moments, which are—that which leads to the action, that which commences with it, that of the re-action, and that which immediately follows the re-action. And——”
“And pray, sir, what has all this to do with the disturbance about which I inquired?” said the young merchant, as much puzzled with the mechanic as he was by the beggar.