384 



PHILOSOPHICAL TRANSACTIONS. 



[anno 1788, 



yi. A Table of the Mean Heat of every Month for Ten Years in London, from 

 1763 to 1772 inclusively. By JVm. Heberden, M. D., F.R.S., and A.S. 



p. 6a. 



12 

 10 

 9 

 7 

 5 

 3 

 2 

 1 

 4 

 6 

 8 

 11 



January- 

 February 

 March 

 April 

 May 

 June 

 July 

 August 

 September 

 October 

 November 

 December 



The first column of figures denotes the order of the months according to their 

 degrees of heat, beginning with August, in which the heat is greatest. The 2d 

 and 3d are the heats marked at the hour expressed at the top of each column, and 

 the 4th is the mean between two. The last column is the mean of the greatest 

 cold at night, observed in Marl borough-street for 20 years, by Lord Charles 

 Cavendish. 



FII. On Centripetal Forces. By Edw. Waring, M.D., F.R.S. p. 67. 



Prop. 1. — 1. Let a curve pjbN (pi. 4, fig. 3), of which the perpendiculars to 

 the two nearest points p and p of the curve are po and jbo, and consequently o 

 the centre of a circle having the same curvature as the given curve in the point 

 p ; draw PY and ly tangents to the curve in the points p and p ; from s draw s^ 

 and sAy respectively perpendiculars to the tangents ly and py; and let sAy cut 

 the tangent ly m h; then will ultimately hr (— p) be the decrement of the per- 

 pendicular sy = p; and the triangles /Ay and pop be similar: for the angles Fop 

 and A/y are equal, and the angles /yA and opp right ones; therefore po : 



p/>:: /y ultimately =± py : yA decrement of the perpendicular, whence vp = 

 yh X PO y/« X PO 



/y pt * 



1. 2. Fig. 4 and 3. The force in the direction ps is as the ultimate ratio of 

 2 X GR (the space through which a body is drawn from the direction of its mo- 

 tion in the tangent in a given time towards the centre of force) ; but ultimately 



2aR = 



2qp^ 



where qp is as the space described in a given time, and conse- 

 quently as the velocity (v) of the bpdy at the given point p, and pv the chord of 

 curvature in the direction sp. 



