1 7.2 case gives the saving equal to of the heat used, or fuel consumed in the common way. In a similar manner the saving may easily be calculated for any other value of t. The preceding investigation is founded on the assertion that the specific heat varies inversely as the temperature; and supposing such to be the case, the saving resulting from heating the steam to 600° after leaving the boiler would be about 4th of the whole fuel used. I shall next suppose that the specific heat does not vary with the temperature, but that during expansion a certain quantity of heat becomes latent, in which case the sum of the sensible and latent heats absorbed by the steam after leaving the boiler (its pressure being the same), multiplied by the specific heat, will give the actual quantity of heat added to the steam in very simple terms. From numerous experiments by Leslie and Dalton, on the heat or cold produced by air during, compression or expansion, Mr. Leslie has deduced the following very simple formula : If denote the density of the air, then 45 (¦; —0) - will denote the number of degrees of cold produced when the air is rarefied to unity, or it will represent the heat that requires to be added so as to keep the temperature unchanged during expansion. The latent heat of steam is about 1000°, wherefore the heat necessary to raise water from 60° into steam is 1000° + 152 1152°, Fahrenheit. Let us suppose, as before, that the steam after leaving the water at the temperature of 212° is heated to 600°, and at the same time that its pressure remains unaltered. As the specific heat of steam, as determined by the most accurate experiments, is 847, that of water being 1.000, the accession of heat necessary to raise steam from 212° to 600° would be 328° if there were no expansion or alteration of volume; for 1 388:847: 328. Supposing the steam to be allowed to expand as the law of expansion is part of its bulk at 32° for each degree of temperature (See Thomson on Heat, p. 9), 100 volumes at 212° become when heated to 600°=159 volumes. 100 159 =*629; therefore 45( *629 629 the heat absorbed by air during *6299 *629 =45( (629-401641) = 45 (598359) its expansion from 100 to 159 volumes, =26 025015 degrees. As the specific heat of steam, however, is greater than that of air, the heat necessary to maintain the temperature of steam during its expansion from 100 to 159 volumes will be 82°. For 2669: 26: 847: 82°; therefore the total heat required to convert 100 volumes of steam into 159 volumes is 1152° + 328° +82°=1562°, the pressure of the steam being supposed to be unaltered. To raise 159 volumes of steam in the common way would require 1831 68°. For 100: 1152::159: 1831 68°; wherefore 1831 68-1562= 270° the saving resulting from the expansion of the steam by heat after it has been generated, 1832÷270=; of the whole fuel used, instead of 7.2' = 1 6.7 as determined by the previous method. Expansion. We have already, at page 12., given some explanation of the principle of working an engine expansively, by which method we showed a large economy of fuel may be realised; and at page 25. we have given a table of hyperbolic or Neperian logarithms, for the purpose of facilitating computations upon this subject. Let the pressure of the steam in the boiler be expressed by unity, and let z represent the space through which the piston has moved whilst urged by the expanding steam. The density will then be and assuming that the dx densities and elasticities are proportionate, 1+ will be the differential of 1 1+x the efficiency, and the efficiency itself will be the integral of this, or, in other words, the Neperian logarithm of the denominator; wherefore the efficiency of the whole stroke will be 1+ Nep. log. (1 + x.) Supposing the pressure of the atmosphere to be 15 lbs., 15+3550 lbs., and if the steam be cut off at of the stroke, it will be expanded into four times its original volume; so that at the termination of the stroke its pressure will be 50÷4-12.2 lbs., or 2.8 lbs. less than the atmospheric pressure. When the steam is cut off at one fourth, it is evident that x=3. In such case the efficiency is 1+ Nep. log. (1+3), or 1+ Nep. log. 4. The Neperian logarithm of 4 is 1-386294, so that the efficiency of the steam becomes 2:386294; that is, by cutting off the steam at 4, more than twice the effect is produced with the same consumption of fuel; in other words, one half of the fuel is saved, CHAPTER IV. PARALLEL MOTION. THE forms of parallel motion which have been used are so various, that we shall not attempt to enumerate the whole. In what follows, however, we shall treat of those varieties that have been most commonly adopted in land or marine engines; and in doing so, it will be our object both to explain their principles of action, and give practical rules for calculating the lengths of the various parts in every assignable case. The forms of parallel motion that we shall discuss are four in number; one adapted to land engines, and represented in fig. 3; the others used for marine engines, and represented in figs. 4, 5, 6. It will be found that all these different arrangements act on the same fundamental principle; and therefore, before going farther, we shall proceed to explain it. Let G C and H F be two levers moving round centres at C and H, and connected together by the rod or link G F. We shall suppose that G C represents the beam of an engine standing in a horizontal position at half stroke. The rod H F represents the radius bar of the parallel motion, and at half stroke it must be horizontal, or parallel to G C. In the present case we shall suppose it to be equal to G C in length. If the beam be made to turn on its centre, so as to cause G to move towards G', the point E in the middle of the link G F will move upwards nearly in a perpendicular line R' S', bisecting the versine D K. This will be evident from the following considerations:- As the point G revolves in the circle G G', the point F revolves with nearly equal rapidity in the equal circle F F'. Both points, it is evident, will, when the motion commences, approach nearer the line R'S'; and since the circles F F' and G Gare of equal radius, and the arcs described are nearly equal, the point F will move towards the line R' S' at the same rate at the point G. Both points will cross that line at the same time, and both will respectively reach F' and G' simultaneously. F' L will evidently be equal to G' K. Now, if the points F and G are always on opposite sides of the line R' S', and at the same distance from it, it is clear that the centre of the link E must always be in it; and, accordingly, this would be mathematically true, if G F, by changing its inclination to the perpendicular, did not alter the perpendicular distance between the points F and G. This, however, it does; and as the points G and F ascend the link, G F gets more nearly perpendicular; thus increasing the perpendicular distance between G and F; in consequence of which, at the point where F crosses the perpendicular R' S', it has not described quite so large an arc as the point G; or, when F is crossing R' S', the point G is still at a small distance from it. This renders the motion of the point E not perfectly coincident with the perpendicular line; but the shortening of the perpendicular distance between G and F, by the vibration of the link G F, when the length of the link is considerable, and the stroke of the beam not greater, in proportion to its length, than usually obtains in steam engines, is so exceedingly small as to be unworthy of the slightest consideration in practice. At either end of the stroke the link G F will have the same inclination as at half stroke, and the point E will therefore be exactly in the perpendicular line R' S', at both these points. Its motion will be represented by the curved line R' OS', fig 7, cutting the perpendicular at R', O, and S', and deviating from it by an almost imperceptible quantity at X and W. From the fact, however, of a deviation being caused by the vibration of the link G F, we may infer the propriety of making that vibration as small as possible: and one very obvious precaution to be taken on this ground is, so to place the levers H F and G C at half stroke that the line R' S' shall bisect both their versines F L and D K. By this means the link G F vibrates equally on both sides of the perpendicular, and, consequently, never deviates from it so much as if it were to vibrate in one direction during the motion of G to G'. It is not always convenient to have the radius bar HF of the same length as the beam G C : it is sometimes longer, and sometimes shorter. In fig. 2 it is represented one half the length of G C. In this case, H F being shorter in proportion to the arc F FF, which it describes, the versine F L is of course greater than in the former case. The lever should still be so placed, however, that the line R' S' bisects its versine L F. Owing to the inequality of the versines L F and G K, the middle point of the length G F can no longer move in the line R' S'; but there is a point E, nearer the end of the link G, that does move nearly in this line. This point is so situated, that GE: EF::FHG C. For, within the limits usually assigned to the arcs de scribed by engine-beams, the versines are nearly in the inverse ratio of the radii; that is to say, vers. L F: vers. D K:: GC: HF. Now the vibrations of the points F and G on each side of the line R' S' are equal to half the versed sines of the arcs described by these points respectively; that is, to Ff and G g. Hence, F f: G g::G C:H F, and by similar triangles Ff: Gg::FE: G E; hence, FE : G E :: G C : H F. As this proportion holds true at any part of the stroke, it proves that the point E, which divides the link in this proportion, moves in the perpendicular line R S'. When, therefore, the lengths of the levers are given, it is easy to find the point E; but in practice it generally happens (as will be shown subsequently) that the point E is fixed: and we have to find H F. This will be G CEG FE done from this proportion, F E : EG:: GC: HF: (A). This proportion is founded on the assumption that the versed sines of the beam and radius bar are inversely as the radii. This, though nearly true, is not exactly so. The versed sines of the smaller radii increase in a greater proportion than the inverse ratio of the radii. The consequence of this is, that the point E in the link G F will be moved too much toward H, and will deviate from the perpendicular in that direction at each end of the stroke. In small engines, and when H F is nearly equal to G C, this deviation will be so small as scarcely to be worthy of notice; but in large engines, and when there is a considerable difference between the lengths of the radius rod and beam, it will be of some consequence. From what has already been said, it will be observed that the deviation is all on one side of the perpendicular; so that the curve described by the point E will be of the shape shown in fig. 8. By making a small addition to the length of the radius bar, we can make the deviation take place equally on each side of the perpendicular. We can add so much to its length as to make the point E move towards H too slowly at half stroke; or, in other words, deviate towards C till the beam has got about quarter stroke from the horizontal position, when the point E will cross the perpendicular, and deviate to an equal amount towards H. The curve described by E will then be of the shape shown in fig. 9, where the deviations at m, n, o, p, are all equal, and only half the deviation at r and s in the last figure. † To facilitate the making of this correction in the length of the radius bar, we give the following table of the amounts to be added to its length for the various proportions that may obtain between it and the beam C G. It is to be observed too, that when the radius bar H F is longer than the beam G C, these amounts are to be subtracted from its length. The beam of an engine is usually made at least three times the length of the stroke: so that the sine of the angle which it makes with the horizontal line at the extreme of its stroke, is equal to of the radius. The angle whose sine is of the radius, is 19° 28′. t Let G C r GGs, and arc GG G'; then G K=vers. ; but by Euclid (III. 35), G K (2 G C —G K )=(} Gʻ G2)2 ... vers. ♦ (2 r-vers. = 2... 2 r vers. =4 82+vers. 20 2 vers. = vers. ; or, r= vers. +vers. o s2 being a constant quantity, this equation shows that the radii are inversely as the versed 12 13 14 Inches. 644 693 ⚫737 776 825 .877 923 .968 1.04 1994 899 5.26 5.43 5.46 5 66 5.64 5 86 6:07 15 4.77 5-16 5.48 5.77 6:03 4.95 551 5.85 6.16 6.44 4 4 42 41 42 43 920 *021 ·023 024 *026 *027 *028 *029 *030 031 *032 032 033 034 034 035 *036 036 037 ⚫038 *038. 03 *039 040 040 C41 041 *042 *042 ⚫043 *043 ·043' ⚫014 048] *052 055 058 *060 *063 065 *067 069 071 073 074 *078 079 080 082 083 *084 *086 *087 ·038' *089 *090 *091 *693 .094 *095 *096 097 *098 *099 085 092 *097 103 107 111 116 119 123 •126 129 132 135 138 141 143 146 .148 •150 152 155 157 •159 •160 163 165 167 *103 170 172 174 175' 133 143 152 160 •168 •176 180 186, •192 197 *202 207 211 215 220 224 •227 2311 235 238 242 245 +248 251 254 257 260 *263 *266 *269 271 1911 206 219 231 241 251 *260 *268 276 284] 291 *297 *304) 510 316 322 •327 333 •3.8 •343 •343 -353 357 362 366 +371 .375 *379 *383 +387 391 261 281 298 314 32 34) 354 365 3-6 +386 +356 405 414 422 430 438 *446 •456] *460 *467 474 •480 486 •4.0 498 *504 510 5:6 521 340 +367 *390 •410 .429 •446 •462 *4771 491 504 517 529 540 551 562 *572 -582 592 600 610 619 *627 635 643 651 *659 *666 *674 •681 4311 464 *493 519 543 565 -585 604 621 *658 *654 669 *684 698 •711| -724 -7.7 749 760 772 783 *794 804 814 •824 *834 .843 853 532 -573 *609 611 670 697 .722 745 767 -788 808 826 844 .862 8.8 -894 910 *924 939 •953 966 98J *993 1.00 1.02 1.03 1.04 1.05 811 843 874 .902, 953 •977 1 00 1.04 1.04 1.06 1.10 1.10 1.12 1-14 1.15 1.17 1.19 1.20 1.22 1.23 1.25 1.26 •965 1.00 1:04 1.07 1.13 1:16 1-19 1.22 1.24 1.26 1.29 1.31 1.33 1.35 1.37 1.39 1.41 1.43 1:45 1.47 1.48 1.50 1:08 1.13 1-18 1.22 1.26 1.30 1.36 1:40 1-41 1.46 1.48 1.49 1-54 1.56 1-59 1.61 1.63 1.66 1.68 1.70 1.72 1.74 1.76 1 04 1-12 1..9 1.26 1:31 1.37 1:41 1:46 1:50 1.54 1.58 1.62 1.65 1.69 1.72 1.75 1.78 1.81 1.84 1.87 1.89 1.92 1.95 1.97 1.99 2.02 2.04 2.06 2.09 2.11 2-13 1:20 1.29 1.37 1.44 1.51 1:57 1-62 1.68 1.73 1.77 1.82 1-86 1.90 1.94 1.98 2.01 2:05 2.08 2-11 2:14 2.17 2.20 2.23 2.26 2.29 2-32 2.34 2-37 2.39 2.42 2:44 1.36 1.47 1.56 1.64 1-72 1.78 1-85 1.91 1.96 2.02 2-07 2-12 2.16 2.21 2.25 2.29 2-33 2.37 2.40 244 2-47 2.51 254 2.57 2.60 2-63 2-67 2.69 2-72 2-75 2-78 151 1.66 1.76 1-85 1.94 2.01 2:09 2.15 2-21 2.28 2.33 2.39 2:44 2:49 2.54 2.58 2.63 2.67 2.71 2.75 2.79 2.83 2.87 2.91 2.94 2.97 3.01 3.04 3:07 3.11 3.14 1.72 1.86 1.97 2.08 2-17 2.26 2.34 2:41 2.49 2.55 2-62 2.68 2.74 2.79 2.84 2.90 2.95 2.99 3.04 3.09 3.13 3:17 3.22 3.26 3.30 3.34 3.37 3:41 3.45 3:48 3.52 1.92 2.07 2.20 2.31 2-42 2.52 2.60 2.69 2.79 2.84 2.92 2.98 3.05 3.11 3.17 3.23 3.28 3.34 3.39 3.44 3.49 3.54 3.58 3.63 3.67 3.72 3.76 3.80 3.84 3.88 3.92 2:13 2.29 2:44 2.56 2.68 2.79 2.89 2-98 3.07 3.15 3.23 3:31 3.38 3.45 3.51 3.58 3.64 3.70 376 3.81 3.87 3.92 3.97 4.02 4.07 4.12 4.16 4.21 4.26 4.30 4.34 4.38 4:43 2:35 2.53 2.68 2.83 2.96 3:07 3.18 3.29 3.38 3.47 3 56 3.64 3.72 3.80 3.87 3.91 4.01 4.08 4.14 4.20 4.26 4.32 4.38 4:43 4.49 4.54 4.59 4.64 4.69 4.74 4.79 4.83 4.88 2.57 2-77 2.95 3.10 3.24 3.37 3.49 3.61 3.77 3.81 3.91 4:00 4.15 4.17 4.25 4.30 4.40 4.47 4:54 4.61 4.68 4.71 4.80 4.86 4.92 4.98 5.04 5.09 5.15 5.20 5.25 5.31 5.35 2:81 3.03 3.22 3:39 3:54 3.69 3.82 3.94 4.05 4.17 4 26 4:37 4.60 4.55 4.64 4.87 4-87 4.89 4.97 5.04 5.11 5.18 5.25 5.32 5.38 5.45 5.51 5.57 5.63 5.69 5.74 5.80 3.66 3.30 3.51 3.69 3.86 4.01 4.16 4.29 4-42 4.54 4.65 4.76 4.86 4.96 5.06 5.15 5.24 5.32 5.41 5.49 5.57 5.64 5.72 5.79 5.86 5.93 5.99 6.06 6-13 6.19 6.25 6.31 121 3:32 3.58 3.80 4.01 4.19 4.36 4.51 4.66 4.79 4.92 5:05 5.16 5.28 5:38 5:49 5.59 5.68 5.78 5.86 5.96 6.04 6.12 6.20 6.28 6.51 6:58 6.65 6.72 6-78 6.85 6.92 3.GO 3.87 4-12 4.33 4.53 4.71 4.88 5.04 5-19 5.33 5.46 5.59 5.64 5.82 5.94 5-97 6:44 6.53 6.62 6.71 6.80 6.88 6.96 7.04 7.12 7.19 7.27 7.34 7.41 7:48 7.55 134 3.88 4.18 4:44 4.67 4-88 5:08 5.59 5.74 5.89 6.02 6.16 6.28 6.40 6.52 6.6.3 6.74 6.84 6.95 7:05 7.14 7.24 7.33 7.42 7.50 7.59 7-67 7.74 7.84 7.91 7.99 8.07 8-14 8-21 8.28 4.17 4:49 4.77 5:03 5.25 5-84 6.01 6.18 6.33 6.48 6.62 6.75 6.88 7:01 7.13 7.25 7:36 7:47 7.58 7.68 7.78 7.88 7.98 8-07 8.168.25 8.34 8.43 8.51 8:59 8.67 8.75 8.83 8.91 144 4:47 4-825-12 5:39 6 27 6.45 6.63 6.79 6.95 7.10 7.26 7.38 7.52 7.65 7.77 7.90 8:01 8.13 8.23 8.34 8.44 8.54 8.65 8-75 8.84 8.94 9.03 9.12 9.21 9.29 9.38 9.46 9.55 6.71 6.90 7:09 7.27 7:44 7.60 7.75 7.90 8.05 8-19 8-32 8.45 8.58 8.70 8.82 8.93 9.05 9-16 9.26 9-37 9.47 9.57 9.67 9.77 9.86 9.96 10:05 10-14 10-23 6 94 7.16 7.37 7.57 7.76 7.94 8.11 8.28 8.44 8.59 8.74 8.88 9.02 9-16 9-28 9.41 9.55 9-66 9.78 9-89 10-02 10-13 10-22 10:34 10-44 10-541064 10-74 10-83 10.93 6.23 6.56 6.86 7.14 7.39 7-63 7.86 8.07 8.27 8-46 8.65 8.82 8.99 9.16 9.31 9.47 9-61 9.76 9-90 10-03 10-16 10-29 10:42 10:54 10-66 10-78 10-89 11-01 11-12 11-22 11:33 11:43 11-54 11-64 6.63 6.98 7.30 7.59 7.86 8.12 8.35 8.58 8.79 9.00 9-25 9:38 9.56 9.80 9-91 10-07 10-23 10-38 10-53 10-67 10-80 10-95 11:08 11-21 11:34 11-46 11:58 11-70 11-82 11-94 12:05 12:16 12-27 12:38 6:15 6 62 7.04 7.41 7.75 8.06 8-35 8-61 8.86 9.11 9.34 9.55 9-76 9-96 10-15 10-34 10-52 10-69 10-85 11-02 11-17 11:33 11:47 11-6211-76 11-90 12:04 12-17 12:30 12:42 1255 12-67 12-79 12-90 13-02 13-14 6:52 7-02 7:46 7.85 8.21 8.54 8.84 9-14 9.40 9.65 9 89 10-12 10:34 10-55 10-76 10-95 11-14 11:32 11:50 11-67 11-84 12:00 12-16 12-3112-46 12-61 12-75 12-89 13-03 13:16 13:30 13:43 13:55 13-6713-80 13.92 6.89 7.43 7.89 8.31 8.68 9.03 9.36 9-66 9-94 10-21 10:47 10-71 10-9411-17 11:38 11-59 11-79 11.98 12-17 12:35 12-53 12-70 12-86 13-03 13-19 13-34 13:49 13-6413-79 13-93 14-07 14-21 14:34 14:47 14.6 14.73 7 28 7.84 8.33 8-77 9-17 9-54 9-88 10-21 10-55 10-7911-06 11:32 11:56 11-80 12-03 12-25 12:45 12:66 12-87 13:05 13-22 13:40 13:58 13-7513-96 14:08 14-24 14:39 14-56 14-71 14-85 14.99 15 14 15 27 15:41 15:54 7.68 8.27 8.79 9.26 9-68 10:07 10-42 10-76 11-17 11:38 11-66 11.93 12-19 12:14 12-68 12-91 13-13 13:35 13:56 13-76 13-96 14-15 14:33 14:51 14-69 14-86 15.03 15-20 15:36 15:52 15-67 15.83 15-98 16:12 16-27 16:41 194 8:09 871 9.26 9-75 10-19 10-60 10.98 11-34 11-67 11.98 12-28 12-57 12-69 13-10 13-26 13:44 13.84 14:06 14-28 14:49 14.70 14-90 15:10 15:29 15:48 15-66 15.84 16:01 16-18 16:35 16:51 16-67 16.83 16.98 17-14 17:28 8.51 9-17 9-74 10-2610-72 11-15 11:55 11-92 12-27 12-60 1292 13-22 13:51 13-7914-05 14:31 14:55 14-79 15:02 15-25 15:46 15.68 15-88 16:08 16-28 16:47 16 66 1684 17-02 17-20 17:37 17-54 17.70 17-86 18-02 18-18 204 8.94 9 63 10-24 10-7811-26 11-72 12-13 12-53 12-89 13 24 13-65 13-89 14-35 14-48 14-86 15-19 15:29 15:54 15-78 16-02 16-25 16:47 16-69 1690 17-11 17:30 17-50 17-69 17-88 18-07 18:25 18:42 18.60 18.78 18-94 19-10 9:38 111 10-89 11-31 11-82 12-29 12.73 13-14 13-53 13.90 14-25 14:58 14.89 15:20 15:49 15-77 16:04 16:31 16:56 16.81 17-05 17:28 17:51 17-73 17-94 18-16 18:36 18-5718-77 18.96 19-15 19:3419-52 19-69 19 87 20-05 9 83 10-59 11:26 11:85 12-29 12-89 13-35 13-78 14-19 14:57 1486 15-2815-46 15 93 16:14 16:37 16-82 17.09 17:36 17.62 17-87 18-12 18-35 18-59 18-81 19-03 19-25 19:46 19-67 19-87 20:07 20-26 20:46 20-61 20-83 21-01 10:30 11:09 11-79 12:4112-97 13:49 13 98 14-43 14-85 15-25 15-63 16-0016-62 17.08 17:30 17-59 17-65 17-90 18 18 18-45 18-71 18.96 19-22 19-46 19-70 19-93 20 16 20-38 20-60 20-81 21-01 21-22 21:42 21-62 21 81 22.00 10-77 11-60 12-33 12-9513-57 14-12 14-62 15-1015-54 15-96 16-35 16-73 17-10 17 45 17-78 18-11 18:42 18-72 19-01 19:30 19-57 19.84 20-10 20-3620-60 20-85 21-08 21-3221-54 21-76 21-98 22-202240 22 61 22-81 23-01 11-25 12-12 12-88 13:56 14-18 14-75 15-28 15-77 16-22 16:67 17-05 17:49 18:40 18-23 18:58 19:49 19-25 19:56 19-87 20-17 20-45 20-73 21-01 21-27 21-53 21-79 22:04 22-27 22:51 22-74 22-97 23-19 23:41 23 63 23-83 24-05 1175 12 66 13:45 14:16 14-80 15:40 15-95 16-46 16-92 17:40 17.76 18-25 18-73 19-03 19:40 19-90 20-10 20-42 20-74 21-05 21-35 21-64 21.93 22-21 22-48 22-74 23-00 23-25 23:50 23-74 23-98 24-21 24 44 24 67 24-88 25-10 12:26 13-20 14:03 14.77 15:44 16-06 16-63 17-17 17-67 18:15 18-61 19-0419-45 19-85 20-23 20-60 20-95 21:30 21-63 21-95 22-27 22:57 22-87 23-16 23-44 23-72 23.99 24-25 24-51 24-76 25 01 25 25 25 49 25 73 25-96 26-18 12-77 13-76 14-62 15:39 16-09 16:73 17-33 17-89 18 44 18-92 19-47 19-8420-20 20-69 21-09 21:32 21.84 22-20 22:54 22-87 23-21 23-52 23-83 24-1324-43 24-72 25 00 25-2725-54 25-81 26-06 26-32 26.56 26-81 27-05 27-28 13:30 14:32 15-22 16:02 16.75 17:42 18:05 18.63 19.18 19-70 20-19 20-66 21-11 21-54 21-95 22-35 22-74 23-11 23:47 23-82 24 16 24 49 24-82 25-13 25 44 25-74 26-03 26-31 26 59 26 87 27-14 27-40 27-66 27-92 28 16 28:41 13.84 140 15 84 16-67 17:43 18-13 18-78 19-38 19-83 20-49 21-01 21-4921-96 22-41 22-84 23-26 23-66 24 04 24 42 24-78 25-14 25-49 25-82 26-15 26-46 26-77 27-08 2738 27-67 27-96 28-24 28:51 28-78 29-04 29 30 29-56 14:39 15 49 16:46 17:33 18-12 18-85 19-52 20-15 20-75 21:31 21.84 22-3522-56 23-30 23-75 23-89 24.60 25 00 25 39 25-76 26 14 26:49 26-84 27-18 27-51 27-83 28-15 28-46 28-78 29-06 29-35 29-64 29-92 30 19 30-46 30-72 14.94 16:09 17-10 18 0: 18-82 19-58 228 20-93 21-60 22-14 22-68 23-21 23-18 24-20 24 67 24-55 25-56 25-97 26-37 26 76 27-16 27-53 27 89 28-24 28-59 28-92 29-25 29-58 29-88 30 20 30-50 30-80 31-10 31-37 31-65 31-93 15:51 16 71 17-75 18-69 19:54 20-32 21-05 21-73 22-37 22-97 23-55 24-1024-62 25-12 25-61 26-07 26-52 26-96 27-38 27-79 28-18 28-57 28-95 29-31 29-67 30-02 30-96 30-70 31-02 31-34 31-66 31.96 32-26 32-56 32-85 33-14 16:09 17:33 18 42 19:39 20-27 21-08 21-84 22-55 23-07 23-82 24-43 25-00 25-58 26-06 26 56 27-02 27.50 27.97 28-40 28-83 29-24 29-64 30-03 30-41 30-78 31-14 31-50 31-84 32-18 32-51 32-83 33 16 33:47 33 78 34:07 34-38 16:68 17-97 19-09 20-10 21-02 21-86 22-64 23-37 24-06 24 71 25-33 25-91 26-48 27-02 27-54 28-04 28-52 28-99 29-44 29-89 30-31 30-72 31-13 31-52 31.90 32-28 32 65 33-01 33-36 33 70 34-04 34-37 34 69 35-01 35-33 35-64 17:28 18-6219-78 20-83 21 77 22-65 23:45 24-21 25-12 25-6 26-24 26-85 27-43 27-99 28-53 29-05 29-55 30-04 30-51 30-96 31-40 31-83 32-25 32-66 33-06 33 45 33-82 34-20 34 56 34-92 35 27 35 61 35-95 36-28 36 60 36-92 17-89 19-27 20-48 21:56 22-54 23:45 24-28 25-07 25-81 26-50 27-17 27-80 28-41 28-98 29-54 30-08 30-60 31-10 31 59 32-06 32-48 32-92 33-35 33-78 34 18 34 58 34-98 35-37 35 79 36 11 36-48 36-83 37-17 37-50 37-85 38-18 18:52 1955 21-19 22-31 23-33 24-21 25-12 25-94 26-50 27-43 28-11 28-77 29-40 29-99 30-57 31-12 31-66 32-18 32-68 33 17 33-64 34:09 34 54 34-985-40 35-82 36-23 36.63 37 03 37-40 37-78 38:14 38-50 38-85 39-20 39-54 19:15 20 6321-92 23-08 24-13 25-0925-99 26-83 27-62 28-36 29-07 29-75 30-40 31-02 31-61 32.19 32-74 33-28 33-80 34-31 34-80 35-27 35-74 36-19 36 63 37 (6 37-48 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135-0136-3 137.5 138 7 G6-72 71-88 76:38 80-41 84-07 87:43 90-55 93:48 96 23 98 84 101-30 103-6 105-9 108-0 110-1 112-2114-1116-0 117-8 119-5121-2 122-9 124-5 126-1127-6 129-1 130-6 132.0 133.4 134-8 136.2 137.5 138-8 140-0 141-3 142-6 67-92 73-17 77-75 81-85 85-58 89-00 92-17 95-17 98-36 100-6 103-1 105.5 107-8 110 1121 114.2116.9 1180 119-8 121-6123-4 125 1 126 7 128-3129-9 131.5 133-0 134.4 135-8 137-2 138 6 139-9 141-3 142-5 143-8 145.1 69-13 74-46 79-13 83-30 87-10 90-58 93-80 96-86 100-49 102-4 104-9 107-4 109-7 1120 1141 116-2 18-2 1201 122-0 123-8 125-6 127-3 129-0 130-6 132-2 133-8 135.3 136.8 138-2 139-7 141-0 142-4 143-8 145 1 146-4 147-6 70-35 75-78 80-53 84-77 88-64 92-18 95-47 98.56 101-8 104-2 106-7 109-3 1116 1139 1161 118-2 120-3 122-2 124-2 126-0127-8 129-6 131-3 132.9 134-6 136-2 137-7 139-2140-7 142-2 143-5 144 9 146-3 147-7 148.9 150-3 71-58 77-10 81-93 86-25 90-18 93-79 97-14 100-27 103 2 106-0 108-61112 113-6 115-9 118-2 120-3 122-4 124-4 126-3 128-2129-9 131-7 133-4 135 1 136-7 138-3 139-9 141-5 1431 144-4 145-9 147-3148-7 150-0 151-4 152-7 72.82 78:44 83:35 87.75 91-75 95-31 98-81 102-0 104-6 107-8 110-5 113.1 1156 117-9 120-2 122-4 124-5 126-5 128-5 130.4 132.3 134.1 135-9 137.7 139-3 141-0 142-6 144-1145-7 147-2 148-61501 151-5 152-9 154-3 155.6 74:06 79-78 84-78 89-25 93-32 96-83 10:48 103.7 106 0 109 7 1124 115-01176 119-9 122-2 124.5 126.6 128.7 130-7 132.7 134-6 136-4 138-2 139-9141.6 143-3 144-9 146-5148-1 149-6 151-1 152-6 154-0 155 4 156:8 158.2 75-33 81-14 86 23 90-77 94-91 98.6 102-2 105.5 108.2 111-5 114.3 117 1196 122-0124-3 126-6 128-3 130-9 132-9 134.9 136-9 138-7 140-5 142-2 144 0 145-7 147-4 149-0 150-6 152-2 153.7 155-2 156-6 158.1 159-5 160-9 76-60 82-51 87-68 92-30 96-50 100 37 103-9 107-3 110-4 113-4 116-3 119-0 121-6 1241 126:4 128.7 131-0 133-1 135-2 137-2 139-2 141-1 142-9 144-7146 5 148-2 149-9 151 6 153-2 154-8 156-3 157-8 159-3 160.8 162-2 163-6 77-88 83-89 89-15 93-85 98-12 102-0 105-6 109-1 113-3 115-3 118.2 121-0123'6 126-1 128.5 130-9 133-2 135-8 137-4 139-4141-4 143-3 145 4 147-2149 0 150-7 152.5 154-2 155-7 157-4 158-9 160-5162-0 163-6 165 0 166:4 79:17 85-28 90-63 95-40 99-75 103-7 107.4 110-9 114-2 117-2 120-2 123:0 125-6 128-2 130-7 133-1 135-4 137 6 139-7 141-8143-9 145-9 147-9 149-7 151-6 153-3 155-1 156-8 158-3 160-1 161-7 163-3 164-8 166-4 167-8 169-2 80:46 86-69 92-13 96-99 101-39 105-46 109-2 112-8 116-1 119-2 122-9 125-1 129-2 130-4 133-8 136-8 137-7 139-9 141-9 144.0 146-2 148-3 150-3 152.1 154-0 155-7 157-5 159-3161-0 162-7 164-3 165-8 167-4 169-1 170-5 171-9 81-79 88-10 93-62 98-56 103-04 107-17 111:00 114-59, 117-96 121-14 124-18 127-07 129-81 132-48 135-03 137-49 139-86 142-14 144-37 146-52 148 6 150-8 152-8 154.7 156-7 158-4 160-3 162-0163-6 165-4 167-1 168-7170-3 171-9 173-4 174-8 83-12 89-32 95-14 100 16 104-37 108-8 1128 116-4119 8 123-06 126-2 129-1 1319 134 5 137-2 139.7 142-1 144-4 146-9 148.9 151-0 153-1 155-2 157-1159-1 160-9 162-7 164-5 166.6 168.0 169-7 171-3 172-9 174-5 176-1 177.6 84-45 90-97 96-67 101-76 106-40 110-66 114-62 118-31 121 80 125.08 128-22 131-20 134-05 136-78 139-42 141-96 144-40 146-77 149-06 151 29 153-4 155-5 157-6 159-6 161-5 163-4 165 2 167 1168.9 170-6 172-3 174-0 175-6 177-2 178-8 180-4 85-8 92:41 98.20 103:39 108 2 1125 1164 120 2 123-7 127 0 130-2 133-21361 138-9 141-5 144 0 146-7 149-0 151-44 153-7 155-9 158 0 160-1 162-1164-1 166-0 167-9 169-7 171-6 173-3 175.0 176.8 178-4 180-0 181-7 183.3 87.15 93-88 99-84 105-02 1100 114-2 118-3 122-1 125-7 129-1 132-3 135-4 138 3 141-2 143-9 146-5149-0 151-4 153-82 156-13 158-4 160-5 162-6 164-7166-7 168-7 170-6 1724 174-3 176-1 177-8 179-6 181-3 182-9 184-6 186-2 88-52 95-25 101-37 106 6 111-6 116-0 120 1 123-9 127-5 131-1 134-3 137-5 1404 143-3 146-1 148-7151-3 153-8 156-24 158-5160-8 162-0 165-2 167-3169-3 171-3 173-2 175-1177-0 178-8 170-6 182-4184-1 185-8 187-5 189-1 89-90 96-84102-90108-3113-2 117-8 122.0 125.9 129 6 1331 136-5 139-6142-7 145-6 148-40 151-1 153.7 156-2 158-66 161-04 163-3 165-6 167-8 169-9 172-0 174-0 175-9 177-9179-8 181-6 183-4 185-2187-0 188-7 190-4 192-0 91-29 98-31 104-5 110-0115 0 119-6 123-8 127-8 131-6 135 1 138-6 141-8145 0 147-9 150-7 153-4 156-0 158-6 161-1 163 5 165-8 168-1 170-4 1725 1746 176-7 178-6 180-6 182-6 184-4 186-2 188-1 189-9 191-6 193-3 195-0 92-68 99-79106-1111-7116-8 121-5 125-8 129-8 133.6 137-3 140-7 144-0147-3 150-2 153 0 155.7 158.5 161-1 163-60 166-0168-4 170-7 173-0 175-1177-3 179-4 181-4 183-4 185-4 187-2 189-1 191-0192-8 194-6 196-2 198-0 94.09 101 3 107-7 113-3118 5 124-3 127-7 131-8135-6 139-3 142-8 146-1 149 4 152-3 155.3 158.1 160-9 163-5 166-1 168 5 171-0 173-3 175-6 177-8 180-0 1821 184-2 186-2188.2 190-1 192-0 193-9 195-7 197-5 199-2 201-0 95.51 1029 109-3 115-1120-3 125-2 129-7 133-8 137-6 141-4 145 0 148-3151-5 154-7 157 7 160-5 163-3 166-0 168-6 171-1 173-6 1760 178-2 180-5 182-7 184-9 187-0 189-0191 0 193-0 195 0 196-8 198-7 200-5 202-3 204.1 96-95 104 4 110-9 1168 1221 127-1 131-6 135 8 139-7 143-5 147-2 150-5153-8 157-0 162-4 162 9 167-7 168-5 171-1 173-6 176-2 178 6 180-9 183-2 185-4 187 6 189-8 191-8 193-9 195-9 197-9 199-7201-6 203-4 205-3 207.1 98.4 1.60 112-6 118-61239 129-1 133-6 137-8141-8 145-7 149-4 152-8 156 2 159-4 162-4 1654 168-2 171-0 173-6 176-2 178-8 181-3 183-6 185-9 188-2 190 4 192-6 194-7196-8 198-8 200-8 202.7 204-6 206-4 208-3 210-2 999 107 5 114-2 120-3125-7 131-1 135-6 139-8 143-9 147-8 151-4 155 1 158.5 161-7 164-8 167-8 170-7 173-5 176-2 178-8181-4 183-9 186-3 188-6 191-0 193-2 195-4 197-6 199-7 201-7 203-7 205-7 207-6 209-5 211-4 213-2 101-3 109-1115-9 122-0127-6 133-0 137 5 141-9146.0 1500 153-4 157-4 160-6 164 0 167-2 1713 173-2 1760 178-8 181-5 184-0 1866 189-0191-4193-8 196-1 198-3 200-5 2026 204-7 206-7 208-7 210-7 212-7 214-5 216-4 1028 1107 117-6 123 8 129-4 134 8 139-3 143-7 148-2 152-2 157-8 159-7 163-0 166-4 169-6 173-2 175-7 178-6 181-4 184.1 186-7 189.3 191-8 194-2 196-6 198-9 201-1 203-4205-5 207 6 2097 211-7 213-7 215-7 217-6 219.6 104-26112-3 119-3 125-6131-3 136-6 141-5 146-0 150-4 154-4 158-3 162-0165-5 168 8 172-1 175 2 178-2 181-2 184-0 186-8189-4 192 0 194-6 197-0199-4 2017 204-0 206-3 208-5 2106 212-8 214-8 216-8 218-8 220-8 222-8 105-8 113-9 121 0 127-4133-2 138-5 143-5 147-1 152-6 156 6 160-5 164-3 167-7 171-2 174-5 177-2180-8 183-8 1866 189-4192-1 1958 197-4 199-8202-3 204-6 207-0 209-3211-5 213-6 215-8 217.9 219-9 222-0 224-0 226-0 107-2 115.5 122-8 129-2 135-1 140-5 145-6 150-3 154-8 158-8 163-2 166-6169 4 173-7 177-0 180-2 183-4 186-4 189-3 192-1194-9 1976 200-2 202-7 205-2 207-6 210-0 212-3 214-5 216-7 218-9 221 0 223.1 225.2 227.2 229-2 108-7 117 1 124-5 131-0137-0 142-7 147-6 152-4 158-9 1611 165-3 169-0172-2 176-1 179-5 182-8 186-0 189-0192-0 194-8 197-6 2004 203-0 205-5208-1 210-5 212-9 215-2217.5 219-7 222-0 224 1 226-2 228.3 230-4 232-4 110-3 118-8 126-2 132-9 139-0 144-5 149-7 154-5 159-1 163-4 167-4 171-4 175 1 178-6 182-1 185-4188-6 1917 1947 197 6 200-4 203 2 205-8 208-4 211-0 213-5 215-9 218-2220-6 222-8 225-1 227-3229-4 231-5 233-6 235-6 111-8 120:4 128-0 134-7 140-9 146-5 151-8 1561161-1 165-6 169-6 173-7 1774 181-1 184-6 188.5 191-2 194-4 197-4 200-3203-2 206'0 208-7 211-3 214-1 216-4 218-9 221 2223-7 225-9 228-2 230-4 232-6 234-7 236-8 238.9 113-4 122-1129-8 136-6 142-8 148-6 153.9 158.8 163-2 167.9 171-8 176-1 179-8 183-6 187.2 191-7 193-9 1971 200 1 203 1 206-0 208 8 211-6 214-2 217-2 219-4 221-9 224-3 226-8 229-1 231-4 233 6 235 8 238 0 240-1 242-2 114.9 123-8 131-6 138-5 144.8 150 6 156-0 161 0 165-5 170-2 174-2 178.5 182-6 186-2 189-8 194-0 1965 199-8 202-9 205-9 208-8 211-6 214-4 217-1 220-3 222-3 224-9 227-3 229-9 232-2 234-5 236-7 116.5 125-5 133-4 140-4 146-8 152-6 158 1 163-3 167-9 172-6 176-7 181-0185-4188-8 192-4 196-4199-2 202-6 205-7 208 8 211-6 214-5 217-3 220-0 223-4 225-3 227-9 230-4 233 0 235-3 237-6 239-9 242-2 244-4 246 6 248-7 118-1 127 3 135-2 142-4149-8 154-7 160-2 166-6 170-6 174-9 179-3 183-4187-4 191-4 195-0 198-9 201-9 205-2 208-4 213-5 214-5 217.5 220-4 223-3226 0 228 4 231 1 233-6236-2 238-6 240-9 243 3 245-6 248 0 250-0 252-3 119-7 128-9 137-0 144-2 150-8 156-8 162-4 167-7 172-6 177-3 181.7 185-9 1900 193-8 197-6 201-2204-6 208-0 211-2 214-4217-4 220-5 223-3 226 2229-0 231-6 234-2 236.8 239-4 241-8 244-2 246 6 218-9 251-3 253-4 255-7 120-3 130-5 138.8 146 0152-8 158-9 164-6 169.9 174-6 179-6 184-1 188-4192-5 196-4 200-2 203-9 207-3 210-8 214-0 217-3220-3 223-5 226-3 229-2 2320 234-8 237-3 240-0 242-6 245-0 247-5 249-9 252-2 254-6 256-8 259-1 122-9 132-4 140-7 148 1 154-8 161-0 166-8 172-2178-6 1820 186-6 190-9 195-0 199-0 202-9 206-6 2101 213-6 2169 220-2 223-3 226-4 229-4 232-2 235 1 237-8 240-5 243-2 245-8 248-3 250-8 253-2 255-6 258 0 260-2 262-5 124-5 134 1 142-5 149-0 156-8 1631 1690 174-5 180-6 1844 189-0 193-4197 6 201-7 205-2 208-8 212-9 216-4 219-7 223 1 226-2 229-4 232-4 235-3238-2 241-0 243-7 246-4 249-0 251-6 254 1 256-5 259-0 261-4 263-6 265-9 126 1 135-9 144-4 152-0 158-9 165-3 171-2 176-8 182-7 186-9 191-5 196-0 200-2 204-4 207-5 210-8 215-8 219-3 222-7 226-0229-3 232-4 235-4 238-4 241-4 244-2 246-9 249-7 252-3 254-9 257-5 260-0 262-4 264-8 267.2 269-5 127-7 137 6 146-3 153-5 161-0 167-4 1734 179-1 184-7 188-4 194-0 198-5 202-8 207-1 209-8 212-9218-6 2221 225-5 228-9 232-2 235-4 238-5 241-5244-5 247-3 250-1 252-9 255-6 258-2 260-8 263-3 265-8 268-2 270.7 273-0 129-4 139-4 148-2 156-0163-1 169-6175-6 181-4 186-7 1918 196-5 201·1 205-4 209-7 2121 215.0 221-4 225 0 228-5 231-9235-2 238-4 241-6 244-6247 6 250-5 253-4 256-2258-9 261-6 264-2 266-7 269-2 271.7 274-2 276.5 131-1 141 2 150-1 158-0165-2 171-7 1779 183-7 189-2 194-2 199-0 203-7 208 0 212-4 215-3 218.5 224-2 227-9 231-4 234-9238-2 241-5 244-7 247-8 250-8 253-7 256-7 259-5262-2 265-0 267-6 270-2 272.7 275-2 277-7 280-1 132-8 143 0 152-0 160-0167-3 174-0 180-2 186-1 191-6 196-7 2016 206-3 2106 215:1 218-5 222-0 227 1 230-8 234-4 237-9 241-3 244-6 247-8 251-0 254-0 257 0 260-0 262-8 265-6 268-4 271-0 273-7 276-2 278-8 281-3 283-7 134-5 145-8 153-9 162-0 169-4 176-2 182-5 188-4 194-0 199-2 2041 208-9 2133 217-8 221-6 225-9 229-9 233-7 237-4 240-9 244-3 247-7 250-9 254-1 257-2 260-2 263-3 266-1268-9 271-8 274-4 277-1 279-7 282-3 284-8 287-3 136-2 146 7 155-8 164.1 171-6 178-4 184-8 190-8196-4 201-7 206-7 211-52161 220-6 224-8 229.9 232-8 236-6 240-4 243-9 247-4 250-8 254-1 257-3 260-5 263-5 266-5 269.5 272-3 275-1 277-9 280-6 283-2 285-8 288-4 290-9 137.9 148 5 157-8 166-1 173-7 180-5 187 1 193-2 198-8 204.2 209-3 214-2 218-8 223-3 227-6 232-2 235-7 239-6 243-4 247-0 250-5 254-0 257-3 260-5 263-8 266-8 269-8 272-9275-7 278-6 281-4 284 0 286-8 289-5 292-0 294-6 139-6 150-4 159-8 168-2 175-9 182-6 189 4 195 6 201-3 206-8 211-9 216-9221 6 226-1 230-5 24.6 238-7 242-6 246 4 250-1253-7 257-2 260-5 263-8 267-1 270-2 273-2 276-3 279-2 282-1 284-9 287-7 290-4 293-2 295-7 298-3 141-3 152-2 161-8 170-3 178-0 184-8 191-8 198-0 203-7 209-3 214-6 219-5 224 2 228-9 234-1 238-8 241-6 245-6 249-4 253-2 256-8 260-3 263-7 267-1 270-4 273-5 276-6 279-7 282-6 285-6 288-4 291-2 294-0 296-8 299-3 302-0 143-0 1541 163-8 172-4 182 187-2 194 2 200-4206-2 211-9 217-3 222-2 226-9 231-7 237-8 241-2 244-6 248-6 252-5 256-3260-0 263-5 267 0 270-4 273-8 276-9 280-0 2831286-1 289-0 292-0 294-8 297-6 300-5 303-0 305-7 144-8 1560 165-8 174-5182-4 189-6 1966 202-9 2 8.8 214-5 220-2 224-9 229 5 234-4 240-3 245-3 247-6 251-7 255-6 29-4 263-2 266 7 270-3 273-5 277-1 280-4 283-4 286-8 289-6 292-6 295 6 298 4 301-2 304-5 307-5 309-4 146 6 157 9 167-8 176-6 184-6 1920 1989 205-4211-42171 223-1 227-7 233 9 237-4 242-8 247-7 250-6 254-8 258-8 262-6 266-4 270-0 273 6 276-7 280-3 283-9 286-9 290-5293-1 296-2 299-2 302-1 304-9 308-5 312-1 313.2 148-4 1598 169-8 178-7186-8 194-3 2013 207-9 213-9 219-7 225-5 230-4236 1 240-2 245-3 250-0 253-6 257-9 261-9 265-8 269-6 273-2 276-9 280-2 283-7 287-2 290-3 293-8296-6 299-8 302-8 305-7308-5 311-7 315-0 317-0 150-1 1617 1718 180-9 189-1 196-7 238 210-3 216-5 222-4 227.9 233-2238 3 243-2 247-8 252-3 256 7 260-9 265-0 269 0 272-8 276-5 280-2 283-7 287-1 290-5 293-8 297-1 300-2 303-3 306-4 309-4 312-2 315-0 317-9 320-8 151-9 1636 173-9 183-0 191-4 199-0 206 2 212-8 219-1 225-1 230-3 236-0 240 5 246-1 250-4 254-7 259-8 264 0 268-2 272-2 276-0 279-8 283-5 287-1 290-5 294-0 297-3 300-6 303-8 306-9 310-0 313-1 316-0 318-8 321-7 324 6 153-7 165 6 176 0 185-2 193-7 201-4 208 6 215-4 221-8 227-8 232-8 238-8 2428 249-0 253-0 257-2 262.9 267-2 271-4 275 4 279-3 283-2 286-9 290-5 294-0 297-5 300-9 304-2 307 4 310-6 313-7 316-8 319-8 322-6 325-6 328-4 155-5 167 5 1780 187-4 195-9 203-7 211-1 217-9224-4 230-4 235-3 241-62451 251-9 255-6 259-5 266 0 270-3 274-6 278-6 282-6 286-5 290-3 293-9 297-5 301 0 304-4 307-8311-0 314-3 317-4 320-5 323-5 326-4 329-4 332-3 157-4 1695 180-1 189-6198-2 206-2 213-6 220-4 227-0 233 1 237-8 244-5 247 4 254-8 258.2 261-9 269-1 273-5 277-8 281-9 286-0 289-8 293-7 297-4 301-0 304-6 308-0 311-4314-7 318-0 321-1 324-3 327-3 330-3 333-3 336-2 159-1 171-5 182-1 191-8 200-6 208-6 2161 223 0 229-6 235-8 241-7 247-3 252-6 257-8 262-7 267-6 2721 276-7 280-9 285-2289-4 293-2 297-0 300-9 304-4 308-0 3114 315-7 318-4 321-5 325 0 328 0 331-0 334-5 337-1 340-2 161-0 173-4 184:3 194-0202-9 2110 218-6 225-6 232-2 238.5 244-5 250-2 255 6 260-8 265-8 270-7275-4 279-9 284-2 288-5 292-7 296-6 300-5 304-4 308-0 311-6 315-1 318-7 322-1 325-3 328-7 331-8 334.9 338-3 341-0 344-1 162-9 175 4 186-4 196-2 205 2 213 4 2211 228-2 234-6 241-2 247-3 253-1258 6 263-8 268.9 273-8 278-5 283-1 287-5 291-8 296-0 300 0 304-0 307-9 311-6 315-2 318-8 322-4 325-8 329-1 332-4 335-6 338-8 342-1 344-9 348-0 164-8 177 5 1886 198-5 207-6 215-9 223-6 230-8 237-5 244 0 250-2 256-0 261-6 266-9 272-0 277-0281-7 286-4 290-8 295-2 299-4 303-5 307-5 311-4 315-2 318-9 322-5 326-1329-5 332-9 336-2 339-5 342-7 345-9 348-9 352-0 166-7 179 5 190-7 200-8 209-9 218-3 226-1 233-4 240-1 246-8 253 0 258-9 264-6 269-9 275-1 280-1 284-9 289-6 294-1 298-6 302-8 307-0 311-0 314-9 318-8 322-5 325-7 329-8 333-2 336-7 3401 343-4 346-6 349-8 352.9 356-0 168-5 181-5 192-9 203-1212-3 220-8 228-7 236-1 243-0 249-6 255-9 261-8 267-6 273-0 278-2 283-3 288-2 292-9 297-5 302-0306-3 310-5 314-6 318.5 322-4 326-2 328-9 333-6 337-0 340-6 344 0 347-3 350-6 353-8 356-9 360-1 170-4 1835 195 1 205-4214-7 223.3 231-3 238-7 215-8 252-4 258-8 264-7270-6 276-1 281-3 286-5 291-4 296-2 300-8 305 3 309-7 313-9 318-1 322-1 326 0 329-9 333-1 337-3340-8 344-4 347-8 351-2 354-6 357-7 360-9 364-1 172-3 185 6 197-3 207-7 217-1 225-8 233-9 241-4248-6 255-3 261-7 267-7273 6 279-2 284-5 289-7 294-7 299-5 304-2 308-7 313-2 317-4 321-6 325-7 329-7 333-6 337-3 341-1344-7 348-2 351-7 355-2 358-5 361-8 365 0 368-2 174-2 187-7 199-5 210-0219-5 228-3 236-5 243-1 251-3 258 1 264-4 270-7276-5 282-3 287-7 292-9298-0 302-8 307-6 312-2 316-7 321-0 325-2 329-3 333-4 337-3 341-1 341-9 348.5 3521 355 6 358 1 362-5 365-9 369-1 372-3 176-2 189-8 2017 212-3 222-0 230-8 239-1 246-8254.0 261 0 267-2 273-7279-5 285-4 290-9 296-1 301-3 306-2 311 0 315-7 320-2 324-6 328-8 333-0 337-1 341 1 344.9 348-7352-4 356-1 359-6 363 1 366-5 370-0 373-2 376.5 178-1 191-9 203-9 214-6 224 4 233-6 241-6 249-5 256-7 263-8 270-0 276-7 282-6 288-5 294-1 299-3304-6 309-6 314-4 319-1323-7 328-1 332-4 336-6 340-8 344-8 348-7 352-5 356 3 360-0 363-5 367-1 370-5 374-0 377-3 380-6 180-1 1940 2061 217-0 226-9 236-0 244-4 252-3 259-5 266 7 272-8 279-8 285-7 291-7 297-3 302-6307-9 313-0 317-9 322-6 327:2 331-7 336-1 340-3 344-5 348-6 3526 356.4 360-2 363.9 367-4 371-1 374-6 378-1 381-4 384-8 182-0 1961 208-3 219-4229-3 238-5 247-1 255 0 262-4 269-6 276-1 282-8 288-8 294-9 300-5 305-9311-2 316-4 321-3 326-1330-8 335-3 339-7 344-0 348-3 352-4 356-4 360-33641 367-9 371-5 375-1 378-7 382-2 385-6 388-9 184-0 198-2 210-6 221-8231-8 2411 249-8 257-8265-4 272-6 279-4 285-9292-0 298-1 303-8 309-3314-6 319-8 324-8 329-6 334-4 339-0 343-4 347-8 352-2 356-2 360-3 364-2368.0 371-9 375-6 379-2 382-9 386-4 389-8 393-1 1-6-0 200-3 212-9 224-1 234-3 243-7 252-5 260-5268 0 275-5 281-7 288-9295-3 301-3 307 1 312-6318-0 323-2 328-3 333-2 338-0 342-5 347-1 351-5 355-9 360-0 364-1 368 1 372-0 375-9 379-6 383-3 386-9 390-5 394 0 397-4 188 0 202-5 215 2 226-5236-8 246-3 255-2 263-3270-7278-5 284-1 292-0 298 6 304-5 310-4 315-9 321-5 326-7 331-8 336-8 341-6 346-3 350-8 355-3 359-6 363-9 368 0 372-0 376-0 379-9 383-6 387-4391-0 394-7 398-2 401-7 196-0 204-6 217-5 228-9 239-3 248-9 257-9 266-1273-7 281-4 287-5 295-1 302-0 307-7 313-7 319-9 324-9 330-2 335-4 340-4 345-2 350 0 354-6 359 1 363-5 367-7 371-9 376-0 380-0 383-9 387-7 391.5 295 2 398-9 402-4 405-9 192-0 206-8 219-8 231-4241-9 251-6 260-6 269-0 276-8 284-4 290-9 298-3305-4 311-0 317-0 324-0328-4 333-7 339-0 344 0 348.9 353-7 358-4 362-9 367-4 371-6 375-8 380-0 384-0 388.0 391-9 395-7 399-4 4031 406-7 410-2 194-0 209 0 222-1 233-7244-4 254-2 263-3 271-8 279-8 287-4 294-3 301-4 308-4 314-3 320-3 326-8 331-8 337-2 342-5 347-6 352-6 357-4 362-2 366-7 371-2 375-5 379-8 384-0 388-1 392-1 396-0 399-9 403-6 407-3 411-0 414-5 1961 2112 224-4 236-3 247-0 256-9 266 1 274-7 282-8 290-4 297-7 304-6 311-2 317-6 323-7 329-6 335-3 340-8 346-1 351-3356-3 361-2 366 0 370-6 375-1 379-5 383-8 388-1392-2 396-2 400 2 404-1407-9 411-6 415-3 418-9 198-1 213 4 226-8 238-7249-6 259-6 268-9 277 6 285-9 293-5 301-1 307.8 314-2 320-9 327-1 332-5 338-8 344-3 349-7 354.9 360-0 365 0 369-8 374 5 378-9 383-5 387-8 392-1 396 3 400-3 404.3 408-2412-1 415-8 419-6 423.2 200-2 215-6 229-2 241-2 252-2 262-3 271-7 280-5 289-0 296-6 304-6 311-0317-2 324-3 330-5 335-4 342-3 347-9 353-4 358-6 363-8 368-8 373-6 378-4 382-8 387-5 391-9 396 2400-4 404 4 408 4 412-4 416-4 420-1 424-0 427-6 202-3 217-8 231-4 243-6 254-8 265-0 274-5 283-4292-1 299-7 308-0 314-2 320-3 327-6 333-9 338-7 345-8 351-4 356:9 362-2367-5 372-6 377-4 382-3 386-6 391-6 395-9 400-2404-5 408-5 412.5 416-5420-6 424-3 428-3 431-9 2013 2201 233-9 246-2 257-4 267-7277-3 286-3 295-1 302-7 311.5 317-5 323-1 331-0 337-4 341-2 349-4 355-1 360-6 366-0 371-3 376-4 381-4 386-2 390-9 395-5 400-0 404-4408-7 412-9 417-0 421-0 4250 425 0 432-8 436-6 (206-4 222-3 236-3 248-7 260-0 270-4 280-1 289-5297-8 305-8 314-0 320-7 326-8 334-4 340-8 345-8 353-0 358-7 364-3 369-8 375-1 380-2 385 1 390-2 394-9 399.5 404 1 408-5412-8 417-1 421-3 425-4 429-4 433 4 437-2 441.1 208-5 224-6 238 7 251-3 262 7 273-2 283-0 292-8 300-6 308-9 316 6 324 0 330-5 337-8 344-3 350-4356-6 362-4 368-1 373-6 379-0 384-1 388-8 394-1398-9 403-6 408-2 412-7417-0 421-4 425-6 429-8 433.8 437·8 441-6 445-6 210-6 226-9 241-1 253-8265 3 2770 285-9 296-0 303-7 3120 319-8 327-2 334 2 341-2 347-7 3550 360 2 366-1 371-8 377-4382-8 387-9 392-9 398-1 402-9 407-7 412-3 416.8 438-2 442-2 446 1 450-1 212-8 229 2 243-5 256 4268 0 278-8 288-8 298-1 306 8 315-2 323-0 339-5 337-7 344 6 351-2 357-6 363-8 369-8 375-6 381-2 386-6 591-9 397-0 402-1 407-0 411-8 416-5 421-0 442-6 446-6 450-6 1454-6 421 2 425-6 429 9 434-1 425-5 429-9 434-2 438:4 It will be observed that the greater the difference between the lengths of the radius bar and beam, the greater is the amount of the correction to be made. As an example of the use of the table, suppose we have the length of the beam C G = 38 inches, and that the radius bar has been found by proportion (A) to be 15 inches; 15÷38 is nearly 4: we shall therefore get for the corrected length of the radius bar 15 + 0817 × 38 = 16.76 inches. The application of this correction to the length of the radius bar, will in all cases diminish the amount of the deviation from the perpendicular by one half; but it should be borne in mind that the parallel motion will work most accurately when the radius bar and beam C G are of the same length; and they should therefore be kept as nearly equal as circumstances will permit. The simple arrangement of two levers connected by a link, which we have now described, is sometimes used as a parallel motion; but additional rods and connecting links are generally superadded, which render the application of the principle more convenient in practice. Fig. 3. represents the parallel motion in most general use for land engines; and fig. 4. a similar one adapted for marine side-lever engines. The general arrangement in both of these is the same, except that the marine engine motion has the reverse side uppermost. We have marked all the corresponding parts in the two figures with the same letters, so that what we have to say of the one will refer equally to the other. In land engines, the radius bar HF is generally either equal to or longer than G C, the part of the beam which works it; while, in the marine engine motion, the radius bar is usually shorter than the part of the beam that gives it motion. This difference is shown in the figures. Referring now to figs. 3 and 4., we shall explain the method of applying the principles we have already described to the calculation of the proportions of the several parts. DC is the beam or side lever moving on the centre C; H F, the radius bar moving on the centre H, and connected with the beam by the rod F G. DP is another rod equal in length to G F; and P F is a rod equal in length to D G. The three rods, therefore, D P, P F, and FG, with the part DG of the beam, form a parallelogram; and the piston-rod is attached to the point P, which, at half stroke, is in the perpendicular line RS, bisecting the versed sine DK. When the engine is put in motion, this point P will move nearly in the perpendicular line R S. For, suppose the beam to be moved upwards into the position D' C, the point will then be in the position P', and the positions of the various other points are denoted by corresponding accented letters. Join C P and C P', and also E E', and we will have, by similar triangles, PE: EC DG: G C :: D'G': G' C, and P' E' : E' Ċ :: D' G. G' C; hence, PE: EC: P' E' E' C. (C) This equation will give us the length of H F; and to get G C, we have GC = a - HF (C') These three equations therefore, (B), (C), and (C') enable us to calculate the proportions of this form of parallel motion in all circumstances. In figs. 5 and 6, two other forms of parallel motion in common use for marine engines are represented. In fig. 5. the radius bar, instead of being connected as formerly to the crosshead, is connected by the rod F Q to the side rod by a pin at Q. FQ is made equal, and parallel to G D ; and F G equal, and parallel to Q D. In fig. 6. the centre H of the radius bar is placed much farther from the main centre. It may be on either side of the piston rod, as is found most convenient. In this motion, too, the end F of the radius bar is connected by a pin to the upright rod G V. The rod GV is made equal and parallel to the side rod D P, and the rod P V is made equal and parallel to DG. To enable us to investigate the method of calculating the lengths of the parts in these motions, join as before CP, and C P', and from the point T where CP cuts FQ in fig. 5. or HF in fig. 6. draw T T' parallel to D P. These lines being drawn in both figures. the following investigation will apply to either: Let D C · b = CG + GT' + T'D It may be proved in the same way, as for fiy. 4. that the point P moves in a line parallel to that described by the point E, so that the inquiry resolves itself as before into an investigation of the relative lengths of C G, and F H, that will cause the point E to move in a perpendicular line. Let us suppose, first, that the height of the centre H of the radius bar, and consequently the height also of the pin Q, is fixed, and that the point G, or the length of C G, is also determined. It is required to find from these data the proper length of H F. By equation (A) we have CG: FH: FE: E G, but by similar triangles F T: GC :: FE: EG; G C G C hence, TF: GC::CG: FH= TF TG but, T'G=CT-CG, and by similar triangles DP: QD::DC ; CT' = DP b ( s − c ) − s · C G G C2 FDG (B). This equation will give us the length of the radius bar HF, when the. length of CG is determined. In land engines the air pump is generally wrought from the point E, and the centre G is fixed so as to be most convenient for that purpose. Formula (B), is therefore very useful for determining the proper length of the radius rod in such cases. In marine engines, however, the position of the centre H of the radius bar is generally fixed from other considerations, and it becomes necessary to find at what point the centre G should be placed, so as to make P move in a perpendicular line. sines only when vers is indefinitely small in comparison with r; and that, by any increase of the versed sine (4 s2 being always constant), the radius diminishes in a less ratio than the versed sine increases, and vice versa. Of course the converse of this is true also; that, if the radius be diminished, the versed sine increases in a greater ratio, and vice versa. When the beam is just leaving the horizontal position, the versed sine is indefinitely small in comparison of the radius; and therefore, at this point, the versed sine of the beam and radius bar will be inversely as the radii; and HF, as determined by equation (A), will be correct for this part of the stroke. At either end of the stroke, however, it ought to be versed sine DKGC equal to Now, as it cannot have both these values, the nearest versed sine FL approach to accuracy we can make is, to make its length intermediate between these two. The corrections in the Table are computed on this principle. If a perpendicular H M be let fall from H on DC, MC will be the horizontal distance of the centre H, from the main centre; and since F G is parallel to P D, it is evident that FH+G Ca=MC+DN. G C s b (s-c)· Again, if the length of GC is not given, but the positions of the centre H, and the pin Q are fixed, let it be required to find the lengths of HF and G C. We shall have the same as above But it was shown above that T' C= a2 s as+b (s-c) TC+a b (s-c) This equation will give the length of H. F, and to get G C we have Again, suppose that the lengths of the levers HF and CG, and consequently the horizontal distance of the centre H from the main centre are given. Let it be required to find the height of the centre H and point Q From equation E we get |