THOUGHTS ON OUR CONCEPTIOiYS OF PHYSICAL LAW. 5 



In the discussion of physical phenomena, we always ignore the greater part 

 of the discussion, by neglecting those elements which are, or are supposed to be, 

 unimportant. In so simple an operation as the weighing of a quantity of matter 

 on a steelyard, we can discuss only the merest elements of the case. The stu- 

 dent of Physics would tell you, that the weights are inversely as the lever arms, 

 ])ut this is far from being the whole story. During the weighing, certain parts of 

 the steel bar are heated; other parts are cooled; still other parts retain their 

 temperature unchanged ; electrical currents are set up within its mass ; its mag- 

 netism is changed; its torsion and elasticity become different — in fact, to discuss 

 all the changes occurring within the bar during so simple an operation, would 

 infinitely transcend the power of the most gifted men. 



If we could discuss completely the laws which govern phenomena, we should 

 find them represented, in many cases, not by the comparatively simple formulae, 

 which have been found sufiicient for practical purposes, but by infinite series, the 

 first terms only of which our mathematicians have been able to deduce, and our 

 physicists to experimentally detect. 



What is here said of physical problems, is also true of problems of pure 

 mathematics. It is stated by mathematicians, " that those problems which have 

 been solved, are but an infinitely small part of those which can be proposed, that 

 they are all special cases, (although sometimes called general) and that if a prob- 

 lem were selected, at random, out of the whole number that might be proposed, 

 the probability would be infinitely slight — that any human being could solve it." 

 Even those problems that have been satisfactorily solved, involve ideas that 

 we cannot comprehend. Let us take a simple problem in Geometry. Imagine 

 two wooden rods, or finite lines intersecting each other, and let us revolve one of 

 them until they become parallel. Consider these lines infinitely prolonged, and 

 let us see what becomes of these prolongations. As one line is revolved the 

 point of intersection travels outwards. Finally the lines might seem to be parallel, 

 but perhaps if we were to travel along the lines for a million of miles, we might 

 come to the point of intersection. The mathematicians say, that when the lines 

 have become parallel, the point of intersection will be removed to an infinite 

 distance, which is, they say, equivalent to saying that the lines will not intersect. 

 Where in space will these lines part company ? Have they ends, which the 

 point of intersection finally reaches, and which then separate from each other? 

 No ! The lines are supposed to be without end. However far the point of inter- 

 section may have travelled, we may straightway regard this distance, as repre- 

 sented by the first term of a divergent series of an infinite number of terms, 

 each term of which is infinitely greater than the one which preceded it. We can 

 form an independent conception of two infinite and absolutely parallel lines, 

 but we cannot imagine how the infinite prolongations of intersecting lines can 

 ever separate; nevertheless, we can continue the rotation of our finite line, 

 until it passes through parallelism, and the point or at least a point of intersection 

 comes travelling towards us from the opposite direction. ^ 



