55 ® 
Mr. Hellins’s unproved Solution of 
+ 1 ? 
6 p 4 q 
— 4 - 
.,3 
5 
T 
>y , which being put = the first side o'f 
y* y J 
the foregoing equation, there will arise as many simple equa- 
tions for determining the coefficients a , b , c, &c. as there are 
letters of that kind in the assumed fluent, from which their 
values will easily be found. For there will be 
6a = from which a = 
= J-, 
zc = S b +f+h 
®/ = |> 
g=z — c , 
6 P = i> 
4 ? = 
^ = 7? ~f 
S = g ~ T 6 > 
b = 
/ = 
/> = 
? = 
12 
-7 
iz 
-5 
16 ' 
3 
8 1 
5 
16 
iz * 
3 
8 • 
— i 
32* 
O. 
The variable part, therefore, of the fluent of the first side of the 
above equation is 
Q [ . — ? 7 - 5 -) j a; ( L _L 5 
\ 12 V 6 12 D 4 l6w J ‘ l 8 J ;y * 
+ 
i zyr 
5 
1 2jr 
3 
J i- — 
> 8 a,4 
16 ^ 3 ; 
i 
16 
iz^ a 1 8y* 32 y y 
Now, to discover the constant quantities which lie concealed in 
this expression, we must proceed as above in Art. 3 . 
