216 



SCIENCE 



[N. S. Vol. L. No. 1287 



and the pressures are larger on the warmer 

 side of the needle. It follows therefore that 

 one can eliminate the radiation discrepancies 

 by work done in partial Tacuum. In fact 

 with the exhaustion somewhat below 70 cm., I 

 heated the ball M (restored) as far as was 

 safe, 60°-70°, without obtaining any ap- 

 preciable effect on the needle. This suggests 

 the method of obtaining trustworthy static 

 data. 



Exhaustions of even 40 cm. give very good 

 results. In Fig. 3 for instance, obtained 

 with the new apparatus (scale distance 265 

 cm.., therefore less sensitive), there is no drift 

 and the whole motion soon becomes steady, so 

 that the triplets (data given on the curve) 

 become repetitions of each other. Between 

 the turning points the motion is uniform. 



A further important result was substan- 

 tiated. The size of the triplets, or better the 

 speed of uniform motion between the turning 

 points was the same, independent of pressure, 

 from a plenum up to 70 cm. In Fig. 3 some of 

 these speeds are given as displacements per 

 5 minutes inscribed on the lines prolonged. 

 Improvement would not be difficult. Hence 

 these resistances independent of the pressure 

 or density of the air must be due purely to the 

 viscosity of the medium and it must be pos- 

 sible to express the gravitational attraction in 

 terms of the viscosity of air. This project is 

 further elucidated tentatively, in the next 



5. Tentative Estimate. — The resistance ex- 

 perienced by a sphere of radius, r moving in 

 a viscous fluid (?;) with the velocity v = Iw, 

 is well known to be 6injrv. I do not happen to 

 be familiar with the corresponding expression 

 for a cylinder of radius r, semi-length I and 

 with hemispherical ends, moving broadsides 

 on. To get a mere order of values, however, I 

 will postulate, that for equal frontal areas, 



irr' =z2r ■ Al 



■the resistances are alike. Thus the element of 

 resistance is 



uri\r2iTrrA(l^) 

 and this is to be iategrated for the double 



length of the needle (20. To carry out the 

 integration put l = nX 2r where m is a serial 

 number. The equation becomes 

 AF = 8a)i;r=V37rA(»^) 



and the problem is reduced to the summation 

 of a series of cubes 



2\rTv?^n{n+ 1), 



the length being 21. Hence finally for two 

 masses M, m, at a distance B apart, disregard- 

 in corrections, 



7^8V375;w(i?Vifm)?i(n -|- 1). 

 The constants of the second apparatus were: 



M = 1602 grams, m = .563 grams, 

 S = 5.1 cm., 2r = .4 cm., 21 = 22.8 cm., r] = .00019, 



» = 28.5. 



In Fig. 3, the last three scale rates have the 

 mean value 2.17 per 5 minutes, or 



w = 2.17/300 X f30 = .00001364 



radians per second, the scale being off 265 

 cm. Inserting these data into the equation, 

 7 ^.10"^ X 6.2, which is much closer to the 

 standard value than, from the improvised ap- 

 paratus and inadequate theory, I had expected 

 to get. It sufficiently substantiates, I think, 

 the assumed purely viscous character of the 

 resistance and moreover shows that the con- 

 stant of gravitation may probably be foimd, 

 with precision, in terms of the resistance, in 

 air, to the uniform motion, broad-sides on, of 

 a cylinder with hemispherical ends. 



Carl Baeus 

 Brown Univeesity, 



PEOVmENCE, R. I. 



SCIENCE 



A Weekly Journal devoted to the Advetncement of 

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 ceedings of the American Association for 

 the Advancement of Science 



Published every Friday by 



THE SCIENCE PRESS 



LANCASTER, PA. GARRISCW, N. Y. 



NEW YORK, N. Y. 



Entered in the post-«fficc at Lancmttct* Pa., ma teoond cUm naOer 



