440 Geological Olservations on unstratified Mountains. 
let fall from that-centre on the lines of direction in which 
the force is applied. 
Let AB (fig. 4.) be the lever, and let the two equal forces 
BM, Bm, act upon it at the point B, in the direction of 
the lines BM, Bm. Draw BN, Ba, respectively equal to 
BM; Bm, and forming the same angles with the line PBa 
perpendicular to AB. To BM, Bm, BN, Bn, produced, 
draw the perpendiculars AY, Ay, AX, Ax. Now, the 
side AX = AY, and Aw = Ay, on account of the equality 
of the triangles, ABX, ABY; and if M/, Ma, be drawn 
perpendicular to Bw, the triangles ABY, BMJ, will be si- 
milar, and also the triangles ABy, Bar a: hence we obtain 
AB: AY = BM:Bi, and ~ i, 
AB: Ay = BM :Ba 
Therefore, ex equo, AY: Ay = Bl: B2. 
‘Complete the’ parallelograms BMoN, Bmw, and BI, 
BA willbe respectively one-half of the diagonals Bo, B Ws 
Now let two equal forees BM, BN, act in these directions 
upon the lever at B, their joint force will be represented by 
the diagonal Bo, and consequently one of the forces BM 
will be represented by BJ = Bo. In the same manner, 
if the two equal forces Bam; Bn, act upon the lever at B, 
their joint force will be represented by Bw, and one of them, 
Bm, will be represented by BA=iBw. Consequently 
the power of the two forces BM, Bm, to turn the lever 
round its centre of niotion, is represented by Bl, Ba, re- 
spectively ; that is, the force BM is to the force Bm as Bi 
is to Ba; thatis, as AY is to Ay, the perpendiculars let 
fall upon the lines of their direction. é 
LXXIIl, Geolog ical Observations, on unstratified Mountains, 
—-andon the Use and Abuse of Geological Theories. By 
Mr, Joun Farny, Senior. (Tod fai 
To Mr. Tilloch. - 
Sir, I, gives me. considerable pleasuse, after so long a 
lapse, to a a Dr, William Richardson returning to the 
subject of geology, in which he has already achieved so - 
much, and from whom we expect still greater things, and 
to see him among the contributors to the Philosophical and 
Geological Magazine; not that T mean to insinuate that the 
doctor’s labours elsewhere oi Fiorin Grass, have been un- 
important or not highly useful; but I confess that J ho not 
ay: : ‘on reg een 
