I90 THE POPULAR SCIENCE MONTHLY 



use of any particular organ, and has familiarized us with the won- 

 derful achievements of nature brought about by sustained and con- 

 tinued effort along some definite direction. Both the physical and 

 the psychic conditions of the observer require their highest and healthi- 

 est development to insure not only the best results with the ever- 

 increasing accuracy or precision required by the steady advance of 

 knowledge, but also to bring about that round- or broad-mindedness 

 needed for the proper interpretation of the results observed. 



The Mathematical Instruments of Eeseaech. 



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

 Instruments or Tools of Eesearch." The predominating 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 

 cosmical phenomena, if not direct misapplications, at least misinter- 

 pretations of the meaning and value of the coefficients derived. Like 

 a certain class of " naturalists," we also may have laid ourselves open 

 to the approbrious term of " nature-fakir," and instead of clarifying 

 the situation our calculations may have actually contributed instead 

 to " befog " it. 



Frequently by the purely mathematical process there have been 

 eliminated, in the attempt to represent a more or less irregularly oc- 

 curring natural phenomenon by a smoothly flowing function, the very 

 things of chief and permanent interest. The normal or average diur- 

 nal temperature curve, for example, or a uniform magnetic distribu- 

 tion over land, so as to yield perfectly regular lines of equal magnetic 

 declination, never occurs in nature. There is thus being impressed 

 upon us more and more forcibly the fact that what we have been re- 

 garding as " abnormal features " — the outstanding residuals between 

 observations and the results derived from the mathematical formula — 

 are in truth not " abnormal " from the standpoint of nature, but 

 are rather to be taken as indicative of the " abnormality " or " nar- 

 row-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 by patient study of the facts as we 

 find them, still leads us away. 



The fundamental law of nature is to invariably follow the paths 

 of least resistance, and by examining these lines of structural weak- 

 ness 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. 



