VOL. XXVIII.] PHILOSOPHICAL TRANSACTIONS. 7 



1 to 11.5 nearly, I multiply the difference 0.045 by 11.5, and the product 

 0.51/5 added to bq, makes 20.5175. Therefore, I suppose secondly Ba = 

 20.51, and there will arise, in the same manner as in the foregoing, np = 

 ig.5092; to which adding bn, the sum is 20.5092, which is less than bq. 

 Wherefore if the difference 0.0008 be multiplied by 11.5, and the product 

 0.0092 be subtracted from bo, there will remain Bq = 20.5008. 



Lastly, let the mean motion be equal to 2°. I suppose bq 30°, and there is 

 found NP = 27.84 ; to which adding 2^, the sum 29.84 is less than 30. And 

 if the difference 0.1 6 be multiplied by 6.3 (for l — cosin. Ba is to l, as 1 to 

 6.3 nearly) it will be 1.008 = aq. Therefore this arc subtracted from bq gives 

 Bq = 28.982. Now that Bq may be corrected, I assume secondly bq = 29 

 degrees ; and by a like process we find b^ = 28.9672. 



Ofjlnding the Centre of Oscillation. By Brook Taylor, Esq, F. R. S. N° 337, 

 j4rt. 2, p. 1 1 . Translated from the Latin, 



Definition. The centre of oscillation is a certain point in a pendulous body, 

 whose single vibrations are performed after the same manner, and in the same 

 time, as if that point only was suspended by a thread at the same distance from 

 the point of suspension. 



Of itself it is hardly sufficiently clear that there is such a point in a body, as 

 that its acceleration ought, by this definition, to be the same in all inclinations 

 of the pendulous body to the horizon, as if it were actuated by its own gravity; 

 the other particles of the whole body giving no disturbance to its motion. 

 Therefore, in order to the investigation of this centre, a proposition or two 

 must be premised, whence it may appear that there is such a point. 



Prop. 1. Prob. I. In any given inclination, of a vibrating body, to the 

 horizon, to find a point, whose acceleration shall be the same, as if it were 

 urged by its own gravity only. 



Let ABD (fig. 5, pi. 1) be a section of the proposed body in a plane perpen- 

 dicular to the horizon, in which the centre of gravity g is moved, c being the 

 centre of suspension. Let the body be distinguished into prismatical elements 

 perpendicular to the plane abd, and therefore always parallel to the horizon ; as 

 will easily appear from the motion of the centre of gravity g in that plane abd. 

 And because of that situation, any such element may be considered as a physi- 

 cal point p placed in the same plane abd at the point z. Therefore let 

 the body proposed be reduced to the physical plane abd, consisting of such 

 particles p. 



To find in this plane a point o, whose proper acceleration is not changed by 

 the action of the other particles, we must attend to the force of every single 



