VOL. L.] PHILOSOPHICAL TRANSACTIONS. J141 



tions to exterminate v, let the latter be divided by the former; so shall ~ = Z- 



J py v^ 



and therefore «3rr= v {a being a constant quantity.) Hence z/7 y = (-/"' X 



I 



.vx-p-i ; and consequently ^^ x rj p ={-) X ^_^^_^ X x p . 



Let there now be proposed the two fluxions x^y^^.v and x^y^ij, the fluent of the 

 former being required to be a maximum or minimum, and that of the latter, at 

 the same time, equal to a given quantity. Then the latter, with the general 

 coeflicient h prefixed, being joined to the former, we shall here have ofy^.v -j- 

 bx^y'^y. Hence, by proceeding as before, hx^y'' = v, and mx^y'"~^ a; -j- qbx^y''~^ 

 y x=. V. From the former of which equations, by taking the fluxions on both 

 sides, will be had pbx^^y^x + qbx^y*~\y (= v) = mx^y"^\v + qbxPy'^^y. 

 Whence pbx^' y" = mx^'y'"-'; and therefore pby'^-'"'^' = mx"-^ + '. Andinthe 

 same manner proper equations, to express the relation of x and y, may be de- 

 rived in any other case, and under any number of limitations. 



LXXXJ^I. On the Alga Marina Latifolia; the Sea Alga with Broad Leaves. 

 By J. A. Peyssonel, M. Z)., F. R. S. Dated Aug. 4, 1758. p. 631. From 

 the French. 



Having cast anchor at Verdun, the road at the entrance of the river of Bour- 

 deaux. Dr. P. was fishing with a kind of drag-net on a bank of sand, which was 

 very fine and muddy. He collected a number of sea-plants, and among them 

 the great broad-leaved alga, which he did not know; and as the root or pedicle 

 of this plant appeared to be very particular, he observed it with attention. The 

 following is its description, and the detail of his observations. 



From a pedicle, which is sometimes flat, and sometimes round (for they vary 

 in these plants, and might be about 3 lines in diameter, and an inch high, of a 

 blackish colour, and coriaceous substance, approaching to the nature of the 

 bodies of lithophyta), a single flat leaf arises, about an inch or an inch and half 

 broad, thick in its middle to about 3 lines, ending at the sides in a kind of edge, 

 like a two-edged sabre, almost like the common alga, formed of longitudinal 

 fibres, interlaced with other very delicate ones, and the whole filled with a thick 

 juice, like the parenchyma of succulent plants, such as the sedum, aloes, and 

 the like, of a clear yellowish green, and transparent. This first leaf is always 

 single, and serves instead of a trunk or stem to ihe whole plant. When it rises 

 to about a foot high, more or less, it throws out at the sides other leaves formed 

 of a continuation of the longitudinal fibres; and these 2d leaves are of the same 

 thickness and substance with the first: they are 2 or 3 feet long, and the whole 

 plant is 5 or 6, or more, for one can hardly tell the length ; and is not capable 



VOL. XT. I I 



