392 
DR. P. E. SHAW ON THE NEWTONIAN CONSTANT OF GRAVITATION, ETC. 
pressure would be called into play, pushing the suspended spheres towards the tube 
and therefore increasing the actual attraction on the suspended small balls. 
Let a be the temperature effect as found in this research, and let dr be the actual 
displacement accounting for it, on the above supposition, we have 
hence 
As 
we have 
n Mm 
Or. —— . a 
r 
2G. dr. 
dr = ar/2. 
r — 15 cm., a = 0'002, 
dr — 0‘015 cm. 
If the mass M have weight W, and hang at distance l from the supports, the force 
required to produce this movement (dr) is 
W. dr/l = 5*5 gm. weight. 
In discussing this hypothesis of greater convection on the inner side of the mass M 
we should notice that the vacuum tube is surrounded by a water screen at about 
11° C., so that one would expect the inner side of the sphere to be colder, not hotter, 
than elsewhere, and the push on the sphere due to convection differences would be 
outwards, not inwards. 
Suppose, however, that through some cause there is greater convection on the 
inner side of M. By applying Bernoulli’s theorem we can calculate what velocity 
is required to give the calculated push of 5*5 gm. weight. 
Let v 0 , v be convection velocities on the outer and inner sides of the sphere ; and 
let p 0 , p be the corresponding pressures ; and let d be tire air density. We have 
V 2 ~Vq _ Po~P 
2 d 
The effective area (i.e., the total resolved area of the sphere on which the pressure 
difference, p 0 —p, acts horizontally) would be not more than 75 cm 2 . Then taking 
v 0 = 0 we find v — 380 cm./sec. If, however, we take v 0 — 100 cm./sec. we find 
v = 360 cm./sec. It is fair to assume that v 0 lies between 0 and 100 cm./sec. 
Thus the upward velocity of a broad column of air on the inner side of the.sphere 
would have to be some 370 cm./sec. to account for the observed effect. This velocity 
is enormous. Even if the large value of 37 cm./sec. were assumed the error introduced 
would be only 1 per cent. 
In a recent paper by H. A. WiLvSON # we find it stated that the velocity of a bunsen 
flame is only 300 cm./sec. So, even supposing there were proved to be excess 
convection on the inner side, we have no reason to think that it would introduce 
a calculable effect.] 
* ‘ Phil. Trans.,’ A, 1915, vol. 216, p. 71. 
