474 



NA TURE 



[February i8, 190Q 



general principles leading up to discoveries. Likewise with 

 the word "observation." Though there are many refer- 

 ences to observations of various kinds, there is no one 

 article for setting forth the general principles of " observa- 

 tions " or the part they play in the discovery of funda- 

 mental facts. The same experience is had with regard to 

 the word "experiment." 



.\o\v let us turn to an encyclopaedia I' invariably read 

 with pleasure and profit; it frequently has supplied me 

 with references to earlier work not to be obtained else- 

 where. We shall find it instructive, though the articles to 

 which I beg to invite your kind attention were written 

 three-fourths of a century ago. I refer to the classic 

 (lehler's " Physikalisches Wbrterbuch " — the revised 

 edition by the noted investigators Brandes, Gmelin, 

 Horner, Littrow, Muncke, and Pfaff, in twenty volumes, 

 and published in Leipzig, 1825-45. A veritable fund of 

 information is found under the headings " Beobachtung " 

 (observation) and " \'ersuch " (experiment). The article 

 on " Beobachtung," by the physicist Munclce, embraces 

 twenty-eight octavo pages. He shows the distinction 

 between " Beobachtungen "(observations) and" Versuche " 

 (experiments) to be that the former pertain to the percep- 

 tions of phenomena presented to us by nature in her un- 

 modified course, whereas in the latter — in the experiments 

 — we are seeking to produce certain results or phenomena, 

 more or less looked for, in order either to verify a law 

 .ilready know^n or to disprove one suspected of being 

 wrong, or even to discover a new one. Both classes of 

 experiences are necessary for a piece of investigation or 

 research work. 



Thus we may behold, either visually or in some other 

 way, certain striking solar phenomena ; these belong to 

 the class of observations which we ourselves are unable to 

 modify in any manner w-hatsoever. Continued observation 

 may, however, reveal a certain law^ which by experiment 

 in the laboratory, conducted along more or less definite 

 lines, we may seek to imitate in the hope of getting some 

 clue to the modus operandi of the observed phenomena. 

 In this article on " observations " the author treats in 

 detail the various elements entering into correct methods 

 of investigation, condition of the observer and of his senses, 

 his being unbiased, character and errors of the instru- 

 ments, errors of results, methods of increasing accuracy, 

 representations of observations by graphs and formulfe, 

 method of least squares, &c. He points out the mistake 

 sometimes made that an established formula satisfying 

 the observed phenomenon within certain limits represents 

 an actual law of nature. 



The article " Versuch " (experiment) consists of forty- 

 four pages, and is contributed by the astronomer Littrow. 

 He shows that the most rapid development takes place in 

 those sciences which afford the greatest opportunity for 

 experimentation, referring, e.g., to the slow and painful 

 progress of the astronomer so long as he had to confine 

 himself to mere celestial observations, and the compara- 

 tively rapid strides which occurred so soon as some of the 

 observed phenomena could be either imitated bv, or be 

 compared with, those derived by laboratory experiment. 

 The investigator, he .says, must be absolutely free from 

 preconceptions, and be careful, cautious, and unbia.sed in 

 his interpretation of what his senses may reveal to him. 

 lie illustrates how man, called jokingly " das Ursach- 

 enthier " (the animal ever bent on ascertaining the cause 

 of things), proceeds in ferreting out the why and where- 

 fore of observed phenomena, and how his methods of 

 circumspection develop with the advance of knowledge. 



Though man cannot determine the " Endursachen," or 

 ultimate causes of things, the field open to him to discover 

 the laws governing phenomena or vice I'ersA, classifying 

 and enumerating those which follow a certain revealed 

 law, is, nevertheless, still verv large and sufficient to tax 

 his energies. Witness, for example, the host of observed 

 phenomena obeying the law of inverse squares ! 



These tw^o articles will show sulificiently the character 

 and scope of similar ones we should like to see in our 

 standard English and .American encyclopaedias.' Such in- 

 formation is contained in .some measure, at least, though 



1 ChamberV^ Encyclop^d-.T i« found to contain a .short article on 

 " Experiment " : also one on " Observation." 



NO. 2051. VOL 



roj 



not as comprehensi\ely, in the modern Gerrnan boolc of 

 reference, Brockhaus's " Conversations-Lexikon," as also 

 in the " Grande Encyclopedic " of the French. 



Our foremost English dictionaries are in general not 

 any more satisfying or edifying regarding the precise 

 meaning of " research " in the scientific sense than are 

 the standard encyclopaedias. Their illustrations of the use 

 of the word are usually Neither apt nor sufficiently com- 

 prehensive. 



A good-sized chapter might be written on the " mathe- 

 matical instruments or tools of research." The predomin- 

 ating tendency of resolving or expressing every natural 

 phenomenon — periodic or otherwise — by a Bessel or a 

 Fourier series or by spherical harmonic functions has 

 brought about at times, especially in geophysical and 

 cosrnical phenomena, if not direct misapplications, at least 

 misinterpretations of the meaning and value of the 

 coefficients derived. 



Frequently by tlic purely mathematical process there 

 have been eliminated, in the attempt to represent a more 

 or less irregularly occurring natural phenomenon by a 

 smoothly flowing function, the very things of chief and 

 permanent interest. The normal or average diurnal 

 temperature curve, for example, or a uniform magnetic 

 distribution over land, so as to yield perfectly regular 

 lines of equal magnetic declination, never occur in nature. 

 There is thus being impressed upon us more and more 

 forcibly the fact that what we have been regarding as 

 " abnormal features " — the outstanding residuals between 

 observations and the results derived from the ^nathematical 

 formula — are in truth not " abnormal " from the stand- 

 point of nature, but are rather to be taken as indicative 

 of the " abnormality " or " narrow-mindedness," which 

 means the same thing, of ourselves in trying to dictate to 

 nature the artificial and regular channels she should 

 pursue in her operations. 



Louis Agassiz said : — 



" The temptation to impose one's own ideas upon 

 Nature, to explain her mysteries by brilliant theories rather 

 than bv patient study of the facts as we find them, still 

 leads us away." 



The fundamental law of nature is to follow invariably 

 the paths of least resistance, and by examining these lines 

 of structural weakness of the opposing systems we may 

 have opened to us the very facts which are to be of real 

 value and of sure benefit to mankind. The irregularity 

 of the banks bordering a natural w\atercoursc serves to 

 differentiate the work of nature from that of the builder 

 of the artificial and regular channel. 



No, instead of rejecting, we must learn to retain the 

 outstanding residuals and study them most carefully and 

 regard them as the true facts' of nature, and not those 

 which we so egotistically and presumptuously try to force 

 on her. What great discoveries may lie open to us when 

 we once have grasped the true significance of the facts 

 we have been so fond of measuring by our own standard 

 and have been terming as " abnormal " or " irregular '_' ! 



An interesting example of not wholly successful applica- 

 tion of the continuous and ever-recurring functions of 

 spherical harmonics to a typical geophysical phenomenon 

 — the distribution of magnetism over the earth's surface 

 — has been discussed by me elsewhere. Though the 

 number of unknowns has been increased in recent com- 

 putations from the original twenty-four of Gauss to forty- 

 eight, nevertheless the difference between theory and 

 observation is of such an order of magnitude as to pre- 

 clude the use of the formula for even the purely practical 

 demands of the navigator and surveyor. Nor has anyone 

 succeeded in giving any physical interpretation of the 

 laboriously derived coefficients beyond the first three. .And 

 what do these three stand for? The simplest possible case 

 of a first approximation to the actual state of the earth's 

 magnetism, viz. that of a uniform magnetisation about a 

 diameter inclined to the axis of rotation ! 



The prime difficulty here may be .summed up in a word. 

 The very surface over which the spherical harmonic func- 

 tions are spread is itself such a prolific source of disturb- 

 ance as to cause effects embracing a continent, a State, 

 or a locality. Such a large number of terms would be 

 requisite for an adequate representation as to inake their 



