March 24, :911] 



SCIENCE 



457 



doubt correct. As far as I have been able to 

 determine, when they first enter the egg, these 

 granules differ in no wise from those in other 

 parts of the food stream that develop into 

 yolk spherules. 



Now the early developmental features of 

 the germ cells in this species point not so 

 much to a process of active differentiation as 

 one of passive isolation, which results in the 

 pole cells retaining or preserving the repro- 

 ductive potentialities of the cleavage nuclei; 

 the pole-disc meanwhile serving as food ma- 

 terial for the pole cells which " as a result of 

 this special kind of nutrition undergo a pe- 

 culiar method of metabolism which differen- 

 tiates them from the somatic cells " — just as a 

 certain kind of food is necessary for the early 

 growth and development of a child, but is by 

 no means the cause of its becoming a man 

 instead of an ape. H. L. Wieman 



University of Cincinnati, 

 January 27, 1911 



THE PYTHAGOREAN THEOREM 



Dr. Northrup's article* is not a proof of 

 what is sometimes — perhaps incorrectly — 

 called the Pons asinorum, unless it be shown 

 experimentally that the kinetic energy of a 

 body is the sum of its energy of translation 

 and of rotation. The deduction, however, of 

 this theorem of energy from the fundamental 

 propositions of mechanics depends on the law 

 of vector superposition, the mathematical ex- 

 pression of which involves the Pythagorean 

 theorem. In general it is not economical to 

 derive mathematical propositions from experi- 

 mental physics; moreover, the process fails to 

 bring out that difference between mathematics 

 and physics which is shown, for example, in 

 Hubert's " Foundations of Geometry " and 

 Mach's " Science of Mechanics." 



I should like to be permitted the liberty of 

 objecting to the statement:" 



" No motion, force or acceleration which 

 exists at the point p can produce rotation of 

 1 — 2 about p as center. This must be so, as 

 it is axiomatic in dynamics that, when there is 



'Science, XXXII., 833, p. 864. 

 = L. c, p. 864. 



a force or acceleration at the center of mass 

 only of a body, there remains no couple to pro- 

 duce rotation " : first, because the word 

 " axiomatic " seems to be used in the Kantian 

 sense of " self-evident," and second, because 

 Dr. Northrup's proof (?) in no way depends 

 on whether p has linear or 1 — 2 has angular 

 acceleration. 



Equation 7 of the paper expresses a geo- 

 metric fact — I am tempted to say " accident " 

 — which text-books raise to the dignity of a 

 theorem. E. F. Deimel 



To THE Editor of Science: Eeferring to 

 your December 16 issue, if we are to have 

 " A Dynamical Proof of the Pythagorean 

 Theorem," why not let it be a simple one? 

 For instance, if the force F whose rectangu- 

 lar components are X and Y, acts upon a par- 

 ticle of mass m until it has imparted the ve- 

 locity g whose components in the same plane 

 are u and v, then the work done upon the 

 particle by X is equal to imu', while the work 

 done by Y is ^mv^. But the work done by the 

 components is identical with the ■ work ^mg° 

 done by their resultant. Equating and can- 

 celling the factor Jm, 



(f^U--\- V-. 



But the velocity components u and v are the 

 two legs of a right triangle of which q is the 

 hypothenuse, so that here again is our Pytha- 

 gorean relation. Mayo D. Hersey 

 U. S. Bureau of Standards, 

 Washington, D. C. 



QUOTATIONS 



the tenure of professorships 

 Among the reforms suggested by the " effi- 

 ciency expert " of the Carnegie Foundation 

 who investigated the administration of some 

 of the principal American universities was the 

 appointment of professors for a brief period, 

 so that they could be dropped without fuss 

 whenever for any reason a change was desired. 

 His idea was to get young, vigorous men, work 

 them hard as long as they could stand the 

 strain, and then pension them off in the in- 

 terest of efficiency. Somewhat similar views 

 have of late been expressed by several univer- 



