86 A New Method of Resolving certain Equations. 
length beneath a clump of bushes, along the course of the 
fluid; while my strength was insufficient to make it pene~ 
trate at all in any other direction. And along the whole 
fifty feet, so evidence of its having passed, was indisputa- 
ble. How the fluid passed through the thirty feet from the 
tree to the wall, may perhaps not be thought quite so cer- 
tain; as it left no signs of its passage above ground, and no 
- indubitable ones could be discovered below by thrustin 
down a staff. But for myself, 1 cannot doubt the first part 
of its course was similar to the latter part; but passing be- 
low a thick and strong turf, and perhaps a little deeper, its 
course could not be so easily traced. If the fluid did not 
ee under ground the first part of its course it must 
e come out of the ground a few feet from the tree, 
sale thirty-feet through the air to the wall, and without 
leaving any trace of its influence on the post and rails, or 
displacing the small stones which composed the wall,* sunk 
quietly .down through the wall to its foundations, ond there 
gone off as above described at right angles to the well, in 
ction of a line from this spot to the tree. I can- 
that it passed the whole way — the tree under 
Art. XV.—A new method of resolving Equations oe i 
third and fourth degree. By Avexanper C, Twin 
To resolve a general equation of the third degree. 
Let the given equation be, 
2° -+3a nt t- Sha hcane, and put z-+-r=2; 
Then we Thane 
z°4+-3r-+-a.z2-+-3r? +2ar+5. 7-9 s-Bar Shed bees. 
Assume, (r-+-a)(7° +3ar? +3br-+-c)= =(r?+2ar +6)? ; 
Expanding ; r* L4ar?-+3b+3a?, 7? +-c+3ab.r+ac= 
r!+4ar°+2b+4a%.r?7+ 4ab.r+ 67; 
And uniting: b —a@?.r? +¢—absr+ac—bh* =o, (A) 
* One of the portions of the flaid after it forked, fell into a heap of simi- 
lar stones, and threw them about very much, 
sarin brent 
