VOL. IX.] PHILOSOPHICAL TRANSACTIONS. 173 



The author of this discourse, much addicted to apply speculations to use and 

 practice, has given in this exercise several instances, wherein the consideration 

 of duplicate and sub-duplicate proportion, or the consideration of sides and 

 their squares, is of use in human affairs. Those instances are — 1. In the 

 drawing or driving powers, which force ships or other bodies through the water, 

 with reference to the respective velocities caused thereby. — 2. In the shapes or 

 sharpness of bodies, cutting or dividing the water, through which they are 

 driven or drawn, and in the different velocities arising from thence, where the 

 bodies and forces are equal. — 3. In the strength of timbers, or other homo- 

 geneous materials applied to buildings, to carts, or any other machinery intended 

 for strength: and how by a model to judge the sufficiency of such engine as is 

 represented by it. — 4. In the effect of oars upon equal and like vessels, accord- 

 ing to their numbers, length, blades, and motions, with or against the stream of 

 smooth or uneven waters. — 5. In the motion or travelling of horses, on their 

 several paces, and with different burthens on them. — 6. In the strength and 

 velocity of mills and their wheels. — 7- In the effects of gunpowder. — 8. In the 

 distance at which sounds may be heard. — Q. In the distances at which odorife- 

 rous matters may be smelt. — 10^ In the distance at which the objects of sight 

 may be seen. — 11. In the time of the returns made by vibrating pendulums. — 

 12. In the lives of men and their duration. — 13. In musical and sounding 

 bodies, such as strings and bells. — 14. In the effects and motions of fire and 

 burning spirits. — 15. In the rising and falling of bodies, but especially of water 

 in pumps, over-shot mills, leaks in ships, the heights of rivers at their head 

 above their fall into the sea. — 16. In bellows. — 17. In the prices of several com- 

 modities, as masts, diamonds, large timber, amber, loadstones, &c. — 18. In 

 mill-dams, sea banks, and the bulwarks or walls of fortresses. — 19. In the com- 

 pression of wool and other elastic bodies, and of the air within diving vessels, 

 as also in the effects of screw-presses upon several materials. 



Having thus enumerated his several instances, wheren duplicate and sub- 

 duplicate proportion is of great importance, he explains what he understands by 

 every material word he uses in this discourse ; such as matter, body, figure, place, 

 motion, quantity, quality, habit, time, proportion, weight, swiftness, force, and 

 elasticity. This done, he makes the applications of the said proportions to each 

 of the respective matters just mentioned. To which he subjoins an appendix on 

 his new theory of elasticity mechanically explained. 



The various pursuits in which Sir Wra. Petty was engaged, show that his genius was capable of any 

 thing to which he chose to apply it: and it is very extraordinary, that a man of so active and busy a 

 temper, could find time to write so many things as it appears he didj which arc even too numerous 

 to be more particularly noticed in this place. 



