LESSONS IN CHEMIs 





TH TWI8TBD POLYGON. 



Th method of finding tho resultant of several forces 

 her they act all in the same plane, or 

 i thorn upwards or downwards from it in different 

 us, K>.r x:iini>lo, five forces, represented by tl. 

 o A, o B, o c, o D, o E, in Fig. 9, are thus applied to a ii'.int, 

 o of a body on tho floor of a room ; two of them, o A, o D, along 

 the floor in t ,vu different directions ; another, o B, pointing to a 

 it wall; a fourth, o C, to tho cross on the 

 a steeple, soon through tho open window ; and tho fifth 

 i:, obliquely downwards, pressing tho body against 

 or. On constructing, in such a case, tho polygon of 

 we should have the figure as represented in perspective 

 one of whoso sides, o A, is on the floor, while the others, 

 i ,. i:, R,, and R, R s , are in tho air. A figure of this kind 

 . tl ii ln-i-.ted polygon, as though its sides had been all 

 - ;imo plane, but, by a twist, some of them had 

 been pulled from it. Yon can 

 see that, since such a polygon 

 cannot bo drawn on paper, so 

 as to have the magnitudes of 

 its sides and angles there ac- 

 curately represented, it can be 

 of no practical use in finding 

 resultants. You might make 

 one by fastening five rods of 

 tlio proper lengths together at 

 tho proper angles, but tho 

 structure would probably break 

 down before you arrived at 

 your resultant, and at the best 

 the operation would be very 

 troublesome. Calculation alone 

 can help in such cases ; but 



the " twisted polygon " has tho educational value of giving the 

 student mechanical ideas. 



EXAMPLES FOR PRACTICE. 



1. Three forces act on a point o A, equal to 3 pounds, o B to 5, and 

 o c to 7. The second lies between the other two, making with o A an 

 angle of SO degrees, and with o c 45 degrees. Find the pounds in the 



't ant, and the angle it makes with tho least force o A. 



2. A roller of a hundred-weight is supported on an incline, the 

 gradient of which is one foot in two, by a force which acts along its 

 slope. Find tho magnitude of this force and the pressure of the roller 

 on the plane. 



3. From two points on a ceiling, five feet apart, a sixty-pound 

 weight is suspended by two strong cords, which meet at the point of 

 suspension. The lengths of the cords are three and four feet respec- 

 tively. Find the magnitudes of the forces by which they are strained. 



4. Three weights of three, four, and five pounds are attached to 

 three cords, which are knotted together at their other ends. The 

 two cords bearing the lesser weights are thrown over two pulleys 

 fastened at a distance of 10 feet from each other, and at the same 

 height, into a wall, the greatest weight hanging between them. Find 

 the position in which the cords und weights will settle into equi- 

 librium. 



You will observe that these problems are to be done by rule 

 and compass, etc. We have not yet come to the more effective 

 method of solving them by calculation. The geometric way, 

 however, of drawing and measuring is the best for giving you 

 accurate ideas of the subject, and therefore indispensable 

 in the first stages. The lines you must carefully lay 

 down by a ruler, and the angles by a circular protractor, 

 keeping in mind, as to the latter, that in every right 

 angle there are ninety degrees. The distances representing the 

 forces you must take from an ordinary scale ; and observe, as 

 to this, that you need not make in every case your drawings so 

 large that a whole inch be given to every pound of force. You 

 may allow a quarter of an inch to each pound, or hundredweight, 

 or ton, or even a tenth, if the numbers be large. All that is ne- 

 cessary is to keep the proportion of your figures right, whether 

 they be on a largo or a small scale, as is done in mapping or 

 drawing plans of buildings. For the above examples a scale 

 of a quarter of an inch for each . pound will be quite sufficient. 

 Perhaps for the third example tenths of an inch will best answer. 



In another lesson the answers to these problems will be 

 given. 



LESSONS IN CHI. -XVIL 



9f> 



'J.'.'-THJ: METALS. 

 BOUON (.SYMBOL, B; COMBINING AVtioHT, 11). 



BORON and silicon are often classed with carbon, for each of 

 those elementa is capable of being produced in three states 

 amorphous, crystalline, and crystallised. 



lenient boron is procured by the action of Bodium oa 

 borocio acid, thus 



B,O. + 6Na 3N,0 + 2B. 



Thus obtained it in a dull greenish powder, slightly soluble in 

 water, from which solution it is precipitated unchanged by sal- 

 ammoniac. It does not oxidise in tho air, but readily with nitric 

 acid. At a very high heat it takes fire, burning into boracic 

 acid (B,0,). 



Tho other two kinds of boron are exhibited by ita action on 

 melted aluminum. 



The crystals of boron are as hard as tho diamond. 



Boracic Acid (B 2 O S ). At Monte Cerboli and Monte Eotondo, 

 in Tuscany, exist " fumeroles," that is, jets of steam escaping 

 from tho ground. This steam is mixed with sulphuretted 

 hydrogen, but holds in solution free boracic acid. The vapour 

 is directed into email lagoons, where it is condensed, and upon 

 evaporating the water crude boracic acid is obtained, which is. 

 the chief source of tho borax of commerce. This acid combined 

 with soda is found in tho tincal from Thibet, and a borate of lime 

 and magnesia exists on the west coast of South America. 



Boracic acid imparts a green tint to the flame of alcohol. Its 

 great value lies in the fact that it imparts to its salts ready 

 fusibility ; hence in tho manufacture of porcelain and in metal* 

 lurgy borax is used as a flux. 



The crude boracic acid, procured as above, is really the 

 hydric borate or 3H 2 OB 2 O 3 , which is usually written H S BO S . 



Borax is the biborate of soda. 



Boric Chloride (BC1 3 ) is obtained by passing dry chlorine 

 through a red-hot porcelain tube containing a mixture of boracic 

 acid and charcoal. It is a gas which condenses into a mobile 

 liquid below 18 Cent. It is decomposed by contact with water, 



thus 



BC1} 



_ HJ BO, + 3IIC1. 



Boric Fluoride (BF 3 ) is procured by heating fluor spar and 

 boracic acid. It is a gas which combines with water, thus 



BF, + 3H a O = 3H,F BO,, 

 forming hydro-fluo-borio acid. 



Boric Sulphide (B 8 S,) is produced when boron is burnt m 

 sulphur. 



Boric Nitride (BN). Like titanium, boron combines with nitro- 

 gen at a red heat, forming a white powder, which has a " greasy " 

 feel. When melted with potash it becomes ammonia and boracio 

 acid, thus 



2BN + 3(H 9 OK:,O) = 3K,O + B,O, + 2NH,, 



and when heated in a current of steam it is resolved into 

 ammonium borate. 



SILICON (SYMBOL, Si; COMBINING WEIGHT, 28). 

 In combination with oxygen as silica, this element is one of 

 the chief components of the earth's crust. It may be isolated 

 by submitting a mixture of equal weights of potassium and tho 

 flnosilicate of that metal to a red heat in a platinum crucible. 

 Silicon and potassium fluoride are the result, and the latter w 

 washed out by water. 



Thus obtained, it is a brown amorphous powder. When 

 heated in oxygen it becomes silicic acid. 



No acid affects it except hydro-fluoric, by which action the 

 terfluoride of silicon is formed, as was noticed, in the etching 

 of glass. 



The " graphitoid " and crystal forms of silicon have been ob- 

 tained. 



Silicic Acid (SiO a , silica, or sflex). It corresponds in its com- 

 position to carbonic dioxide (C0 2 ). It is found pure in quarts, 

 when it appears as rock crystal ; it is nearly pure in flint, 

 chalcedony, agate, opal, etc., and it constitutes the main ingre- 

 dient of all sandstones. Silex can only be fused by the oxy- 

 hydrogen blow-pipe. Water has no action on it ; but with 

 steam at a high temperature, it seems to be dissolved. This 

 accounts for the concretions of silex in the throats of furnaces. 

 . r, it can be rendered soluble- If rock crystal be heated 

 to redness, and then suddenly cooled in water, it can be easily 



