NATURAL PHILOSOPHY. 141 



be known, must bear to be told that this assumption may be one of its little 

 mistakes, or may be a true exposition of its own power?, and may be a 

 matter on which no certainty can be arrived at. 



In prescribing conditions of solution, and form of result, we dictate to ex- 

 istence ; we determine that our mental nature shall be so constructed that 

 we shall know beforehand Avhat means are wanted, and what form the result 

 shall appear in, the matter being one on which the very necessity of propos- 

 ing the problem shows our ignorance. And when we fail, we quarrel with 

 the universe, as Porson did, when he proposed to himself the problem of 

 taking up the candlestick, his condition being that in which two images of 

 objects appear, one the consequences of the laws of light, the other what a 

 psychologist would perhaps call purely subjective. He accordingly handled 

 the wrong image, which of course did not prevent his fingers from meeting. 



Incensed at this, he exclaimed, " D the nature of things ! '' He had 



better have attended to preliminaries under which so simple a problem might 

 have been solved without a quadratic equation. 



Undoubtedly the dictation of conditions and of form has been attended with 

 the most advantageous results. Abundance of possibles have been turned 

 up in digging for impossibles. Alchemy invented chemistry ; astrology 

 greatly improved astronomy ; the effort to find a certainty of winning in 

 gambling nurtured the science under which insurance is safe and intelligible, 

 and the inscrutable inquiry into ens quatenus ens, so properly placed p.era. TO. 

 QvcriKa, has added much to our powers of investigating homo quatenus homo. 



There was a separate dictation of conditions in arithmetic and in geome- 

 try. In arithmetic, the simple definite number or fraction, the earliest ob- 

 ject of our attention, was declared to be the universal mode of expression. 

 It was prescribed to the circle that it should be, in circumference, a definitely 

 expressible derivation from the diameter ; it was demanded of the nature of 

 things that by cutting the circumference into a certain number of equal parts, 

 a certain number of those parts should give the diameter ; and vice versa. 



In geometry, Euclid laid down, as his prescribed instruments, the straight 

 line and circle. Of all the infinite number of lines which exist, he would 

 use none except the straight line and circle. It was demanded of the nature 

 of things that it should be possible to construct a square equal to a given 

 circle, without the use of any curve except the circle. 



The second demand was not quite so impudent as the first. It was soon 

 discovered and proved that there is no square root to 2, as a definite fraction 

 of a unit. That is, there is nothing but an interminable series of decimals, 

 1.4142135 ; by help of which we discover the square root of frac- 

 tions within any degree of nearness to 2 we please. And yet, with such a 

 result as this known to all, it was thought the most reasonable thing in the 

 world to demand that the ratio of the circumference to the diameter should 

 be that of number to number. 



I will now speak of several problems of popular interest. 



1. The three bodies. This is the problem of determining the motion of a 

 planet attracted, not only by the sun, but by another planet. In the early 

 days of the integral calculus, it was demanded of the nature of things that 



