E ; WEDOB, 



But the triangle x<? b aimilar to esa ; therefore 

 rf K : d a : : as : ae, 



nd consequently P :* : : 2a(-an) : or. 



The position of the point e when the separation of the material U 

 upposed to take place varies for different materials, and can only bo 

 estimated, or found from experiment : if it were supposed to coincide 

 with c, we should have 



p : B : : 2oH : ac ; 



cir by similar triangles dkc, ABO, 



p : B : : AD : AC. 



If the force of the wedge at the points a or 6 were to be estimated 

 in the direction xa or yb ; as when it is required, neglecting friction. 

 to find the force with which a given pressure p hi the direction M c, 

 on the head of the wedge, would make a body at a or 6 slide in a 

 direction perpendicular to no : then, B' representing that force, and e 

 coinciding with c, or ad being now perpendicular to AC, we should 

 have 



r : B' : : 2rfs : So, or as Zav to KC, or as AD to EC. 



The point c still coinciding with c, let represent the angle ACE, or 

 half the angle of the wedge : then 



- = sin 0, or = 2 sin 0; 

 . also AB : EC : : 2 sin : cos : 

 it follows, radius being unity, that 



p : B : : 2 sin 0:1, or r = 2 B sin 8 ; 

 alaop :B' : : 2 sin fl : cos 0, or p=2n' tan 0; 



where B and B' represent the pressures perpendicular to A c and to E c 

 respectively. 



If it were required to find an equation for the motion of a wedge 

 when acted upon by a force of percussion, a process corresponding to 

 that which follows must be employed. 



Let, as before, ADC be a section of the wedge, which may be sup- 

 posed of iron : let it be introduced between the parts of a body which 

 can yield only hi a lateral direction ; and let it be driven by a mass of 

 iron falling upon it from a point at some given height above. Both 

 the wedge and the hammer, or falling body, must be understood to be 

 elastic ; and it will bo convenient to represent the latter by a 

 parallelepiped of iron whose base is equal to the rectangular head of 

 the wedge : let the height of such solid be represented by P, and let 

 the space through which it is supposed to fall bo represented by It ; 

 then, by dynamics, Zyh will be equal to the square of the velocity of 

 impact. In like manner, let the friction of the wedge, estimated in a 

 direction parallel to CM, be represented by the weight of a parallele- 

 piped of iron whose base is the rectangular head of the wedge ; and 

 let the height of such parallelepiped be represented by Q. 



When the collision takes place, both the falling body and the wedge 

 will be compressed in the direction of their length. Let the linear 

 contraction of p be represented by p, and that of the wedge, supposed 

 at present immoveable, by o (both p and q coinciding in direction with 

 MC). Then if represent the modulus of clastieity (or the height of a 

 vertical column of iron, having a bane equal to the head of the wedge, 

 whose weight would, by the compression it causes, reduce the height 

 p or Q of the supposed masses of iron to zero) and the forces of com- 

 pression be assumed proportional to the contractions which they 



produce, we shall have and for the forces by which the falling 



body and the wedge are respectively compressed in consequence of 

 the collision; or the forces by which they tend to recover their 

 original state : let these be represented by mp and nq respectively ; 

 or, in terms of the force of gravity, by myp and 71.77. Then 11.77 will 

 represent the motive force by which the movement of the falling body 



is resisted after the impact, or -p- will represent the retardative 



force against that body. 



But from the equality of action and re-action wo havemp nj; 



mm 



whence j> , and p-tq, or the sum of the compressions, is equal 



WEEDS. * 



and integrating, v repreeenting the velocity at the instant of impact 

 at which time = 0, 



But when the wedge begins to move, the friction U equal to the 

 force by which the falling body is compressed ; therefore, making 4 



equal to ^^j (=?) we have - J^ * i which being substituted 

 in the above equation, wo have 



mp 



Now the wedge being uniformly resisted by friction, while moving 

 in consequence of the impact, the retardative force /, expressed hi 



times of gravity, will be p^J, w representing the weight of the 



wedge in terms homologous to P. Therefore since, by dynamics, 



S> ; if we represent the space through which the wedge moves hi 



he direction MC by z, we Jiave, on substituting for e* and / their 

 values, and for v* putting its equivalent 2</A, where A is the height due 

 'i the velocity v, 



' h fro + n) Q\ 



to 



- 3 : let this be represented by i ; then q 



nnjt 



** (T+ Tip' Now, by dynamics, accelcrative or retardative force la 



civ 

 represented by t> TJ , r here being the velocity of the falling body at 



any time I between the instant of impact and that at which its motion 

 it extinguished by the resistance : therefore 



n/c 



The values of m and n, that is, of - and - , may be found, since *, 



he modulus for iron, is known to be about 10,000,000 feet; an I 

 consequently the relation between z and <J can be determined in 

 numbers. 



WEDNESDAY. [WEEK.] 



WEEDS. Every plant which grows in a field other than that of 

 which the seed has been sown by the husbandman is a weed, and, 

 nasmuch as it interferes with the intended crop, should be car. 

 eradicated. One of the principal uses of summer fallows is to destroy 

 he weeds, which come up in spring, and which would shed their seed* 

 in summer, if they were not destroyed before the seeds ripen. Whin 

 roots ore sown in drills, and carefully hoed, they produce the same 

 cleansing effect, and supersede the fallow ; but in heavy loams which 

 lave been neglected and overrun with weeds, a clean fallow is some 

 iiines indispensable before any improved method can bo ad> 

 When a farmer enters on lands which are in a foul state, it is the 

 cheapest way, in the end, to sacrifice a crop, and thoroughly purge his 

 fields from weeds, especially those which have vivacious roots, and can- 

 not be extirpated by simple ploughing. The mode of doing this must 

 depend on the nature and duration of the weeds, whether their roots 

 are perennial or die off after the plant has borne seed. Annual 

 weeds are most readily extirpated by repeated harrowings, by winch 

 ;he seeds are brought within the influence of the atmosphere, and when 

 Jjey have fairly vegetated may be buried or rooted out, and by ex- 

 posing then- roots to the influence of a hot sun they are effectually 

 lestroyed. The seeds of annual weeds are chiefly brought on the land 

 in the manure which is made in the yards, where the cattle fed on hay 

 or straw swallow the seeds, which pass through them undigested. 

 They are also largely sown by the farmer himself in foul seed which 

 lie buys of the seedsman. 



One of the great advantages of straw, of artificial manures, and of 

 composts made with human excrements mixed with earths and mineral 

 substances, is that they introduce no weeds into the soil. It is re- 

 ported that in China, where the dung of cattle is little used, in com- 

 parison with human excrements, no weeds are to be found in the 

 fields; and if more attention were paid to the preservation of this 

 highly-enriching manure, and its proper application to the soil, much 

 expense would be saved which is now unavoidably incurred in destroying 

 weeds. Feeding sheep on roots and corn, while they are foldi-d 

 hind, is another mode of manuring a field without introducing weeds, 

 especially if no hay is given them, except clover-hay of the second crop, 

 which is generally most free from the seeds of weeds. 



Perennial weeds, such as various thistles, docks, &a, are very difficult 

 to eradicate, as the rooto strike deep in the ground, and throw up 

 fresh shoots every year. The most effectual mode of destroying tli.-M 

 is to draw them whenever the stem is grown sufficiently to give a good 

 hold of the crown of the root. 



Besides the common couch gran, ZViticum repent, which is the 

 pest of farmers on light soils, there are a variety of plants which spread 

 Uith liy the roots and by creeping along the surface. Of this kind aro 

 thi! tlillerent sort* of quitcha, as they are provincial!}' called, winch 

 firmv in wet soils. The only mode of extirpating these last is draining 

 and careful tillage. The most elToctual means of destroying common 

 couch is by the fork. If, after the ground has been once plough, d, it 

 bo forked up carefully in dry weather, and the tufts of c.>ncli with 

 their roots be exposed to the hot sun, they may be raked off and 

 burnt. 



There are many other weeds, both in arable anil pasture land, which 

 indicate slovenly culture, and which disappear on careful culth 

 such are briars, furze, broom, and rushes ; the last being a well-known 



