On the one hand, the student has been informed by some writers that the only certain way lies in the use of the entropy-function and the thermodynamic potentials; on the other hand, he is told with equal authority that the method used by the original investigators has been the consideration of cyclic processes, and that the former method is nothing but a mathematical (perhaps unnecessary) refinement of the results obtained by the latter. These extreme attitudes appear to me to be unfortunate, and more especially when one observes the physical clearness introduced by the use of cyclic processes, but at the same time remembers that most of the results obtained by separate investigators using cyclic processes had, with a great many more, previously been found by J. Willard Gibbs by means of a purely analytical method.
J. R. PartingtonRelated topics
appear authority certain clearness cyclic equal found great nothing perhaps refinement tell unfortunate use using way means Gibbs liesRelated quotes
The marks of former convulsions on every part of the surface of our planet are obvious and striking. The remains of marine animals imbedded in the solid strata are so abundant, that they may be expected to force themselves on the observation of every people who have made some progress in refinement; and especially where one class of men are expressly set apart from the rest for study and contemplation. ...Those modern writers, who are disposed to disparage the former intellectual advancement and civilization of eastern nations, might concede some foundation of observed facts for the curious theories now under consideration, without indulging in exaggerated opinions of the progress of science; especially as universal catastrophes of the world, and exterminations of organic beings, in the sense in which they were understood by the Brahmin, are untenable doctrines.
Charles Lyell
A guilty system recognizes no innocents. As with any power apparatus which thinks everybody's either for it or against it, we're against it. You would be too, if you thought about it. The very way you think places you among its enemies. This might not be your fault, because every society imposes some of its values on those raised within it, but the point is that some societies try to maximize that effect, and some try to minimize it. You come from one of the latter and you're being asked to explain yourself to one of the former. Prevarication will be more difficult than you imagine; neutrality is probably impossible. You cannot choose not to have the politics you do; they are not some separate set of entities somehow detachable from the rest of your being; they are a function of your existence. I know that and they know that; you had better accept it.
Iain Banks
The noble lord who moved the address had, in the course of his speech, warned the House not to let an anxiety for liberty lead to a compromise of the safety of the state. He, for his part, could not separate those things. The safety of the state could only be found in the protection of the liberties of the people. Whatever was destructive of the latter also destroyed the former...The discontent existing in the country had been insisted on as a ground for the adoption of some measures...But there was another axiom no less true-that there never was an extensive discontent without great misgovernment...When no attention was paid to the calls of the people for relief, when their petitions were rejected and their sufferings aggravated, was it wonderful that at last public discontents should assume a formidable aspect?
Charles Grey, 2nd Earl Grey
Although there is no study which presents so simple a beginning as that of geometry, there is none in which difficulties grow more rapidly as we proceed, and what may appear at first rather paradoxical, the more acute the student the more serious will the impediments in the way of his progress appear. This necessarily follows in a science which consists of reasoning from the very commencement, for it is evident that every student will feel a claim to have his objections answered, not by authority, but by argument, and that the intelligent student will perceive more readily than another the force of an objection and the obscurity arising from an unexplained difficulty, as the greater is the ordinary light the more will occasional darkness be felt. To remove some of these difficulties is the principal object of this Treatise.
Augustus De Morgan
It is not true, out of geometry, that the mathematical sciences are, in all their parts those models of finished accuracy which many suppose. The extreme boundaries of analysis have always been as imperfectly understood as the tract beyond the boundaries was absolutely unknown. But the way to enlarge the settled country has not been by keeping within it, but by making voyages of discovery, and I am perfectly convinced that the student should be exercised in this manner; that is, that he should be taught how to examine the boundary, as well as how to cultivate the interior. ...allowing all students whose capacity will let them read on the higher branches of applied mathematics, to have each his chance of being led to the cultivation of those parts of analysis on which rather depends its future progress than its present use in the sciences of matter.
Augustus De Morgan