614 



SCIENCE 



[N. S. Vol. LI. No. 1329 



Gregory is designed to extend to the scientific 

 men of New Zealand and Australia, and to 

 take into consideration the larger work of the 

 future, particularly as suggested by the van- 

 ishing anthropology of Polynesia. Unless this 

 work is begun immediately and carried 

 through with great energy and system, it will 

 not be done at all. The material in physical 

 anthropology is disappearing with almost in- 

 credible rapidity. The ravages of influenza 

 during the past two years have swept away 

 a large part of the members of the Polynesian 

 race. The survivors on certain of the Islands 

 constitute a very small percentage of the 

 original population. 



Scientific cooperation has begim. through 

 the special research in physical anthropology 

 of the Hawaiian group established between 

 the Bishop Museum and the American Mu- 

 seum of Natural History. Dr. Louis E. 

 Sullivan of the American Museum staff has 

 already left for the Islands and will make as 

 complete a survey as possible of the pure and 

 mixed Hawaiian races among the remnants. 

 These results will be published in the Memoirs 

 of the Bishop Museum. It is expected also 

 that Curator Clark Wissler will represent the 

 American Museum at the Pan-Pacific Sci- 

 entific Congress in August. 



Henry Pairfield Osborn 



the energy of small oscillations 

 To THE Editor of Science : The well-known 

 theorem that in any linear harmonic oscilla- 

 tion the total energy is, on the average, half 

 kinetic and half potential is so impoirtant in 

 many fields that perhaps the following very 

 simple and elementary proof will be of gen- 

 eral interest. It can hardly be new, it is so 

 simple and obvious, but at any rate it is not 

 common, for it does not appear in any of 

 the best known treatments which have been 

 consulted. 



Consider a particle of mass m which is 

 displaced from its equilibrium position a dis- 

 tance X, and is vibrating in a circle. Then, 

 as is well known, the kinetic energy is equal 

 to the potential energy. Por let the elastic 

 restoring force be given by hx. "We must 



then have Jcx= mv-/x for steady motion. 

 The potential energy of the particle when at 

 a distance x from the equilibrium position is 

 equal to the work done in displacing it this 

 distance, which equals the distance times the 

 average force, which equals l/2(kx)-x. Sub- 

 stituting the above value of kx we have for 

 the potential energy l/2inv^, and the proposi- 

 tion as stated is established. But any such 

 circular vibration may be thought of as com- 

 posed of two exactly similar linear harmonic 

 oscillations. (When considering energy the 

 phase difference and direction of oscillation 

 is obviously irrelevant.) Therefore we must 

 associate, on the average, half of the total 

 kinetic and half of the total potential energy 

 of the circular vibration with each of the 

 linear vibrations. Since these are equal in 

 the case of the circular vibration they must 

 also be equal in the case of the linear 

 vibration. The result is obviously perfectly 

 general for any linear harmonic oscillation. 



Warren Weaver 

 CALirosNiA Institute or Technology 



CARBON DIOXIDE AND INCREASED CROP 

 PRODUCTION 



To THE Editor op Science: Should one 

 infer from Mr. Harrow's note in the latest 

 issue of Science (May 7, 1920) that the ques- 

 tion of " fertilizing " with carbon dioxide 

 were not known to plant-physiologists and 

 agricultural chemists in this country? 



If so, it might be worth while to mention 

 that for a number of years, at least for the 

 last ten years, this topic has been the subject 

 of many experiments in Europe, especially in 

 Germany. 



The botanists, Hugo Fischer and AdoK 

 Hansen among others, have contributed much 

 to its study. It has even found its place in 

 modern German text-books of plant physiology 

 — for instance in Molisch's " Pflanzenphysio- 

 logie" — and no doubt, also in those of agri- 

 cultural chemistry, such as Schneidewind's 

 " Ernahrung der landwirtschaf tlichen Kultur- 

 pflanzen." 



M. W. Senstius 



