September 8, 1905.] 



SCIENCE. 



11 



+ 7.78 

 + 4.13 



[xp] 



— 8.00 



— 11.G3 



4.8 

 4.9 



The result is similar to that in the fore- 

 going, [xp'] is negative with respect to con- 

 secutive trials. I have not calculated the 

 values for all of the five trials because reac- 

 tion time is not a good case; the distributions 

 being asymmetrical, a disturbing factor is 

 present. This vpill require special investiga- 

 tion. 



These few observations lead to the following 

 hypothesis : When a geometric form is taken 

 as the type of biological activity the correla- 

 tion between one dimension, taken as fixed, 

 and its variation from another dimension will 

 range indefinitely as positive or negative ac- 

 cording to the geometric relations between the 

 points from which the measurements are 

 made. When two dimensions are correlated 

 the degree of correlation will be increased or 

 decreased by virtue of the equalization be- 

 tween the above correlation and the correla- 

 tion between the parts common to both. 



The method used by Spearman to determine 

 the true correlation for psychological tests in 

 which t^ and t., seem to represent ordinates of 

 a similar curve, assumes that [pg] will be 

 constant for the successive trials. Turning 

 to our last formula and substituting - 



[pq] = [ar] + [xp]. 



we have shown that [a;p] is a variable of un- 

 certain range causing [pq] to vary. Thus an 

 unl\:nown variable is introduced by the use of 

 the Spearman formula. There is reason for 

 assuming that [xp] will be negative in many 

 psychological tests, thus reducing [pq], 

 whence the method of Spearman will give 

 correlations artificially increased. 



To put it in another way, the formula of 

 Spearman assumes that 



%t2 - 



[pq] 



[pq] 



1. 



It is evident that this can be only when 

 t^ and t.^ are identical. [pq] will be a con- 



stant when t^ and i^ are of the same type. We 

 have shown above that the method of observa- 

 tion will sometimes result in a geometrical 

 relation between t^ and t, causing [pq] to vary. 

 Whenever this occurs the method fails. 



Clark Wissler. 



treatment of simple harmoxic motion. 



The very great importance of simple har- 

 monic motion in the physical world demands 

 very careful consideration of the method of 

 presenting and treating it for students begin- 

 ning the work in advanced physics. 



From the books on physics which I have at 

 hand, I have selected fourteen which are used 

 by a large portion of American students for 

 their first study of simple harmonic motion. 

 Eleven of these present and define simple 

 harmonic motion merely as the projection on 

 a diameter of uniform circular motion, de- 

 riving equations and other definitions by use 

 of this uniform circular motion. Some of 

 them scarcely suggest the question whether 

 there really is such motion; much less, under 

 what conditions or by what law of force it 

 would occur. 



Three of the fourteen texts give simple har- 

 monic motion a dynamic definition, presenting 

 it as produced by a force acting toward and 

 varying as the distance from a center. But 

 even these three, in treatment, make the 

 auxiliary circle very prominent. 



An experience of a good many years with 

 large numbers of students leads me to believe 

 that in the minds of very many the auxiliary 

 circle with its functions and circular motion 

 ' looms larger ' than the actual simple har- 

 monic motion. It seems to me highly de- 

 sirable to dispense with the auxiliaiy circle 

 in both definition and treatment. 



The definition should be dynamic. This 

 dynamic definition should be drawn from ex- 

 periments. 



The treatment should be a problem, a study 

 of the motion caused by a force acting by 

 the law found in the experiments. 



I offer the following as an illustration of 

 treating simple harmonic motion as above sug- 

 gested; and for students not using calculus. 



Experiments. — One or more on each, flexure. 



