446 Mr. Harley on Black Currant Wine. 



all the positive terms that precede it from both sides of the 



preceding equation, I get 



-T n{n-\) .(n-r + 1) , j. • .__ - rQ^ !)»»■. fo-r+0 ^ 



_ ^-i; !»-"*, + &C. = + 



1.2 



1.2 



And similarly it can be shown, that the theorem is true in 

 the binomiation of any polynomial. 



On the General Theory of Oscillation. 



Let y=f(xz) be the equation of any curve or curve sur- 

 face. Binomiating according to any constant in the equation, 



Now,/y 4-/'j/, is evidently the equation of a straight line, 

 or of a plane surface ; and by the dinomial theorem, the sum 

 of these two terms is either greater than y, or less than y, 

 when the exponent is not unity: therefore, fy+f'.y, 1S the 

 equation of the asymptote of the first order. And for the 

 same reason fy +fy +f"y is the equation of the asymptote 

 of the second order, &c. 



Dinomiating the equation y=f(x,z), I get 



y'= y 4- dy 4- d 2 y 4- d 3 y 4- &c. 



In this, y+dy is the equation of a straight line or plane 

 surface, and is either greater than y' or less than y, when the 

 exponent is not unitv ; therefore, y 4- dy is the equation of 

 osculation of the first order. And for the same reason, 

 y + dy + d i y is the equation of osculation of the second order, 

 &c. Taking the dinomials of the independent variables, po- 

 sitive and negative : then, if the sums of the terms which con- 

 stitute the equation of osculation, are each greater than y, or 

 each less than y, the equation is one of contact ; but li one 

 sum is greater, and this less than y', the equation is one of in- 

 tersection. 



Cork, June 10, 1824. J- Walsh. 



LXXIII. On Black Currant Wine. By C. G. Harley, Esq. 



To the Editors of the Philosophical Magazine and Journal. 



Gentlemen, 

 I" AM induced to send you the following statement, because 

 -*- your valuable Magazine is a general repository for every 

 scientific discovery, as well as for such observations as arise 

 out of objects commonly presented to our attention. I be- 

 lieve 



