446 
MR. BAILY ON THE CORRECTION OF 
their centre of gyration from the axis of suspension, have been computed 
agreeably to the following formulae, which have been obligingly furnished me 
by Professor Airy*. 
“ Let r denote the weight of adhesive air dragged by one inch of the rod 
“ (equal, in the present cases, to of the whole quantity dragged by these 
“ rods as found in the 13th set of experiments); and let us suppose that any 
“ one rod begins at x inches from the axis of motion, and ends at y inches 
“ from the same axis: then will the effect of the air adhering to that rod be 
“ represented by-^ ( y 3 — x 3 ). This is the same as if the whole quantity of 
“ air, r (y — x), had been attached at the distance \J ^ ^ ; which, in 
“ fact, is the distance of the centre of gyration of that rod from the axis of 
“ motion. The effect of the air adhering to several such rods will be repre- 
“ sented by — 2 (y 3 — x 3 ). Therefore the ratio which such quantity will bear 
“ to that carried by a rod of the length of the whole rod, if in one uninter- 
“ rupted piece from end to end of the given pendulum, will be as — 2 (y 3 — ^ 3 ) 
“ to — (Y 3 — X 3 ); where X and Y are the distances, from the knife edge, of 
“ the extremities of the whole rod: whence, the weight of adhesive air, to be 
“ used in the formula (10), will be 
« = r (Y-X) X YfeY r (11) 
“ And the distance of the centre of gyration, from the axis of motion, for a 
“ system of rods, is 
/ S (v 3 — x 3 ) 
a — V 3 S (y — x) ( 12 ) 
“ where, in each formula, x = 0 when the rod begins from the knife edget ” 
* I am indebted to Professor Airy not only for these and other formulae noticed in this paper, but 
also for various hints and suggestions during the progress of the experiments; and in general for the 
lively interest which he has taken in this inquiry: without which encouragement I certainly should 
not have extended the subject to its present length. 
t It is in this manner that I have computed the weight of adhesive air due not only to the spheres 
in this set of experiments, but also to the cylinders and discs in the 17th, 18th, and 19th sets of 
experiments. 
