VOL. XXIV.] PHILOSOPHICAL TRANSACTIONS. gj 



To find the fluent, assume mz = — w^iv ; 



u • • 2fl + 2r o. J . .^ / r*tf* 4fl + 4r I .20 + 2r „v , 



hence .r = zt; ; — w'w, and ?/ = z^\/ — r-r H 7— w — ( — ; — «^ 1 ; 



the fluents of which, found by the known methods, are 



2a + 2r o , 2o' — ra^ — 2aw^ — nu* . 



Example 4, To find a curve equal to the cubical parabola, whose equation is 

 3a** = wK Hence 5^ = ^ it>^, and therefore y = \/-i^^ + 27nzi;ir ■— 7»*i^ 

 To find the fluent, assume 

 mz = —^'. hence x =1 iu ^ — m;, and y = —^^32^2 _j_ ^^2 . ^.^^ ^.j^g fluents 



are X = a - gj;, and y = ^,^ = -j^— • 3»^ + 4«'. 



From infinite other values of the quantity mz rightly assumed, may be found 

 infinite curves equal to the given one. It may be further observed, that this 

 problem has some kind of affinity with a certain Diophantine problem. His 

 problem is, to divide the sum of two squares into two other squares, having 

 their sides rational ; and Bernouilli's problem is, to divide the sum of two 

 squares into two other squares, the fluents of whose sides may be found. And 

 as the solution of Diophantus's problem depends only on the common algebra, 

 so the solution of Bernouilli's problem requires only the common inverse method 

 of fluxions. The artifice of each consists in a due assumption of the sides re- 

 quired ; that of Diophantus that the sides may be rational, that of Bernouilli 

 that the fluents of the sides may be found. 



!i^ strange Effect of the late great Storm in Sussex, By John Fuller , Esq, in a 

 Letter of Dec. 6, 1703. N° 289, p. 1530. 

 We live 10 miles from the sea in a direct line, and yet cannot persuade the 

 country people but that the sea water was blown thus far, or that during the 

 tempest the rain was salt ; for all the twigs of the trees the day after were white 

 and tasted very salt, as I am informed almost by every body, though I did not 

 taste them time enough myself, nor observe it; and that not only upon this 

 hill where we live facing the sea, but in all other places within 14 or 15 miles 

 of the sea, as well in the valleys, between which and the sea are several very high 

 hills, as on the hills themselves. 



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