Effects of Three Body Transformed Hamiltonian

Effects of Three Body Transformed Hamiltonian CHAPTER – 6 CONTRIBUTION OF THREE BODY TRANSFORMED HAMILTONIAN () THROUGH FULL CONNECTED TRIPLE EXCITATION COUPLED CLUSTER OPERATORS TO VALENCE IONIZATION POTENTIALS OF F2 AND Cl2 COMPUTED VIA EIP-VUMRCCSDÏ„ SCHEME 6.1 Introduction In this work, the effects of three body transformed Hamiltonian through full connected triples is studied on F2 and Cl2. To see the role of [1] in terms of magnitude, two kinds of computations named scheme–A and scheme–B are done. Scheme – A includes along with the other usual diagrams for EIP-MRCCSDà ¯Ã‚ Ã‚ ´ matrix [1-4]. In scheme–B, the term is totally absent. In this calculations, two chemically interesting and challenging molecules F2, and Cl2 ( because Fluorine atom is most electronegative, and Cl2 contains as many as 34 electrons ) are considered . The basis sets cc-pVDZ and cc-pVTZ (spherical Gaussians) [5] and experimental equilibrium geometry are used in these computations. The basis sets were collected from : http://www.emsl.pnl.gov:2080/forms/basisform.html. Table 6.1 and 6.2 contain all results. 6.2. Results and Discussion Both the molecules are linear and centro-symmetric and hence their point group is D∞h out of which we consider only the largest abelian sub-group D2h. All outer-valence main vertical IPs are presented in Table 6.1. Since independent particle model is valid here, some Koopmans’ configurations appear while going from one basis to another. Naturally, there is same one-to-one correspondence between scheme-A and scheme-B also. For single bonded molecule F2, the contribution of is small. For 2ÃŽ  u state , the differences in the case of cc-pVDZ and cc-pVTZ are 0.026 eV(.600 kcal/mol) and 0.029 eV(0.669 kcal/mol) respectively. For 2ÃŽ  u state of Cl2, the difference (cc-pVDZ) 0.040 eV(0.922 kcal/mol) is significant in view of that we are considering here the correlation dynamics of outer valence electrons. Experimental IPs are presented in the Tables with a view to realizing the reliability of our theoretical results only. Too accurate comparison is not possible here because of the restraint of our starting basis sets. For that, approaching towards basis set saturation as much as possible is necessary. Since scheme-A (as it includes ) gives more accurate IP. From now on or unless otherwise explicitly mentioned, it will be assumed that a theoretical IP value relates to scheme-A only. In the inner valence region, the sizes of the basis sets sometimes influence the IP-profile of the same molecule in higher energy regions considerably. The single bonded F2 molecule is studied first, the IPs of which are presented in Table 6.2. The first 2ÃŽ £g+ satellite of F2 shows that maximum contribution of is by an amount 1.117 eV(25.758 kcal/mol) for cc-pVDZ basis and 0.910 eV(20.985 kcal/mol) for cc-pVTZ basis. The difference (cc-pVTZ) 1.117 eV(25.758 kcal/mol) for 2ÃŽ £g+ is significant. In 2ÃŽ  u state, the maximum contributions are 0.773 eV(17.826 kcal/mol) for cc-pVDZ basis and 0.911 eV(21.001 kcal/mol) for cc-pVTZ basis respectively. In 2ÃŽ £u+ state, the contributions are 0.256 eV(5.903 kcal/mol) for cc-pVDZ basis and 0.267 eV(6.157 kcal/mol) for cc-pVTZ basis. Other satellites do not have the basis-to-basis correspondence. However, scheme-A to scheme-B correspondence is retained, which is based on the dominant configurations with expansion co-efficient à ¯Ã‚ Ã‚ ¾ 0 .3 or more. The next test case is Cl2 molecule, the IPs of which are presented in Table 6.2. The first 2ÃŽ £g+ satellite of Cl2 shows that maximum contribution of is by an amount 0.223 eV(5.142 kcal/mol) for cc-pVDZ basis and 1.305 eV(30.094 kcal/mol) for cc-pVTZ basis, respectively. In 2ÃŽ  u state, the contribution is 0.167 eV(3.851 kcal/mol) for cc-pVDZ basis. In 2ÃŽ £u+ state, the maximum contribution is 1.269 eV(29.263 kcal/mol) for cc-pVDZ basis, no such value for cc-pVTZ basis is found. The IPs onwards are arranged on the basis of dominant configurations. If dominant configurations differ from basis-to-basis substantially, they are put in different rows in the tables. Thus, some IP values which appear in case of cc-pVDZ may not appear at all in case of cc-pVTZ, and vice versa. Similarly, an IP for a basis appearing in scheme-A may be absent in scheme-B, and vice versa. While in the first case it is due to basis-set effect, in the second case it is due to . If for an IP, scheme-A to scheme-B correspondence is observed, only then it is possible to make a comment on the amount by which the IP has been shifted to what extent in scheme-B relative to Scheme-A. In other words, a quantitative picture of the effect of can be made. For quite a few IPs, the contributions of are significant. The values mentioned in parenthesis are relative intensities along with IPs. Molecule States Configurations Basis :cc-pVDZ Basis: cc-pVTZ Expt Scheme-A Scheme-B à ¢Ã¢â€š ¬Ã…’Ãâ€"â‚ ¬DiffÃâ€"â‚ ¬(eV) Scheme-A Scheme-B Ãâ€"â‚ ¬Diffà ¢Ã¢â€š ¬Ã…’à ¢Ã¢â€š ¬Ã…’à ¢Ã¢â€š ¬Ã…’Ãâ€"â‚ ¬ (eV) F2 2ÃŽ  g 1Ï€g -1 15.124 (0.933) 15.136 (0.932) 0.012 15.415 (0.928) 15.429 (0.927) 0.014 15.87a 15.70b 2ÃŽ  u 1Ï€u -1 18.190 (0.873) 18.216 (0.867) 0.026 18.492 (0.874) 18.521 (0.869) 0.029 18.8a 18.4b 2ÃŽ £+g 3ÏÆ'g -1 20.671 (0.956) 20.652 (0.954) 0.019 20.926 (0.948) 20.908 (0.947) 0.018 21.1a Cl2 2ÃŽ  g 2Ï€g -1 11.138 (0.954) 11.136 (0.954) 0.002 11.318 (0.948) 11.315 (0.948) 0.003 11.49b 2ÃŽ  u 2Ï€u -1 14.037 (0.059) 13.997 (0.916) 0.040 14.162 (0.911) 14.160 (0.911) 0.002 14.0b 2ÃŽ £+g 5ÏÆ'g -1 15.687 (0.952) 17.467 (0.018) 17.446 (0.018) 0.021 15.806 (0.942) 15.792 (0.942) 19.698 (0.008) 0.014 15.8b Table 6.1 : Contribution of the diagrams for three-body transformed Hamiltonian of 3h2p-3h2p block of EIP-MRCCSDÏ„ matrix (Fig.3.3, Chap. 3 ) to vertical ionization potentials ( in eV) of outer valence region (relative intensities have been put in the parentheses ) 1 eV = 23 .06035 kcal/mol aRef.[6] bRef.[7] Table 6.2 : Contribution of the diagrams for three-body transformed Hamiltonian of 3h2p-3h2p block of EIP-MRCCSDÏ„ matrix (Fig.3.3, Chap. 3) to inner valence main and satellite vertical ionization potentials ( in eV) of F2 and Cl2 Mol States Basis : cc-pVDZ Basis : cc-pVTZ Expt. Scheme-A Scheme- B à Ã¢â‚¬   Diff à Ã¢â‚¬   Scheme- A Scheme- B I Diff I F2 2ÃŽ £+g 29.680(0.016) 40.785(0.043) 42.672(0.436) 50.701(0.056) 54.836(0.101) 28.863(0.015) 40.835(0.015) 42.653(0.047) 50.600(0.060) 53.719(0.056) 0.817 0.050 0.019 0.101 1.117 41.916(0.659) 42.800(0.157) 42.889(0.048) 50.482(0.190) 41.961(0.617) 42.910(0.149) 42.385(0.059) 50.367(0.032) 0.045 0.910 0.404 0.115 41.75c 2ÃŽ  u 24.524(0.028) 32.416(0.065) 33.151(0.014) 33.671(0.021) 45.999(0.011) 51.633(0.015) 24.461(0.032) 31.643(0.050) 44.431(0.020) 50.239(0.020) 0.063 0.773 25.014(0.026) 32.936(0.039) 24.940(0.029) 32.025(0.052) 0.074 0.911 2ÃŽ  g 41.063(0.021) 42.117(0.013) 47.846(0.022) 40.314(0.067) 0.251 42.491(0.011) 48.659(0.013) 40.691(0.047) 2ÃŽ £+u 29.110(0.015) 29.203(0.040) 32.669(0.017) 37.491(0.675) 28.857(0.012) 32.413(0.017) 37.480(0.743) 0.253 0.256 0.011 29.690(0.030) 29.762(0.038) 33.195(0.022) 29.432(0.039) 32.928(0.023) 37.289(0.667) 0.330 0.267 37.47c cRef.[8] Table 6.2 continued Mol States Basis : cc-pVDZ Basis : cc-pVTZ Expt. Scheme-A Scheme- B à Ã¢â‚¬   Diff à Ã¢â‚¬   Scheme- A Scheme- B I Diff I Cl2 2ÃŽ £+g 22.222(0.027) 25.085(0.013) 28.214(0.650) 29.962(0.020) 37.302(0.038) 22.137(0.026) 25.041(0.012) 28.202(0.635) 29.739(0.029) 37.237(0.038) 0.085 0.044 0.012 0.223 0.065 22.443(0.034) 26.423(0.019) 26.655(0.073) 27.479(0.164) 29.939(0.032) 34.358(0.021) 22.356(0.033) 26.637(0.019) 26.684(0.059) 27.477(0.152) 31.244(0.048) 35.660(0.004) 35.631(0.048) 0.087 0.214 0.029 0.002 1.305 2ÃŽ  u 23.119(0.083) 22.974(0.059) 31.017(0.017) 22.967(0.059) 27.466(0.002) 29.075(0.002) 29.514(0.003) 30.663(0.002) 31.000(0.018) 31.258(0.009) 0.007 0.017 2ÃŽ  g 25.579(0.029) 25.412(0.023) 0.167 22.607(0.002) 25.606(0.015) 31.139(0.002) 33.351(0.014) 33.470(0.012) 34.804(0.010) 25.534(0.011) 26.019(0.006) 31.076(0.002) 33.308(0.008) 33.404(0.011) 34.099(0.003) 34.804(0.003) 34.844(0.011) 36.413(0.007) 37.059(0.002) 37.728(0.002) 38.080(0.002) 38.619(0.001) 48.004(0.001) 48.067(0.001) 0.072 0.063 0.043 0.066 0.040 2ÃŽ £+u 22.258(0.297) 24.399(0.279) 26.268(0.185) 38.132(0.025) 41.469(0.025) 22.222(0.275) 24.339(0.289) 26.220(0.184) 38.082(0.023) 40.200(0.018) 0.036 0.000 0.048 0.050 1.269 22.404(0.424) 24.413(0.111) 26.214(0.071) 31.646(0.033) 34.124(0.021) 36.911(0.042) 37.325(0.013) 22.376(0.341) 24.413(0.274) 31.587(0.032) 34.076(0.022) 34.454(0.029) 36.803(0.045) 38.207(0.027) 0.028 0.000 0.059 0.048 0.108 6.3 Conclusion The present calculations show that for F2 and Cl2, the above-said effect sometimes is considerably high and may even be more than 21 kcal/mol (F2 : cc-pVTZ) and 29 kcal/mol (Cl2 : cc-pVDZ) which are much presumably due to high electronegativity of F and Cl atoms. This suggests that inclusion of is essential in high accuracy EIP-VUMRCC IP calculations. References [1] K. Adhikari, S. Chattopadhyay, R. K. Nath, B. K. De, D. Sinha, Chem. Phys. Lett.  474 (2009) 199. [2] S. Chattopadhyay, A. Mitra, D. Jana, P. Ghosh and D. Sinha, Chem. Phys. Lett. 361  (2002) 298. [3] S. Chattopadhyay, A. Mitra and D. Sinha, J. Chem. Phys. 125 (2006) 244111. [4] K. Adhikari, S. Chattopadhyaya, B. K. De, A. Sharma, R. K. Nath, D. Sinha, J. Comp.  Chem. 34 (2013) 1291. [5] EMSL Basis Set Library (www.emsl.pnl.gov/forms/basisform.html). [6] G. Bieri, A. Schemelzer, L. Ã…sbrink and M. Jonsson, Chem. Phys. 49 (1980) 213. [7] A. B. cornfored, D. C. Frost, C. A. McDowell, J. L. Ragle, and I. A. Stenhouse, J.  Chem. Phys. 54 (1971) 2651. [8] P. Weightman, T. D. Thomas and D. R. Jennison, J. Chem. Phys. 78 (1983) 1652. 1

Deriving Meaning from William Carlos Williams, The Young Housewife Ess

Deriving Meaning from William Carlos Williams', The Young Housewife Everything depends on perspective. The uniqueness we bring to our reading is essential to the absorption of poems with Imagist elements. An example of this is the poem, "The Young Housewife", by William Carlos Williams. Perhaps it was a streak of laziness on my part, but I had very little imagination to offer this poem. Having had no experience as such, I didn't identify with the young housewife, the fish-man, the ice-man, or even the dramatically fallen leaf. What I initially saw was a jumble of thoughts arranged neatly into three very brief verses. The biographical information about the author provided in the Third Edition of the Heath Anthology of American Literature ¹ describes Williams' writings as reflections on the "...disjunction of modern life in broken lines and flashes of incomplete thought." Exactly. Only, I was left to wonder how it could be that this was meant by the biographer to be complimentary. Seems to me that somewhere along the way I picked up the notion that incomplete thoughts were a bad thing.... Granted, the concept of Imagism is not lost on me. Read after read of this poem led me to believe that it is very true that reality is created in the act of our perceiving it. I could take on any perspective or mindset and find applicable passages that would lend themselves wholeheartedly to whatever arguments of meaning I could come up with. Perhaps I have an imagination after all. Considering the lack of natural meaning that I initially got out of the poem, I ended up doing a systematic dissection of the lines to extract a meaning I could expound upon. Despite the fact that doing this meant go... ...ing. Here we have the husband taking action in his own way to ensure that his leaf remain not only under a watchful eye, but also under the thumb of his silent, yet ultimately draining, power. Little thought is obviously given to whether the leaf itself remains young and vibrant or if it slowly dries up. Williams use of visual writing enables the poem to close with a vivid flourish and a tone of smugness as the narrator finally passes by with a bow and a smile. You sense the crushing of another leaf whom he'd help to fall unwittingly. It's a stretch, yes, but when you read the poem with the sympathy this theory evokes, its meaning is changed and so too is your view. There's suddenly a reason for this poem. 1.) Lauter, Paul (1998). pg. The Heath Anthology of American Literature, Third Edition. Houghton Mifflin, New York, NY

The Host Chapter 35: Tried

I groaned. My head felt all swirly and disconnected. My stomach rolled nauseatingly. â€Å"Finally,† someone murmured in relief. Ian. Of course. â€Å"Hungry?† I thought about that and then made an involuntary gagging sound. â€Å"Oh. Never mind. Sorry. Again. We had to do it. People got all†¦ paranoid when we took you outside.† â€Å"‘S okay,† I sighed. â€Å"Want some water?† â€Å"No.† I opened my eyes, trying to focus in the darkness. I could see two stars through the cracks overhead. Still night. Or night again, who knew? â€Å"Where am I?† I asked. The shapes of the cracks were unfamiliar. I would swear I'd never stared at this ceiling before. â€Å"Your room,† Ian said. I searched for his face in the darkness but could only make out the black shape that was his head. With my fingers, I examined the surface I lay on; it was a real mattress. There was a pillow under my head. My searching hand touched his, and he caught my fingers before I could withdraw them. â€Å"Whose room is it really?† â€Å"Yours.† â€Å"Ian†¦Ã¢â‚¬  â€Å"It used to be ours-Kyle's and mine. Kyle's being†¦ held in the hospital wing until things can be decided. I can move in with Wes.† â€Å"I'm not taking your room. And what do you mean, until things can be decided?† â€Å"I told you there would be a tribunal.† â€Å"When?† â€Å"Why do you want to know?† â€Å"Because if you're going through with that, then I have to be there. To explain.† â€Å"To lie.† â€Å"When?† I asked again. â€Å"First light. I won't take you.† â€Å"Then I'll take myself. I know I'll be able to walk as soon as my head stops spinning.† â€Å"You would, wouldn't you?† â€Å"Yes. It's not fair if you don't let me speak.† Ian sighed. He dropped my hand and straightened slowly to his feet. I could hear his joints pop as he stood. How long had he been sitting in the dark, waiting for me to wake? â€Å"I'll be back soon. You might not be hungry, but I'm starving.† â€Å"You had a long night.† â€Å"Yes.† â€Å"If it gets light, I won't sit here waiting for you.† He chuckled without humor. â€Å"I'm sure that's true. So I'll be back before that, and I will help you get where you're going.† He leaned one of the doors away from the entrance to his cave, stepped around it, and then let it fall back into place. I frowned. That might be hard to do on one leg. I hoped Ian truly was coming back. While I waited for him, I stared up at the two stars I could see and let my head slowly become stationary. I really didn't like human drugs. Ugh. My body hurt, but the lurching in my head was worse. Time passed slowly, but I didn't fall asleep. I'd been sleeping most of the last twenty-four hours. I probably was hungry, too. I would have to wait for my stomach to calm before I was sure. Ian came back before the light, just as he'd promised. â€Å"Feeling any better?† he asked as he stepped around the door. â€Å"I think so. I haven't moved my head yet.† â€Å"Do you think it's you reacting to the morphine, or Melanie's body?† â€Å"It's Mel. She reacts badly to most painkillers. She found that out when she broke her wrist ten years ago.† He thought about that for a moment. â€Å"It's†¦ odd. Dealing with two people at once.† â€Å"Odd,† I agreed. â€Å"Are you hungry yet?† I smiled. â€Å"I thought I smelled bread. Yes, I think my stomach is past the worst.† â€Å"I was hoping you'd say that.† His shadow sprawled out beside me. He felt for my hand, then pulled my fingers open and placed a familiar round shape in it. â€Å"Help me up?† I asked. He put his arm carefully around my shoulders and folded me up in one stiff piece, minimizing the ache in my side. I could feel something foreign on the skin there, tight and rigid. â€Å"Thanks,† I said, a little breathless. My head spun slowly. I touched my side with my free hand. Something adhered to my skin, under my shirt. â€Å"Are my ribs broken, then?† â€Å"Doc's not sure. He's doing as much as he can.† â€Å"He tries so hard.† â€Å"He does.† â€Å"I feel bad†¦ that I used to not like him,† I admitted. Ian laughed. â€Å"Of course you didn't. I'm amazed you can like any of us.† â€Å"You've got that turned around,† I mumbled, and dug my teeth into the hard roll. I chewed mechanically and then swallowed, setting the bread down as I waited to see how it hit my stomach. â€Å"Not very appetizing, I know,† Ian said. I shrugged. â€Å"Just testing-to see if the nausea's really passed.† â€Å"Maybe something more appealing†¦Ã¢â‚¬  I looked at him, curious, but I couldn't see his face. I listened to a sharp crackle and a ripping sound†¦ and then I could smell, and I understood. â€Å"Cheetos!† I cried. â€Å"Really? For me?† Something touched my lip, and I crunched into the delicacy he offered. â€Å"I've been dreaming about this.† I sighed as I chewed. That made him laugh. He put the bag in my hands. I downed the contents of the small bag quickly, and then finished my roll, seasoned by the cheese flavor still in my mouth. He handed me a bottle of water before I could ask. â€Å"Thank you. For more than the Cheetos, you know. For so much.† â€Å"You're more than welcome, Wanda.† I stared into his dark blue eyes, trying to decipher everything he was saying with that sentence-there seemed to be something more than just courtesy in the words. And then I realized that I could see the color of Ian's eyes; I glanced quickly up at the cracks above. The stars were gone, and the sky was turning pale gray. Dawn was coming. First light. â€Å"Are you sure you have to do this?† Ian asked, his hands already half-extended as if to pick me up. I nodded. â€Å"You don't have to carry me. My leg feels better.† â€Å"We'll see.† He helped me to my feet, leaving his arm around my waist and pulling my arm around his neck. â€Å"Careful, now. How's that?† I hobbled forward a step. It hurt, but I could do it. â€Å"Great. Let's go.† I think Ian likes you too much. Too much? I was surprised to hear from Melanie, and so distinctly. Lately, she only spoke up like this when Jared was around. I'm here, too. Does he even care about that? Of course he does. He believes us more than anyone besides Jamie and Jeb. I don't mean that. What do you mean? But she was gone. It took us a long time. I was surprised by how far we had to go. I'd been thinking we were going to the big plaza or the kitchen-the usual places for congregating. But we went through the eastern field and kept going until we finally reached the big, deep black cave that Jeb had called the game room. I hadn't been here since my first tour. The biting scent of the sulfurous spring greeted me. Unlike most of the caverns here, the game room was much wider than it was tall. I could see that now because the dim blue lights hung from the ceiling rather than resting on the floor. The ceiling was only a few feet over my head, the height of a normal ceiling in a house. But I couldn't even see the walls, they were so distant from the lights. I couldn't see the smelly spring, tucked away in some far corner, but I could hear it dribble and gush. Kyle sat in the brightest spot of light. He had his long arms wrapped around his legs. His face was set in a stiff mask. He didn't look up when Ian helped me limp in. On either side of him were Jared and Doc, on their feet, both with their arms hanging loose and ready at their sides. As though they were†¦ guards. Jeb stood beside Jared, his gun slung over one shoulder. He appeared relaxed, but I knew how quickly that could change. Jamie held his free hand†¦ no, Jeb had his hand around Jamie's wrist, and Jamie didn't seem happy about it. When he saw me come in, though, he smiled and waved. He took a deep breath and looked pointedly at Jeb. Jeb dropped Jamie's wrist. Sharon stood beside Doc, with Aunt Maggie at her other side. Ian pulled me toward the edge of the darkness surrounding the tableau. We weren't alone there. I could see the shapes of many others, but not their faces. It was strange; through the caves, Ian had supported most of my weight with ease. Now, though, he seemed to have tired. His arm around my waist was slack. I lurched and hopped forward as best I could until he picked the spot he wanted. He settled me to the floor, and then sat beside me. â€Å"Ouch,† I heard someone whisper. I turned and could just make out Trudy. She scooted closer to us, Geoffrey and then Heath copying her. â€Å"You look rotten,† she told me. â€Å"How bad are you hurt?† I shrugged. â€Å"I'm fine.† I started to wonder if Ian had let me struggle just to make a show of my injuries-to make me testify against Kyle without words. I frowned at his innocent expression. Wes and Lily arrived then and came to sit with my little group of allies. Brandt entered a few seconds later, and then Heidi, and then Andy and Paige. Aaron was last. â€Å"That's everybody,† he said. â€Å"Lucina's staying with her kids. She doesn't want them here-she said to go on without her.† Aaron sat beside Andy, and there was a short moment of silence. â€Å"Okay, then,† Jeb said in a loud voice meant to be heard by all. â€Å"Here's how it's gonna work. Straight-up majority vote. As usual, I'll make my own decision if I have a problem with the majority, 'cause this -â€Å" â€Å"Is my house,† several voices interjected in chorus. Someone chuckled but stopped quickly. This wasn't funny. A human was on trial for trying to kill an alien. This had to be a horrible day for all of them. â€Å"Who's speaking against Kyle?† Jeb asked. Ian started to stand beside me. â€Å"No!† I whispered, tugging on his elbow. He shrugged me off and rose to his feet. â€Å"This is simple enough,† Ian said. I wanted to jump up and clap my hand over his mouth, but I didn't think I could get to my feet without help. â€Å"My brother was warned. He was not in any doubt about Jeb's ruling on this. Wanda is one of our community-the same rules and protections apply to her as to any of us. Jeb told Kyle point-blank that if he couldn't live with her here, he should move on. Kyle decided to stay. He knew then and he knows now the penalty for murder in this place.† â€Å"It's still alive,† Kyle grunted. â€Å"Which is why I'm not asking for your death,† Ian snapped back. â€Å"But you can't live here anymore. Not if you're a murderer at heart.† Ian stared at his brother for a moment, then sat on the ground beside me again. â€Å"But he could get caught, and we'd have no idea,† Brandt protested, rising to his feet. â€Å"He'll lead them back here, and we'd have no warning.† There was a murmur through the room. Kyle glared at Brandt. â€Å"They'll never get me alive.† â€Å"Then it's a death sentence after all,† someone muttered at the same time that Andy said, â€Å"You can't guarantee that.† â€Å"One at a time,† Jeb warned. â€Å"I've survived on the outside before,† Kyle said angrily. Another voice came from the darkness. â€Å"It's a risk.† I couldn't make out the owners of the voices-they were just hissing whispers. And another. â€Å"What did Kyle do wrong? Nothing.† Jeb took a step toward the voice, glowering. â€Å"My rules.† â€Å"She's not one of us,† someone else protested. Ian started to rise again. â€Å"Hey!† Jared exploded. His voice was so loud that everyone jumped. â€Å"Wanda's not on trial here! Does someone have a concrete complaint against her-against Wanda herself? Then ask for another tribunal. But we all know she hasn't harmed anyone here. In fact, she saved his life.† He stabbed one finger toward Kyle's back. Kyle's shoulders hunched, like he'd felt the jab. â€Å"Just seconds after he tried to throw her into the river, she risked her life to keep him from the same painful death. She had to know that if she let him fall she would be safer here. She saved him anyway. Would any of you have done the same-rescue your enemy? He tried to kill her, and yet will she even speak against him?† I felt all the eyes in the dark room on my face as Jared now held his hand out, palm up, toward me. â€Å"Will you speak against him, Wanda?† I stared at him wide-eyed, stunned that he was speaking for me, that he was speaking to me, that he was using my name. Melanie was in shock, too, torn in half. She was overjoyed at the kindness in his face as he looked at us, the softness in his eyes that had been absent so long. But it was my name he'd said†¦ It was a few seconds before I could find my voice. â€Å"This is all a misunderstanding,† I whispered. â€Å"We both fell when the floor caved in. Nothing else happened.† I hoped the whisper would make it harder to hear the lie in my voice, but as soon as I was done, Ian chuckled. I nudged him with my elbow, but that didn't stop him. Jared actually smiled at me. â€Å"You see. She even tries to lie in his defense.† â€Å"Tries being the operative word,† Ian added. â€Å"Who says it's lying? Who can prove that?† Maggie asked harshly, stepping forward into the empty space beside Kyle. â€Å"Who can prove that it's not the truth that sounds so false on its lips?† â€Å"Mag -† Jeb started. â€Å"Shut up, Jebediah-I'm speaking. There is no reason for us to be here. No human was attacked. The insidious trespasser offers no complaint. This is a waste of all our time.† â€Å"I second that,† Sharon added in a clear, loud voice. Doc shot her a pained look. Trudy jumped to her feet. â€Å"We can't house a murderer-and just wait around for him to be successful!† â€Å"Murder is a subjective term,† Maggie hissed. â€Å"I only consider it murder when something human is killed.† I felt Ian's arm wrap around my shoulder. I didn't realize that I was trembling until his motionless body was against mine. â€Å"Human is a subjective term as well, Magnolia,† Jared said, glowering at her. â€Å"I thought the definition embraced some compassion, some little bit of mercy.† â€Å"Let's vote,† Sharon said before her mother could answer him. â€Å"Raise your hand if you think Kyle should be allowed to stay here, with no penalty for the†¦ misunderstanding.† She shot a glance not at me, but at Ian beside me when she used the word I'd used. Hands began to rise. I watched Jared's face as his features settled into a scowl. I struggled to raise my hand, but Ian tightened his hold around my arms and made an irritated noise through his nose. I held my palm as high as I could get it. In the end, though, my vote wasn't necessary. Jeb counted out loud. â€Å"Ten†¦ fifteen†¦ twenty†¦ twenty-three. Okay, that's a clear majority.† I didn't look around to see who had voted how. It was enough that in my little corner all arms were crossed tightly over chests and all eyes stared at Jeb with expectant expressions. Jamie walked away from Jeb to come squeeze in between Trudy and me. He put his arm around me, under Ian's. â€Å"Maybe your souls were right about us,† he said, loud enough for most to hear his high, hard voice. â€Å"The majority are no better than -â€Å" â€Å"Hush!† I hissed at him. â€Å"Okay,† Jeb said. Everyone went silent. Jeb looked down at Kyle, then at me, and then at Jared. â€Å"Okay, I'm inclined to go with the majority on this.† â€Å"Jeb -† Jared and Ian said simultaneously. â€Å"My house, my rules,† Jeb reminded them. â€Å"Never forget that. So you listen to me, Kyle. And you'd better listen, too, I think, Magnolia. Anyone who tries to hurt Wanda again will not get a tribunal, they will get a burial.† He slapped the butt of his gun for emphasis. I flinched. Magnolia glared hatefully at her brother. Kyle nodded, as if accepting the terms. Jeb looked around the unevenly spaced audience, locking eyes with each member except the little group beside me. â€Å"Tribunal's over,† Jeb announced. â€Å"Who's up for a game?†

Biography of Christiaan Huygens, Inventor of the Pendulum Clock

Christiaan Huygens (April 14, 1629-July 8, 1695), a Dutch natural scientist, was one of the great figures of the scientific revolution. While his best-known invention is the pendulum clock, Huygens is remembered for a wide range of inventions and discoveries  in the fields of physics, mathematics, astronomy, and horology. In addition to creating the influential timekeeping device, Huygens discovered the shape of Saturns rings,  the moon Titan,  the wave theory of light, and the formula for centripetal force.   Full Name: Christiaan HuygensAlso Known As: Christian HuyghensOccupation: Dutch astronomer, physicist, mathematician, horologistDate of Birth: April 14,  1629Place of Birth: The Hague, Dutch RepublicDate of Death: July 8, 1695 (age 66)Place of Death:  The Hague, Dutch RepublicEducation: University of Leiden, University of AngersSpouse: Never marriedChildren: None Key Accomplishments Invented the pendulum clockDiscovered the moon TitanDiscovered the shape of Saturns ringsFormulated the equations for centripetal force, elastic collisions, and diffractionProposed the wave theory of lightInvented the Huygenian eyepiece for telescopes Fun Fact: Huygens  tended to publish long after making  his discoveries. He wanted to make certain his work was correct before submitting it to his peers. Did You Know?  Huygens  believed life might be possible on other planets. In Cosmotheoros, he wrote that the key to  extraterrestrial  life was the presence of water on other planets. The Life of Christiaan Huygens mihaiulia / Getty Images Christiaan Huygens was born on April 14, 1629, in The Hague, Netherlands, to Constantijn Huygens and Suzanna van Baerle. His father was a wealthy diplomat, poet, and musician. Constantijn educated Christiaan at home until he was 16 years old. Christiaans liberal education included math, geography, logic, and languages, as well as music, horse riding, fencing, and dancing. Huygens entered the University of Leiden in 1645 to study law and mathematics. In 1647, he entered Orange College in  Breda, where his father served as a curator. Following the completion of his studies in 1649, Huygens embarked on a career as a diplomat with Henry, Duke of Nassau. However, the political climate changed, removing the influence of Huygens father. In 1654, Huygens returned to The Hague to pursue a scholarly life. Huygens moved to Paris in 1666, where he became a founding member of the French Academy of Sciences. During his time  in Paris, he met German philosopher and mathematician Gottfried Wilhelm Leibniz and published Horologium Oscillatorium. This work included the derivation of the formula for the oscillation of a pendulum, a theory on the mathematics of curves, and the law of centrifugal force. Huygens returned  to The Hague in 1681, where he later  died at the age of 66. Huygens the Horologist Giallo / Pexels In 1656, Huygens invented the pendulum clock  based on Galileos earlier research into pendulums. The clock became the worlds most accurate timepiece and remained so for the next 275 years. Nonetheless, there were problems with the invention. Huygens had invented the pendulum clock to be used as a marine chronometer, but the rocking motion of a ship prevented the pendulum from functioning properly. As a result, the device wasnt popular. While Huygens successfully filed a patent for his invention in The Hague, he wasnt granted rights in France or England. Huygens also invented a balance spring watch, independently of Robert Hooke. Huygens patented a pocket watch in 1675. Huygens the Natural Philosopher shulz / Getty Images Huygens made many contributions to the fields of mathematics and physics (called natural philosophy at the time). He formulated laws to describe the elastic collision between two bodies, wrote a quadratic equation for what would become Newtons second law of motion, wrote the first treatise about probability theory, and derived the formula for centripetal force. However, he is best remembered for his work in optics. He may have been the inventor of the magic lantern, an early type of image projector. He experimented with birefringence (double diffraction), which he explained with a wave theory of light. Huygens wave theory was published in 1690 in Traità © de la lumià ¨re. The wave theory was in opposition to Newtons corpuscular theory of light. Huygens theory was not proven until 1801 when Thomas Young conducted interference experiments. The Nature of Saturns Rings and the Discovery of Titan Johannes Gerhardus Swanepoel / Getty Images In 1654, Huygens turned his attention from mathematics to optics. Working alongside his brother, Huygens devised a better method for grinding and polishing lenses. He described the law of refraction, which he used to calculate the focal distance of the lenses and build improved lenses and telescopes. In 1655, Huygens pointed one of his new telescopes at Saturn. What had once appeared to be vague bulges on the sides of the planet (as seen through inferior telescopes) were revealed to be rings. Huygens could also see that the planet had a large moon, which was named Titan. Other Contributions TheDigitalArtist / Pixabay In addition to Huygens most famous discoveries, he is credited with several other notable contributions: Huygens innovated a 31 equal temperament  musical scale, which is related to Francisco de Salinas meantone scale.In 1680, Huygens designed an internal combustion engine that used gunpowder as its fuel. He never built it.Huygens completed Cosmotheoros shortly before his death. It was published posthumously. In addition to discussing the possibility of life on other planets, he proposed that the key criteria for finding extraterrestrial life would be the existence of water. He also proposed a method for estimating distances between stars. Selected Published Works 1651:  Cyclometriae1656:  De Saturni Luna observatio nova (about the discovery of TItan)1659:Systema saturnium (about the planet Saturn)1659: De vi centrifuga (about centrifugal force, published in 1703)1673: Horologium oscillatorium sive de motu pendularium (design of the pendulum clock)1684: Astroscopia Compendiaria tubi optici molimine liberata (compound telescopes without a tube)1690: Traità © de la lumià ¨re (treatise on light)1691:Lettre touchant le cycle harmonique (about the 31-tone system)1698: Cosmotheoros (about cosmology and life in the universe) Sources Andriesse, C. D. Huygens: The Man Behind the Principle. Sally Miedema (Translator), 1st Edition, Cambridge University Press, September 26, 2005. Basnage, Henri of Beauval. Letter from Mr. Huygens to the Author concerning the Harmonic Cycle. Stichting Huygens-Fokker, October 1691, Rotterdam. Huygens, Christian. Christiani Hugenii ... Astroscopia compendiaria, tubi optici molimine liberata. Astronomical instruments, Leers, 1684. Huygens, Christiaan. Cristiani Hugenii Zulichemii, Const. f. Systema Saturnium : sive, De causis mirandorum Saturni phaenomenà ´n, et comite ejus Planeta Novo. Vlacq, Adriaan (printer), Jacob Hollingworth (former owner), Smithsonian Libraries, Hagae-Comitis, 1659. Huygens, Christiaan (Also Huyghens, Christian). Encyclopedia, November 6, 2019. Huygens, Christiaan. Treatise On Light. Osmania University. Universallibrary, Macmillan And Company Limited, 1912. Mahoney, M.S. (translator). Christian Huygens On Centrifugal Force. De vi centrifuga, in Oeuvres complà ¨tes, Vol. XVI, Princeton University, 2019, Princeton, NJ. The Cosmotheoros of Christiaan Huygens (1698). Adriaan Moetjens in The Hague, Utrecht University, 1698. Yoder, Joella. A Catalogue of the Manuscripts of Christiaan Huygens including a concordance with his Oeuvres Complà ¨tes. History of Science and Medicine Library, BRILL, May 17, 2013. Yoder, Joella. Unrolling Time. Cambridge University Press, July 8, 2004.