1816.] - when viewed in a certain Position. 207 
Through B in the triangle VA B draw B N parallel to V T, and 
through B N pass a plane perpendicular to the plane V A B, and let 
the common section of this plane with conical superficies be the 
line N LB K, N L.BK shall be a circle. 
In B N take any point I, and through I pass a plane parallel to 
the base. Let the common intersection of this plane, and of the 
conical superficies, be D K EL, which by Prop. 2 will be an 
ellipse similar to the base. Let the common intersection of the 
planes DLE K and NLBK be LK. Now as the axis of the 
cone is perpendicular to the base, the plane A G B O (18, xi.) is at 
right angles to the plane V A B, consequently D L K E is at right 
angles to V AB; but,the plane N LB K was made at right angles 
to V AB; therefore (19, xi.) LK is at right angles to the plane 
VAB and LIN, LID are both right angles. 
Now as B N is parallel to V T, and D E is parallel to A T, the 
triangles DI N, A T V, and the triangles IE B, V BT, are 
similar. Hence DI:N1I::AT:VT,andIE:1B:: TB: VT. 
Therefore DI,IE:NI,1B:: AT, TB:VT?; but by construc- 
tion AT, TB: V T?:: A B*?: OG* Therefore DI, IE: NI, 
ie .n 8: OG: AC: € G?, 
Lastly, by Prop. 2, D E is the minor axis of D K E L, and by 
the corollary DI, IE :1L?:: A C?: C G*. Butit has been shown 
that DI, I E: NI, I B:: A C*?: C G*; therefore DI, LE: I L?:: 
DI, 1E:N1,IB; consequently I L? = NI,1I B, and by lemma 
1, NLB isa semicircle. 
Cor. 1.—As / OG? —AB?:0G:: VB: VT,OG: /O G2—AB? 
: sineof VA B:sineof VTA or NBA. If the cone becomes a 
cylinder, V A B becomes a right angle, and OG: / OG* — AB* 
z: radius : sine of N B A. 
Cor. 2.—V N L BK will become a scalene cone; therefore any 
plane parallel to N LB K, or any plane which forms the subcon- 
trary section, will give a circle. 
ArTicLe IV. 
Letter of Dr. Schiibler, Professor of Natural Philosophy and Che- 
mical Agriculture in the Institute, of Hofwyl, to Professor M. A. 
Pictet, on the Physical Analysis of Soils.* 
Hofwyl, July 14, 1815, 
In consequence of your desire, during your recent visit to Hofwyl, 
to know the result of my researches on the physical qualities of 
arable soils, I do myself the honour of transmitting to you the fol- 
lowing comparative table. 1 shall likewise explain the way in which 
' my experiments were performed :— 
* Translated from the Bibliotheque Britannique, Agriculture, p, 248, July, 1815, 
