ON THE TEACHING OF NATURAL PHILOSOPHY. 



349 



Thus, for instance, we can tell why the rain- 

 bow has the form of a portion of a circle sur- 

 rounding the point opposite to the sun ; why it 

 is red on the outer edge ; what is the order of the 

 other colors, and why they are much less pure 

 than the red ; why the whole of the background 

 inclosed within it is brighter than that just out- 

 side, and so on. Also, why there is a second 

 (also circular) rainbow ; why it is concentric with 

 the first, and why its colors are arranged in the 

 reverse order, etc. 



But, so long at least as we keep to geomet- 

 rical optics, we cannot explain the spurious bows 

 which are usually seen, like ripples, within the 

 primary and outside the second rainbow ; nor why 

 the light of both bows is polarized, and so forth. 

 We must apply to a higher branch of our science ; 

 and we find that Physical Optics, which gives the 

 results to which those of geometrical optics are 

 only approximations, enables us to supply the ex- 

 planation of these phenomena also. 



When we turn to the aurora we find nothing 

 bo definite to explain. This may, to some extent 

 at least, account for our present ignorance. We 

 remark, no doubt, a general relation between the 

 direction of the earth's magnetic force and that 

 of the streamers ; but their appearance is capri- 

 cious and variable in the extreme. Usually they 

 have a pale-green color, which the spectroscope 

 shows to be due to homogeneous light ; but in 

 very fine displays they are sometimes blood-red, 

 sometimes blue. Auroral arches give sometimes 

 a sensibly continuous spectrum, sometimes a sin- 

 gle bright line. We can imitate many of the 

 phenomena by passing electric discharges through 

 rarefied gases ; and we find that the streamers so 

 produced are influenced by magnetic force. But 

 we do not yet know for certain the source of the 

 discharges which produce the aurora, nor do we 

 even know what substance it is to whose incan- 

 descence its light is due. We find by a statistical 

 method that auroras, like cyclones, are most nu- 

 merous when there are. most spots on the sun; 

 but the connection between these phenomena is 

 not yet known. Here, in fact, we are only begin- 

 ning to understand, and can but confess our igno- 

 rance. 



But do not imagine that there is nothing 

 about the rainbow which we cannot explain, even 

 of that which is seen at once by untrained ob- 

 servers. All the phenomena connected with it 

 which we can explain are mathematical deduc- 

 tions from observed facts which are assumed in 

 the investigation. But these facts are, in the 

 main, themselves not yet explained. Just as 



there are many exceedingly expert calculators 

 who habitually and usefully employ logarithmic 

 tables without having the least idea of what a 

 logarithm really is, or of the manner in which 

 the tables themselves were originally calculated ; 

 so the natural philosopher uses the observed 

 facts of refraction and reflection without having 

 as yet anything better than guesses as to their 

 possible proximate cause. And it is so through- 

 out our whole subject : assuming one result, we can 

 prove that the others must follow. In this direc- 

 tion great advances have been made, and every 

 extension of mathematics renders more of such 

 deductions possible. But when we try to reverse 

 the process, and thus to explain our hitherto as- 

 sumed results, we are met by difficulties of a very 

 different order. 



The subject of Physical Astronomy, to which 

 I have already alluded, gives at once one of the 

 most striking and one of the most easily intelli- 

 gible illustrations of this point. Given the law 

 of gravitation, the masses of the sun and planets, 

 and their relative positions and motions at any 

 one instant — the investigation of their future mo- 

 tions, until new disturbing causes come in, is en- 

 tirely within the power of the mathematician. 

 But how shall we account for gravitation ? This 

 is a question of an entirely different nature from 

 the other, and but one even plausible attempt to 

 answer it has yet been made. 



But to resume. The digression I have just 

 made had for its object to show you how closely 

 full knowledge and absolute ignorance may be 

 and arc associated in many parts of our subject — 

 absolute command of the necessary consaquences 

 of a phenomenon, entire ignorance of its actual 

 nature or cause. 



And in every branch of physics the student 

 ought to be most carefully instructed about mat- 

 ters of this kind. A comparatively small amount 

 of mathematical training will often be found suffi- 

 cient to enable him to trace the consequences of 

 a known truth to a considerable distance ; and 

 no such training is necessary to enable him to see 

 (provided it be properly presented to him) the 

 boundary between our knowledge and our igno- 

 rance — at least when that ignorance is not di- 

 rectly dependent upon the inadequacy of our de- 

 ductive powers. 



The work of Lucretius is perhaps the only 

 really successful attempt at scientific poetry. 

 And it is so because it was written before there 

 was any true physical science. The methods 

 throughout employed are entirely those of a priori 

 reasoning, and therefore worse than worthless, 



