VOL. XIX.] VHILOSOPHICAL TRANSACTIONS. 12g 



The maple, both that which is miscalled the sycamore, and the lesser, bleed a 

 fermentable juice copiously, on the breaking up of hard frosts. Also the willow, 

 walnut, poplar, whicking, are all said to bleed in their seasons a vinous juice. 

 To extract the juice of vegetables, as opium for example, (as is usual in the 

 best preparations and methods of making laudanum) with spirit of wine, is not, 

 probably, to separate any one part of that coagulate juice from the other, as 

 the serum or whey, for example, from the caseous part of the juice, but only 

 to depurate or defecate the opium. 



The whey of lactuca sylv. can be only dissolved in cold water, the curds wholly 

 refusing to mix with it. And the same probably in other juices, so as to make 

 good that simple adage, water is the best menstruum, and that it really sepa- 

 rates, what spirit of wine only depurates. 



Solution to two Problems, proposed by Mr. John Bernouilli* in a Letter to Sir 



Charles Mountague, Pres. of the R. S. from Mr. .-^ N° 224, p. 384. 



Translated from the Latin. 



Sir, I yesterday received copies of two problems, proposed by that most 

 acute mathematician, Mr. John Bernouilli, printed at Groningen, Cal. Jan. 

 1697, of which the following are solutions. 



* John Bernouilli, the younger brother of James, by whom he was initiated into the mathematical 

 sciences, was born at Basil in \667 ■ John soon became equally eminent with his brother in those 

 sciences; after which,, their mutual communications, and even violent contestations, contributed at 

 once to their own improvement, and that of their favourite study ; as by their emulous struggles for 

 superiority, many valuable discoveries were made. John B. was professor of mathematics at 

 Groningen, while his brother James held the same office at Basil, and where he succeeded him also, 

 on the death of James in 1705 ; after which, it was held by John till his death, in 174S, in the 8 1st 

 year of his age. This long life, spent in a continual study and improvement of his favourite science, 

 gave occasion to this latter to make many and important discoveries in it, and to produce voluminous 

 writings on it ; though his genius seems to have been rather less brilliant than that of his brother 

 James. In the more early part of his career, John B. adopted the notion of the vortices of 

 Descartes, and endeavoured to explain the celestial phaenomena by them ; but he was afterwards 

 obliged reluctantly to adopt (he powerful principles of Newton's philosophy. Our author first ex- 

 plained the principles of Leibnitz's integral calculus ; the catenarian curves the curve of swiftest de- 

 scent; and isoperiraetrical problems ; he discovered the mercurial phosphorus, or luminous barometer; 

 with many other ingenious discoveries ; as may be seen in the collection of his works, published 

 17-12, in 4 vols. 4to. 



Of five sons, which he had, three pursued the same science with himself: one of these died be- 

 fore him; the two others, Nicolas and Daniel, he lived to see become eminent professors of it, in 

 different universities, like himself; and to this day some of their descendants still adorn (he mathe- 

 matical and astronomical sciences; like the family of the Gregorys in this country, to whom in 

 several respects they have a very near resemblance. 



+ This letter, containing these solutions, is here anonymous; but tradition has justly ascribed it 

 VOL. IV. S 



