GRAVITATION AS AFFECTED BY TEMPERATURE. 
391 
For much general assistance from friends and colleagues, during the progress of this 
work, I gladly acknowledge my indebtedness. All the readings have been taken by 
myself; but on many occasions during the preparation of the apparatus, I have 
received most willing aid in various ways. To the many who have thus assisted me 
in accomplishing the present work I wish to record my thanks. I am also much 
indebted to Messrs. Baird and Tatlock, Hatton Garden, E.C., for great help in glass 
blowing. 
This investigation could not have started nor continued without considerable 
expenditure on apparatus. At the kind suggestion of Prof. W. H. Heaton, the 
Council of University College, Nottingham, made a generous grant at the outset, 
eight years ago ; while Prof. E. H. Barton has greatly helped by his unquestioning 
supply of material. 
Finally, I wish to acknowledge my obligation to Prof. C. V. Boys and the late 
Prof. J. H. Po anting for kind advice at the commencement of the work. 
\JSfotes added April 25, 1910 .—Since the reading of this paper two possible sources 
of error, in addition to those in the table above (p. 386), have been suggested :—- 
I. As temperature rises, the air surrounding the spheres, M, M, will decrease in 
density, so that the total gravitative pull felt by the torsion system, due to the 
external system, will be reduced. 
Let p be the mean density of lead and lagging and let p be the mean air density. 
The effective large mass is really M(l—p'/p). Both lead and air expand, and we 
must calculate (a) the mass of cold air displaced by the expanding lead ; ( b ) the mass 
of air expelled from the field by expansion of air shells round the lead. 
Under the first head. Lqt the sphere have radius r and expand to (r + cfr), with 
rise of temperature 0°. The mass of the air shell displaced is, calling /3 its coefficient 
of expansion, 
4-7rr 2 . (<b'). p 
= 47rr 2 (V/30) p 
— l/l4 gm., approximately. 
But M = 50,000 gms., so the proportionate change in the attraction due to this 
cause would be 1/700,000. This is negligible. 
Under the second head. Suppose, as an extreme case, a shell of cold air equal 
in volume to the lead were removed from the field by expansion ; the mass of this 
would be 1/9000 of the mass M. • This also is negligible, since the temperature effect 
observed is 1/500. 
II. With the high temperature of the lead spheres (250° C.) considerable convection 
currents would 'be set up round them, even when lagged. 
In the region where the spheres are close to the tube, the air velocity might be 
very much larger than on the outer regions ; and, as a consequence, difference of 
