VOL. XXXII.] l?HILOSOPHlCAL TRANSACTIONS. 571 



magnitude, but of different weights, fall on a yielding substance, as tallow, 

 wax, clay, or the like, from heights reciprocally proportional to the weights of 

 the globes. This experiment engaged in particular my attention, as it is brought 

 with design to overturn one of the first principles established in natural philo- 

 sophy; for I can by no means admit of the deduction drawn from it, viz, that 

 because the globes make in this experiment equal impressions in the yielding 

 substance, therefore they strike upon it with equal force; by which it is at- 

 tempted to prove the assertion of Mr. Leibnitz, that the force of the same 

 body in descending is proportional to the height from whence it falls; or, in 

 all motions, proportional to the square of the velocity, and not to the velocity 

 itself, as is commonly thought. On the contrary, I think that this very expe- 

 riment proves the great unreasonableness of Mr. Leibnitz's notion. 



It is surprising that so careful a writer as Polenus appears to be, from the 

 accuracy shown in his experiments, should not rather suspect his reasoning in 

 an intricate case, than thus contradict a principle in philosophy, that has been 

 directly proved by a multitude of experiments, in particular by those Sir Isaac 

 Newton recommends for that pur{)ose, Princip. p. IQ. Certainly this experi- 

 ment of Polenus is much more fit to inform us of the law by which these 

 yielding substances resist the motion of bodies striking them, than to show the 

 forces with which bodies strike ; for whatever those forces be, the effects must 

 be very different, according to the difference there may be in the rule observed 

 by such resistance. 



Now this experiment shows, that if two globes in motion bear against equal 



Besides the doctor's writings above-mentioned, he wrote numerous other pieces; as, 1. Epistola ad 

 Amicum de Cotesii inventis ; demonstrating Cotes's celebrated theorem, and showing how his theorems 

 by ratios and logarithms may be done by the circle and hyperbola. 2. Observations on Poetry, espe- 

 cially the epic, occasioned by Glover's Leonidas. 3. A plan of a free state, with a king at the head: 

 not published. 4. Account of the ancient ode, printed in the preface to West's Pindar. 5. On the 

 Dispute about Fluxions; in the 2d vol. of Robins's works. 6. On the Alteration of the Style and 

 Calendar. 7. On reducing the Weights and Measures to one standard. 8. A Dissertation on 

 Eclipses. 9. On the Loci Plani, &c. His numerous communications to the Royal Society, on a 

 variety of interesting subjects, extend from the 32d to the 62d vol. of the Philos. Trans. 



After his death, many valuable pieces were found among his papers, viz. A short History of Tri- 

 gonometry, from Menelaus to Napier. A comment on an English translation of Newton's Principia. 

 Demonstrations of tlie spherics and spherical projections, enough to compose a treatise on those sub- 

 jects. A Dissertation on Archimedes's Screw. Improvements in Gauging. In a given latitude to 

 find the point of the Ecliptic that ascends the slowest. To find when the Oblique Ascension differs 

 most from the arch to which it belongs. On the principles of Mercator's and Middle-latitude sailing. 

 To find the Heliacal Rising of a Star. To compute the Moon's Parallax. To determine the Course 

 of a Comet in a Parabolic Orbit. And others, all neatly performed. On the whole. Dr. Pemberton 

 appears to have been a clear and industrious author, but his writings are too diffuse and laboured. 



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