194 THE POPULAR SCIENCE MONTHLY 



statement of the general principles of research, such as has already 

 been given. 



A prevalent fault is observed in scientific publications whenever the 

 investigator has had good training only on the observational side and 

 but very little experience in scientific computing. He is very apt to 

 violate one of the first and fundamental principles of good observing, 

 viz., to employ such a method or scheme of ohserving as will yield 

 tut one definite result, and that with the highest possible accuracy 

 and ivith the least amount of computation. Oftener than may be 

 thought, schemes of observation are used which leave an arbitrary ele- 

 ment to the computer, and in consequence a different result is forth- 

 coming, according to who makes the computation. Had we time apt 

 illustrations could readily be given from published works. The 

 point made, that the observer must also bear in mind the computa- 

 tion side, and work up his results as soon as possible, is of funda- 

 mental importance in research ivorh. 



It may be worth while to consider briefly the insatiable desire 

 of the analyst to " ring " in a series of sines and cosines to resemble the 

 course of some natural phenomenon of which he does not know the 

 exact law. Is this the old story over again, though in somewhat 

 altered garb, of the epicycles and deferents of ancient astronomical 

 mechanics, which received its highest development in the Ptolemaic 

 System of the Universe? You will recall that Ptolemy, building on 

 the suggestions of Appollonius and Hipparchus, supposed a planet to 

 describe an epicycle by a uniform revolution in a circle whose center 

 was carried uniformly in an eccentric round the earth. By suitable 

 assumptions as to his variable factors, he was thus able to represent 

 with considerable accuracy the apparent motions of the planets and to 

 reproduce qiiite satisfactorily other astronomical facts. This was the 

 artifice employed by the astronomer of the period before the modern 

 and more subtle art of simulating nature, by the sine-cosine method, 

 had become known. 



What seemed so intricate and complex in Ptolemy's time could 

 be expressed in very simple language indeed, when a Kepler discovered 

 the true functions as embodied in his three fundamental laws. The 

 present method of hiding our ignorance of the real law, which seems 

 at times to exert such a mesmerizing influence over us as to make us 

 mistake the fictitious for the real, reminds one of the old conundrum: 

 " Patch on, patch on, hole in the middle ; if you guess this riddle, 

 I'll give you a golden fiddle." If the sine and cosine of the angle 

 does not represent the curve of observation, patch on a sine and 

 cosine of twice the angle ; then, if necessary, thrice the angle ; next, four 

 times, and so ad infinitum ! Now guess the riddle ! 



Of course I do not mean to discard this useful and in fact indis- 



