570 



SCIENCE 



[Vol. LV, No. 1430 



specific acidity, developed his metiiod so that 

 it would yield just this degree of precision. 

 These points are mentioned specially because 

 Olsen, in the Danish paper, criticizes the 

 writer's method severely on the basis of "inac- 

 curacy." But if a soil, the acidity of which 

 varies in general by a factor of 3, is sampled 

 at an arbitrary depth and then altered by long 

 soaking and filtration, there is certainly noth- 

 ing to be gained by making highly precise 

 acidity determinations on the resulting extract. 

 Indeed, both Arrhenius and Olsen, upon assem- 

 bling the results obtained on given species or 

 associations of plants, also find that there is 

 always a range of at least 0.5 in pg (a factor 

 of 3 in specific acidity). The fact that all 

 three come to recognize the same range indi- 

 cates that it is of fundamental significance. 



All three investigators find that the soils of 

 native plants in general extend from a specific 

 acidity of a few thousand to a specific alka- 

 linity of about 10. All find that the greatest 

 number of species as well as of individuals 

 occur in soils lying just to the acid side of the 

 neutral point. And, most remarkable of all, it 

 turns out that many individual species of plants 

 have essentially the same soil acidity prefer- 

 ences in Europe as in America, indicating that 

 this is not a question of location, climate, or 

 surroundings, but a physiological feature of 

 the species. For illustration : the lily-of-the- 

 valley, Convallaria majalis, grows in Denmark 

 in soils of specific acidity 1000 to 400. Iso- 

 lated colonies of this plant ir the southern 

 Appalachian Mountains have been studied by 

 the writer and found to have specific acidity 

 500 to 300, practically the same range. He- 

 patica (Hepatica triloba or Anemone Hepatica) 

 shows in Denmark preference for soils rang- 

 ing from neutral (specific alkalinity 1) to spe- 

 cific alkalinity 8. In America a near relative 

 of the European plant thrives best in black 

 leafmold with an average specific alkalinity 

 of 3. 



How soil acidity alfects plants is a subject 

 requiring further investigation. Olsen's data 

 led him to infer that the action may be direct, 

 but others have found that it is usually indi- 

 rect. There is evidence both for and against 

 the view that the acidity affects primarily sym- 



biotic organisms, and only indirectly through 

 them the higher plants. Eeeent American 

 work has indicated that the effect of acidity is 

 produced largely through the agency of alum- 

 inium or iron salts, although Olsen is unable 

 to find evidence of their toxicity. But in view 

 of the general agreement of the results of the 

 three independent investigators as above out- 

 lined, it can no longer be questioned that soil 

 acidity is of fundamental importance in con- 

 trolling the distribution of native plants. 



Edgab T. Wherry 

 'U. S. Department of Ageiculture, 

 Washington, D. C. 



SPECIAL ARTICLES 



THE EINSTEIN EQUATIONS FOR THE SOLAR 



FIELD FROM THE NEWTONIAN POINT 



OF VIEW 



1. About a year ago I determined the law 

 of attraction from the Newtonian point of 

 view of action at a distance which gives the 

 equations of planetary motion obtained in the 

 Einstein theory. Two months ago Professor 

 Birkhoft', of Harvard, told me that he had ob- 

 tained similar results in his class this year, and 

 suggested that I publish my results. In doing 

 so I am not advocating the rejection of the 

 Einstein point of view which seems to me the 

 correct one, but I am merely indicating a mod- 

 ification in the Newtonian law which will ac- 

 count for the motion of the perihelion of Mer- 

 cury and the deflection of light rays. It may 

 be also that by means of this formulation of 

 the law it will be possible to solve, with suffi- 

 cient accuracy, problems which are not readily 

 handled by means of the equations of general 

 relativity. 



2. The Schwarzschild form of the linear ele- 

 ment of the Einstein field' of gravitation of a 

 mass m at rest with respect to the space-time 

 frame of reference is 



(1) ds"- = 



(2m\ 1 

 1 )df^ (fr2 — r2(dg2^sin2edq)2) 

 r ' 2m 



1 



r 



where r, 6 and cp are the space coordinates as 

 measured by astronomers, and * is the coor- 

 dinate of time. 



