354 
Hence 
__—(3b-a*) + y {(3b- a?) — 4(3ac - &) (3b — a®)}, 
‘ 2(3d — a?) 
but in the equation 
w'+ Aa’?+3A'a'+d=0, 2 =-4A+4(A- 270) 
by completing the cube, and transposing c. Therefore, also, 
Olah 
a or —| 
x 
, 32+ 2az+b +2] 327+ Qaz+b \3 Pail (3 
~ S234 az+bze+e 3 l\\e+az2+bz+ce] B@+az+bs+el 
° a 
( 32+2a2+6 *// 322+2az+5b \3 PH “1 
=3/- rs + a 2 hoi 3 
| 2+az2+bz+e et+aet+be+e) 2+az*+bz+e 
but 2’ + z=, by the hypothesis in the original equation: 
'U=2 
(32? + 2az + b) 327+ 2az+b \3 20 = 
2+az*+bz+e Stae+bz+e)/ 24a22+bz+6¢ 
consequently, substitute the foregoing value of z into this last 
formula, and it gives the value of the unknown quantity in 
any cubic of the form that I proposed.” 
Rey. Professor Haughton made a communication ‘On 
the Depth of the Sea deducible from Tidal Observations,” of 
which the following is an abstract. 
He stated that, in consequence of his having succeeded in 
separating the effects of the sun and moon in the diurnal tide, 
he was enabled to make calculations of the depth of the sea in 
which the tidal wave was produced, which he believed to be 
worthy of the greatest attention. .The depth of the sea may 
be inferred from three distinct observations, viz., of heights 
of diurnal tide; of solitidal and lunitidal intervals; and of the 
age of the lunar tide compared -with the lunitidal interval. 
