VOL. XXIX.] PHILOSOPHICAL TRANSACTIONS. . Q'/ 



to be reciprocally proportional to the radii or distances; and therefore the arcs 

 described in the same time will also be in the same reciprocal ratio of the radii ; 

 whence it easily appears, that the sectors described in the same time will be 

 equal. 



In all other curves, since the velocity is to the velocity of a body moving in 



a circle, at the same distance, as -7-to jb, or as -ik to kn; while the body in 



its trajectory describes the lineola ik, another body, moving at the same distance, 

 will describe an arc = - X kn; and the area of the circular sector, and tl^at of 



a 



b 



the trajectory described in the same time, will be - x kn X iCN and kn x -I^cn, 

 which two areas are in the given ratio of b to a. Therefore, when a-=.by as 

 it is in the hyperbolic spiral, the area so described, will always be equal to the 

 area of the circular sector, described in an equal time. 



Rules for correcting the usual Methods of computing j^mounts and present lvalues 

 by Compound as well as Simple Interest, and of stating Interest Accounts. 

 Offered to Consideration by Thomas JVatkins, Gent, F. R. S, N*^ 340, p. 111. 



The computations of interest, and other accounts, being found in numberless 

 small books, which are in every one's possession, it is no ways interesting to 

 retain this paper on the present occasion. 



An Account of the Rain which fell every Year at Upminster in Essex, for 

 18 Years; with Remarks on that of the Year 1714. By W. Derham, F.R.S. 

 Also a Comparison of what has been observed of that kind at Paris, By M. 

 De la Hire. N° 341, p. 130. 



Last Year, 1713, having been so dry, that the ponds about Upminster were 

 mostly dried up, and the springs very low, I made an extract from my registers 

 of the weather, &c. of the quantity of rain which had fallen at Upminster the 

 last 18 years; for which see the following table, which shows the depth in 

 inches and centesimals of inches, or what height it would have been had it not 

 been imbibed by the earth, or lessened by exhalations, but been suffered to have 

 stagnated on the ground. 



In 1704 the drought was so considerable at Venice, that they were forced to 

 fetch their water in barks 5 leagues off", as far as the Brenta. Yet we have had 

 several years drier than that at Upminster. But of all, none was comparable 

 to 1714, in which the whole quantity of rain was only 11. IQ inches; whereas 

 the least quantity of any [of the preceding 18 years exceeded 15 inches in 

 depth. 



VOL. VI, O 



