320 



PHILOSOPHICAL TRANSACTIONS. 



[anno 17 5g. 



inquiry when I have made only one remark more. It is this : the shortness of 

 the brachia diminishes the resistance of the engine to motion : and therefore the 

 inequality which I proposed in them, was in part to avail myself of that obvious 

 advantage, without incurring the inconvenience of enlarging the pump-bores. 

 I say it is an obvious advantage ; for, the matter in the brachia, that the equi- 

 librium may be preserved, being inversely as their lengths, and the resistance 

 to motion in the direct ratio of the squares of those lengths, the resistance of 

 the longer arm is to that of the shorter as the lengths of them directly. 



//. Observatiojis on the Growth of Trees. By Robert Marshamy of Stratton 



in Norfolk, Esq. p. 7- 



Measures of Trees, taken in April 1743, before they began to shoot ; and again in Autumn 1758, after 

 the Year's Growth was completed. The Measure taken at 5 Feet from the Earth. 



First Table. 



1. Ash, planted since l647 



2. Oak, past thriving, but sound 



3. Oak, about 80 years old, . . . 

 4-. Scotch Fir, seed in 1698. . . . 



5. Oak, planted above 60 years. 



6. Spanish Chestnut, near 60 years old 



7. Another, 45 or 46 years old. 



8. Oak, planted in 1720 



9. Scotch Fir, planted 1734, 2 feet high 



10. Pinaster, planted in 1734 or 1735!2 



11. Oak, set an acorn in spring 1719 I 



12. Oak, planted in 1720 or 17 21. . . 2 



circumf. 



in Spring 



1743. 



Now as the 12 trees above, contained 213 cubic feet 300 inches of timber 

 in spring 1743, and have increased to 322 cubic feet 333 inches in autumn 

 1758; that is, lOQ cubic feet 33 inches in 16 years growth ; if all the trees 

 were of the same kind, lOQ feet pays 3 per cent, for standing: and the 6 oaks 

 pay near the same interest, though one of them, N*^ 2, appeared past thriving 

 in 1743 ; for the increase of the (3 oaks is from 1 12 feet 1 quarter 171 inches of 

 timber, to 167 feet 138 inches, i. e. 54 feet 2 quarters 399 inches; which is 

 above 3 per cent. But if we take only the 5 thriving oaks, then their content 

 is, from 57 feet 3 quarters 267 inches, to 103 feet 2 quarters 58 inches ; i. e. 

 45 feet 2 quarters 223 inches of timber ; or near 5 per cent. And the increase 

 of the most thriving oak, N° 8, appears, by the above table, to pay above 124- per 

 cent, and the Scotch fir, N° 9, being under 2-i- feet of timber in spring 1743, 



