686 



SCIENCE. 



[N. S. Vol. IX. No. 228- 



PHILOSOPHICAL SOCIETY OF WASHINGTON. 



The 501st meeting of the Philosophical So- 

 ciety of Washington was held at the Cosmos 

 Club on April 29th. An informal communica- 

 tion was first made by the Secretary on Recent 

 Geodetic Operations in Spain, special attention 

 being given to the Base of Madridejos and to the 

 Triaugulation connecting Spain and Algiers. 

 The results from the Base Measurement showed 

 it to be one of extreme accuracy. The manner 

 in which the work was carried out threw new 

 light on the most desirable lengths of Base 

 Lines in general, inasmuch as it was shown that 

 greater economy with equal accuracy can be at- 

 tained by measuring short lines and expanding 

 them by careful triangulation. The geodetic 

 connection across the Mediterranean was made 

 the occasion to demonstrate that longitudes 

 may be determined by means of optical signals 

 quite as accurately as by the electric telegraph. 



The first regular paper of the evening was by 

 Mr. J. F. Hay ford. The author made a state- 

 ment of a new treatment of refraction in trigo- 

 nometric-height computations recently used by 

 the Coast and Geodetic Survey in connection 

 with triangulation in Colorado, Utah and Ne- 

 vada, involving lines of sight from 100 to 182 

 miles long. The term of the strict formula (See 

 Wright's Adjustments, p. 387), which involves 

 the square of the distance and the difference of 

 the refraction coeflScients at the two ends of the 

 line, and which is usually neglected, was here 

 retained with marked improvement in the re- 

 sults. It was assumed that the refraction coef- 

 ficient is a linear function of the height of a sta- 

 tion above sea level and of the air temperature 

 at the station. 



The second paper was by Dr. H. S. Pritchett, 

 on ' An estimate of the population of the United 

 States in 1900 derived from an empirical 

 formula. ' Dr. Pritchett first called attention to 

 the general form of the curve defining the re- 

 lation between the population and the time. 

 The data now at hand enabled the author to 

 write eleven conditional equations of the form 



where p represents the" population (the unit be- 

 ing one million), i is the time counted from 1840 

 the epoch of the sixth census results and A B 



Cand D are constants to be determined. The 

 solution of the normal equations led to the fol- 

 lowing empirical formula 



p = 17.4841 -f 5.102i + Q.QZt' + O.OSO^s. 



Attention was called to the very close agree- 

 ment between the curve and the actual popula- 

 tion at the time of taking the census, the two 

 largest discrepancies being in 1860 and 1870. 

 Both these values were abnormal, partly because 

 of the exceptional conditions then existing, the 

 Civil War, lack of immigration, etc., and partly 

 on account of inaccurate census results in one 

 or both cases. 



The differentiation of the formula brought out 

 the fact that the rate of increase is continually 

 growing less, having fallen off from 32^ per 

 decade in 1790 to 24 /c in 1890. 



The result of the investigation was that the 

 best value for the population of the United 

 States in 1900, based on its growth since 1790 

 is 77,472,000 with a probable error of about 

 250,000. As a matter of curiosity the author 

 added that if the same law holds good in the 

 future we would have in 1990 a population of 339 

 billions, in the year 2500 nearly 12 trillions and 

 at the epoch 2900 this already appalling figure 

 will have grown to such an extent that there 

 will, on the average, be 11,000 inhabitants to 

 the square mile. 



The third paper by Professor J. H. Gore, on 

 ' Geodetic Work in Spitsbergen,' was not given 

 on account of lack of time. Professor Gore, how- 

 ever, showed a number of interesting lantern 

 slides illustrating his recent visit and scientific 

 work in that country. The paper will be given 

 at a subsequent meeting of the Society. 



E. D. Preston, 



Secretary. 



DISCUSSION AND CORRESPONDENCE. 



PROFESSOR JAMES ON TELEPATHY. 



To THE Editor of Science : It is evident 

 that Professor James and I have been writing 

 at cross purposes. On the point that Lehmann 

 has not ' established ' his explanation of the 

 Sidgwick results I am heartily at one with 

 James, Sidgwick, Parish and Lehmann himself. 

 But Professor James need not have awaited the 

 return mail from Copenhagen to wrest this 



