I will always remember

the moment you first touched my heart.

You gave to me the most precious gift

I could ever hope to have.

Your love

It shines through the darkest day

and lights each moment.

You are the sun,

You are the moon,

You are the stars that grace the night.

Loving you

fills my heart, my soul, my life.

I cannot imagine my life

without you...

without the sound of your voice

to fill the silence...

without the warm caress of your smile.

I cannot imagine waking to face a day

that doesn't include you.

You, my love,

make each day complete.

I love you.

I love you...

words alone

cannot express

the depth,

the strengh,

the completeness

of the love I have for you.

the language of love

the music of the heart

the dance of two souls

becoming one.

the words you used

the first time

caress my memory now.

I hear them in the whisper of the breeze;

I hear them in the rush of waves upon the shore;

and I'll feel them in the reaches of my heart

forevermore.

Your birth-date has a modifying influence on your life. Below are the dates and the traits they signify.

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31

This number is suggestive of a good measure of executive and leadership qualities. You are curious and dedicative. When you are interested in something, everything else has to wait. A birthday on the day 1 of any month gives greater will power and self- confidence. You have an innovative approach to things. This 1 energy may undermine your ability to ability and desire to get into details. You may be sensitive, but you choose to repress your feelings. You believe in love at first sight. You won't wait to learn more about the person. Vice versa, people who fail to impress you will hardly get a chance to be your friend. Your emotion is on the extreme. You can only love or hate, nothing in between and this often shows in your ex-pression. Try not to end a relationship in a quarrel.

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This number is responsible in adding a degree of sensitivity, emotion and intuition to your reading. 2 is a very social number which enables you to make friends easily and quickly. You are prone to become nervy in the company of a large group. You are by nature warm-hearted and emotional. You have great common sense but usually fail to follow through. This might happen because you are too busy with your mission and shut yourself from the outside world. You constantly seek affection. You have a tendency to become depressed and temperamental. You suffer from anxiety and mental turmoil. Once depression sets in, you find it hard to bounce back to reality. You seem to be contented with your unrequited love. Your are a romantic and loyal lover.

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Number 3 adds a good deal of vitality to your life. It enables you to bounce back rapidly from setbacks - mental or physical. Although you are innocent and romantic but your ex-pression often mislead others into thinking that you are an active and fun loving. You are restless and are able to portray a carefree attitude. You are vocal about your thoughts and are a good conversationalist. You are capable of making a very good impression. You are too good with your words and excel in writing, speaking and possibly singing. You have a keen imagination, but you tend to scatter your energies and become involved with too many superficial matters. You are loving, affectionate and too sensitive at times. You are subject to rapid ups and downs. No one can bring you to see reason when you are in love. Your confidence might lead you to the track your parent disagree.

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Being born on the 4th day of the month, you are blessed with managerial and organisational qualities. You are serious, honest and a hard working individual. You usually think before acting. Your feelings are likely to be repressed at times. The number makes you inhibitional in expressing your affections because your feelings are closely regulated and controlled. You often are the one who give yourself a hard time by being paranoid. People might not truly understand you but you are really nice to be around. You always surprise others with your new
character when you are in love. Your love trap often comes unexpectedly and your love life is full of surprises. You are rational, practical and conscious of details. The number is associated with a good deal of rigidity and stubbornness.

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Although you are on the quiet side, but you enjoy excitement and changes. You are inclined to work well with people and enjoy them. You are versatile and talented and very good when it comes to the presentation of your ideas. Because of your extreme confidence, you hardly ask others for opinion. You believe in leading your own life, and you have got the gift in doing so. You need change and traveling is a good option. You are blessed with a quick, clever and an analytical mind. You get easily bored with routine as you are impatient and restless by nature. You have a tendency to shirk responsibility. Nothing can stop you from making progress in your love life. Once you are in love, you feel the ownership of your lover. A third party can only make your jealousy becomes worse.

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The number 6 adds a tone of responsibility, understanding and helpfulness to your character. You are generous with people in need, sometimes to an extreme that people find you nosey. Those born on the sixth are honest and open with everyone. Your hidden courage and dedication often surprise others. Your imagination is extremely unique. You are caring about family and friends too. 6 is a number associated with responsibility and caring. Your love life is on the smooth track because it grows from friendship. Although you may not make a sweet lover but your sincerity bring happiness to your couple.

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Those born on the 7th are something of a perfectionist. You are individualistic in many ways. You are capable in-depth mental analysis and complicated reasoning. You are sensitive to changes around you but your feeling is hardly expressed. You hate exaggerations. You are intuitive and should follow your hunches. You can't take orders too well. Therefore you can work best in a situation where either you work alone or you are the boss. You have a tendency to be somewhat stubborn and self-centered. You have enormous courage to please your lover. Your relationship often progress quickly.

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You can conceive and plan on a grand scale. You have good executive skills and you are a good judge of values. You should aim at owning your own business. You simply love to be in control. People look up to
your wit and imagination. You are unpredictable and hardly complete what you started, which sometimes create negative impact on people around you. You are honest in financial matters and can be trusted easily. You are idealistic by nature, and never too busy to spend time on worthwhile causes, especially if managerial support are needed. There is a potential for material success associated with this number. Falling in love becomes your routine. Most of the time, you are lucky. You fascinate people with good taste but you never have enough with one. Although your love progresses very fast, it never lasts.

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The number 9 adds a tone of idealism and humanitarianism to your personality. You can work easily with people on the virtue of being broadminded, generous and tolerant. You often have problem in promoting yourself, just because you don't know how to express your true self. On the other hand, you don't really care what people think. This is why people misunderstand you until they really get a chance to learn about your pleasant personality. You are sensitive to other's needs and feelings. You are also compassionate and sympathetic. Your feelings run deep and you often find yourself in dramatically charged situations. The 9 energy tends to give more than it gets. Your first love lasts forever. You are responsible to the feeling of your lover. The chance to betray your lover is none. You have luck with children.

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A tone of independence and energy is added to your Life Path on the virtue of being born on the 10th day of the month. You are very capable. If you are a woman, you have high chance to be renowned workingwoman. If you are a man, your path to fame and honor is near. You have greater will power and self-confidence and an original approach to things. You are good in implementing your imagination and share it with others. You are always well dressed. The 1 energy may undermine your ability to handle details. You are sensitive but like to keep your feelings to yourself. You often lose your love ones from being too jealous. You always feel like you own the person you fall in love with and that often blows your relationship.

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You are an idealist and a dreamer. You are gracious, elegant and prudent. You can work with people very well because you believe in persuasion rather than force. You are spiritually inclined and have intuitive qualities inherent in you. People admire your qualities and some even become jealous of you. You are realistic, flexible and adaptable. You are often temperamental but nonetheless you are sensitive. You have an analytical mind and may not feel comfortable in the business world. You are creative and this make you more of a dreamer than a doer. You are willing to sacrifice yourself for the one you love. Your lover will always have your gentleness, care and loyalty. You will always be happy to hand around the one you love.

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Being born on the 12th day of the month, the energy of 3 adds a good amount of vitality to your life. The energy of 3 allows you bounce back rapidly from setbacks, physical or mental. There is a restlessness in your nature, but you seem to be able to portray an easygoing, sometimes "couldn't care less" attitude. You have a natural ability to express yourself in public, and you always make a very good impression. Good with words, you excel in writing, speaking, and possibly singing. You are energetic and always a good conversationalist. You have a keen imagination, but you tend to scatter your energies and become involved with too may superficial matters. Your mind is practical and rational despite this tendency to jump about. You are affectionate and loving, but very sensitive. You are subject to rapid ups and downs.

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The number 13 should help make you a better manager and organizer, but it may also gives you a dominating attitude. You are friendly, humorous and full of energy. You are open-minded. You are sincere, truthful and a dedicated and hard working individual. Your weak point is your hot temper. You may have to confront various limitations due to this 4 energy. Your feeling are likely to be repressed at times. Your insistence on being meticulous about details can be irritating to some. You are willing to start off in one-sided love affairs because you strongly believe that you will eventually win his/her heart. On the other hand, once you are together, you always want to do things your way, which is often the fire starter. You usually run in and out of love quickly.

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You are so confident that sometimes you forget about the people around you. If you have to be in one of the two teams, you will choose to be in the winning team. You are inclined to work well with people and enjoy them. You versatile and talented. You are pretty good in putting forth your ideas and your organizational skills can be matched by few. you are kind and caring but above all, you care for your own benefits. Your imagination is unique and often gets implemented shortly after it comes across. You need change and love traveling. You tend to be very progressive, imaginative and adaptable. You have a quick, clever and analytical mind. You are by nature restless which makes you impatient and bored with routine. You have a tendency to shirk responsibility. You will not get soft with the one you don't really like, no matter how hard he/she tries. But once you feel for someone you have chosen, there's no getting back.

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With a birthday on the 15th of any month, you are inclined to have really strong attachments to home and family. The 1 and 5 equaling 6, provide the sort of energy that makes you an excellent parent or teacher. You are outgoing and love to be at the center of attention. From the outside, you may seem flashy, flirtatious, and tricky but your true self is strong, full of hope to be the leader. You like harmony in your environment and strive to maintain it. When you fail to convince someone, you will get frustrated, and perhaps let your temper show. You learn a lot by observation rather than study and research. You may like to cook, but you probably don't follow recipes. This number shows artistic leanings and would certainly support an talents that may be otherwise in your makeup. You're a very generous and giving person, but perhaps a bit stubborn in certain ways. You are emotional. Many can win your heart at once, but not for long. This is why you hardly win a decent relationship.

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You always follow the good and the right instead of listening to your heart. You are a perfectionist. You care for every word people say about you. You are by nature lonely and generally have the desire to work alone. You are inflexible, and insist on your independence. You need a good deal of time to rest and to introspect. You are a little stubborn sometimes. It is primarily due to this that you find it difficult to maintain permanent relationships. You are a dreamer who is ready to get over the edge to make your dream come true. But nevertheless you are a very homely person and may eventually end up having a family. You have an inclination to the technical, the scientific, and to the religious explorations. You may be emotional, but find it tough to express them. Because of this, there may be some difficulty in giving or receiving affection. You often fall in love with a person who is much different from you, in age and other aspects. Your relationship grows on friendship. Love at first sight is not your style.

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Your birth on the 17th day of the month suggests that you are financially very fortunate. This date blesses you with a very solid business sense. Despite being honest and ethical, this birthday enables you to be shrewd and successful in the world of business and commercial enterprise. You are bestowed with excellent organizational, managerial, and administrative skills that enable you to tackle large projects and significant amounts of money with ease. You are ambitious and highly goal-oriented. You are good with starting projects than you are at finishing them. You neither want to be interfered nor have the desire to mess with others' life. But you are friendly and occasionally a party animal. You often do things in your own way that occasionally go beyond the acceptable limit. People may find you childish and not very attractive in that sense. You like to hide your sensitive self from the others. This makes it hard for you to give or receive affection. Your fun-loving character attracts opposite sex.

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At first glance, people think you are quiet type of person. Actually you are cheerful, but conditionally. You will show your jovial character only in good mood. When you are moody, no one would dare to be around. Because of your emotional fluctuation and frank character, some find you hard to be around. Your birthday on the 18th day of the month suggests that you work well with a group, but still remain someone who needs to maintain individual identity. You have a philanthropic approach to business circumstances in which you find yourself. You are an able organizer and administrator. You are broad-minded, tolerant, generous and compassionate. You have the capability to inspire others with imaginative ideas. You repress your feelings more than expressing them. You have a dramatic way of expressing yourself to others. Strangely enough, you don't expect as much in return as you give. You hardly show your feeling towards opposite sex no matter how much you like him/her. Your partner also has similar character so your love affairs often take quite a while to flourish. Time tells it all. Your sincerity makes you very attractive.

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Your birth on the 19th day of the month adds a tone of independence and extra energy to your Life Path. On the other hand, it poses a number of obstacles for you to surmount before you can actually as independent as you would like to be. You are great in managing everything in your life and this is how you gain respect from others. Because of this quality, you sometimes feel that you are better than the rest. Birth on the 19th day of any month, gives greater self-confidence, will power and very often a rather original approach. Extreme confidence might lead you to the wrong path. You may have a self-centered attitude to life. This 1 energy may undermine your ability and desire to go into the details. You are sensitive, but your feeling stay somewhat repressed. You have a compelling manner that can be dominating in many situations. You do not prefer to conform to conventions. You also don't pay much heed to advices. Consequently, you tend to learn through experiences. Both 19 and 1 are loner numbers and will often tend to experience bouts of loneliness even after you are married. You may take on a tendency to be nervy and prone to anger. When you are in love, nothing can stop you. You may often fight with your partner but, soon after that, you will make up in a way that surprises others.

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You are prudent, circumspect and take things seriously. Before you make any move, you will think of a few alternatives that might take a while. You have a touch of emotion, sensitivity and intuition to your personality. The 2 energy makes you amicable and social which in turn allows you to make friends easily and quickly. Nevertheless you tend to get nervous in the company of a large group. You are by nature warm-hearted and are gifted with emotional understanding. You are patient, imaginative and target oriented. You value friendship more than anything else. You are in constant need of affection. You are subject to mood swings and often suffer from anxiety and mental turmoil. It can be hard for you to bounce back to reality when depression sets in. You usually study your partner carefully before making any move. You never demand anything beyond the natural quality of that person. Your sincerity doesn't bring excitement in your love life but it brings deeply grown relationship.

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The energy of 3 helps you to bounce back rapidly from setbacks, physical or mental. You are impatient by nature, but seem to be able to portray a carefree attitude. You are articulate and invariably leave a good impression whenever you express yourself in public. You are good with your words and excel in speaking, writing and possibly singing. You have a keen imagination, but you tend to dispel your energies and become involved with too may superficial matters. You have a practical and rational mind. You are loving, affectionate and very sensitive. Your life is subject to rapid ups and downs.

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You are bossy but not a leader. You are capable of tackling large scale undertakings, often by applying unorthodox methods. You can assume great responsibility, work hard for long hours to get the work done. You are often rigid and stubborn and have a tendency to repress feelings. Most people look up to you for your capability and confidence although they find you quite stubborn. You should listen more to others. Idealistic, you work for the greater good with a good deal of inner strength and charisma. An extremely capable organizer, you seldom pay attention to details. You are very aware and intuitive. You are a unique and a charming individual. You are subject to a good deal of nervous tension. You hardly take the moderate track. You either love or hate someone. Whom you call friends are the chosen ones. If any of them betray you, you won't let them get away without having hard time.

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You never live your life in the way others want you to. You are talented and versatile, very good at presenting ideas. You love to take up challenges and excitement, and are even ready to face the upshot of your choice. You may have a tendency to get itchy feet at times and need change and travel. You tend to be very progressive, imaginative and adaptable. Your mind is quick, clever and analytical. A restlessness in your nature may make you a bit impatient and easily bored with routine. You may have a tendency to shirk responsibility. Very sociable, you make friends easily and you are an excellent traveling companion. You are usually the one your friends count on. Because you love excitements, you occasionally get involved in forbidden love affairs. You may fall in love with a married person and no one can stop you from making progress. You are very charming, although you might not realize it.

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Born on the 24th, you have a great capacity to take up responsibility and help others. You may also become the mediator and peacemaker in inharmonious situations or situations where tension prevails. You are devoted to family and tend to manage and protect. This birth date adds to the emotional nature and to the sensitivities. Affections are important to you; both the giving and the receiving.

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You are very optimistic and that's why you always enjoy life. You are gifted in entertaining others. Your birth on the 25th day of the month (7 energy) gives you some special interest in technical, scientific, or other complex and often hard to understand subjects. You may become something of a perfectionist and a stickler for details. Your thinking is logical and intuitive, rational and responsible. Your feelings may run deep, but you are not very likely to let them show. This birthday makes you a more private person, more introspective and perhaps more inflexible. In friendships you are very cautious and reserved. You are probably inventive, and given to unique approaches and solutions. Your friends love and trust you. You'll be the first they come to when they are in need of someone to speak their heart out. Sometimes you fall in love just because you want to be in love, not that you really like that person. You always be seen as a sweet couple but you can't really get over your love ones from past. Your partner is usually crazy about you because you are remarkably charming and romantic.

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You are always curious and responsive to changes. Routine life is not the way you choose to live. Your birth on the 26th day of the month modifies your life path by increasing your capability to succeed in the business world. It is the 2 and 6 energies that enable you to co-ordinate well with others, in terms of work. There is a marked increase in organizational, managerial, and administrative abilities. You are efficient in handling finance. Ambitious and energetic, while generally remaining cooperative and adaptable. This birthday is practical and realistic, often seeking material satisfaction. Travelling is your favorite hobby because excitement is what you are after. You will not stand being around the one you dislike. Your love comes and goes quickly. You can be deeply in love but soon after you will be looking around for the next one.

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Your birth on the 27th day of the month (9 energy) adds a tone of selflessness and humanitarianism to your life path. You are sensitive and vulnerable. Tears often run down your cheeks even when the matter is not that bad. This might be the result from being to pessimistic. You might seem cold on the shell, but your inner self is a kind loving person. You need a good amount of time to be with yourself in order to contemplate. This birthday makes you generous. cooperative and broad minded. You are the type of person who likes to use persuasion rather than force to achieve your ends. You might seem cold on the shell, but your inner self is a kind loving person. You tend to be very sensitive to others' feelings and needs. You are giving in nature where friendship is concerned, without expecting much from them in return. You will be elegantly dressed, no matter how casually dressed your date may be. You are demanding in love and sometimes to an unacceptable extend.

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You are a capable person but you usually underestimate your own ability. This is the cause of missing numbers of opportunity to step forward. You are endowed with executive ability and leadership qualities. A birthday on the 28th of any month gives greater will power and self-confidence, and very often a rather innovative approach. Unlike much of the other 1 energy, this birthday is one that endows with the ability to initiate a job and continue with it until it is finished. You can handle details pretty well. You are sensitive and restrained with your feelings. sensitive, but your feeling stay somewhat repressed. If you try to give yourself a chance, you can be successful in life. Try to see things on the bright side and you will be happier than ever. You are quite unlucky in love. The one in your arm is not the one in your heart. Your love has so many ups and downs. You often chicken out before seeing any progress in love.

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You can trust your sixth sense. Life is exciting so routine job is not your interest. You have great ideas and fantastic imagination. Your birthday on the 29th adds a tone of idealism to your nature. You are imaginative and creative, but feel rather uncomfortable in the corporate world. You are very aware and sensitive, with outstanding intuitive skills and analytical abilities. You often feel tired of things and people around you. The 29 reduces to 11, one of the master numbers which often produces much nervousness and anxiety. This is the birthday of the dreamer rather than the doer. You do, however, work very well with people. You can tell what's in the mind of another person just from looking into his/her eyes. You are paranoid and jealous and these are the cause of fights between you and your lover. Sometimes the thing you believe in is just your imagination.

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Your birth on this day shows that individual self-ex-pression is necessary for your happiness. You have a good way of expressing yourself clearly and understandably with words. You are always surrounded by a circle of friends. You are friendly and fun to be with. Although you occasionally disappoint them by being stubborn, but over all, they love you for what you are. You have a good chance of success in fields requiring skill with words. You are pretty dramatic in your presentation and you may be a good actor or a natural mimic. You have a vivid imagination that can help you in becoming a good writer or story-teller. You are strong in your opinions, always tend to think that you are on the right side of an issue. There may be a tendency in you to dispel your energies and have a lot of loose ends in your work. You may have significant artistic talent and can be very creative.

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Your birthday on the 31st of the month makes you a good organizer, manager, an energetic and dependable worker. They all in turn may help you achieve success in the business world. Serious and sincere, you have the patience and determination necessary to accomplish a great deal. Your approach can be original, but often stubborn and rigid. Sensitivity may be present, but feeling are likely to be repressed. You are good with detail and insist on accuracy, but at times scatter energies. You are a practical thinker but not devoid of imagination. You love to travel and don't like to live alone. You should probably marry early, for responsibility is necessary for your stability.

10 free amazing secrets of naturally-thin people help to lose weight without dieting. These non-diet solutions from Sound Feelings provide easy self-study techniques for overweight and weight-management. You probably already know everything you care to know about "weight-loss plans," "weight-reducing diets," "weight-reducing plans," "healthy diet" and exercise. Yet, for most people, something still seems to be missing! What follows will very likely be this missing link. Best wishes on your success!

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1 Develop Your Ability to Focus.

The mind of the naturally-thin person tends to be focused, with attention on one thing at a time. This quality simply mirrors itself in the body as narrow, pointed, intense or small. In contrast, the mind of the person who has a problem with their weight tends to be distracted, with attention on many things at once. This quality simply mirrors itself in the body as expanded, broad, encompassing or large. These are generalizations, of course, with many exceptions, but consider the overall message here. Because of the mind/body connection, it is suggested that the body will usually reflect the condition of the mind. As you narrow the focus of your mind, you will gradually experience a similar thinning within your body. Focusing in its pure sense takes no effort. It exists simply as the absence of distraction.

2 Release the Cellular Memory.

It is crucial to release the cellular imprint from the cells of the body itself so that once the preferred weight is established you won't still "feel fat." Otherwise, even after losing weight, every metabolic function will tend to continue as if you are still overweight. No wonder it is so natural to gain weight back. Different emotions are linked to various parts of the body. Fat will often collect in these areas — to create a type of protection from feeling an old hurt or anger. By finally releasing the old pain or anger, the weight will have nothing to cling to. This might be called "emotional weight loss"— an actual reduction of negative emotional energy. There are at least 37 modalities known to serve as catalysts to begin the release of negative cellular patterns. Many of these systems involve direct physical touch or manipulation. Others are more subtle, involving "energetic" healing. Music is also known to trigger a release of the cellular memory.

3 Fear of Food Keeps You Fat.

It is advantageous to change broadly-ingrained attitudes and assumptions that repeatedly sabotage success in attaining permanent weight loss. Interestingly, these attitudes and assumptions seem to be common among people with weight problems and not among people who are naturally-thin. There are three reasons why fear of food keeps one fat. (1) You overcompensate later. (2) The body thinks it's starving and literally stores calories. (3) (the least obvious) Food absorbs an emotional "charge" and will affect the person eating it.

4 Eat Only When You Are Hungry.

Don't eat when you are not hungry. A naturally-thin person simply would refuse food if he or she is not hungry.

5 Eat Regular Meals.

Have you noticed that naturally-thin people do not skip meals? Why do you? Especially breakfast — Do you skip meals hoping to lose weight put on from the previous day? Please stop this — it only backfires.

6 Treat Yourself to the Foods You Like.

Assuming you basically have a good diet, you must give yourself a treat once in a while. However, try to do it in moderation, the way a naturally-thin person would. For example, if you want some cookies, have two, three, four... then have one or two more, if you still want them. Then stop. THE TREAT IS OVER! If you keep eating, the treat now becomes the curse!

7 Never Eat in a Hurry.

It seems that the people who eat standing up are the people who claim that there is no time to eat. They eat while they are cooking, while they are walking. The problem here is that not enough importance is placed on eating. But it is very important. When we rush, we end up feeling un-nourished, even though our stomach might be full. This will cause us to ultimately eat more than we want. How many times do you you see a naturally-thin person eating standing up, in a hurry? They instinctively place a high value on the pleasure of dining. They don't want to rush it. Think about it.

8 Redefine the "Perfect Body."

By today's strange standards, most people would consider Marilyn Monroe to be overweight! Yet putting things in perspective, if Marilyn Monroe had lived in the Renaissance period, she would have been considered too thin! She would have been "sickly" compared to the cherubic ideal. This was when food was scarce and to be what we now call "fat" was considered a sign of health and wealth.There are many many perfect body-types and it is extremely unfortunate that we allow ourselves to be influenced by society's narrow, limiting, and unhealthy standards. Invariably, people set a goal of what they would prefer to look like in their mind. This goal usually is not only disrespectful to that person's inherent body structure, but the process of reaching it would be to cause a severe risk to his or her health. We must change our individual and collective body image. We must change our distorted perceptions of what constitutes a beautiful body. Until then, people will continue to strive for the impossible, remaining in a constant state of self-hatred and unhappiness.

9 Visualize Your Success.

All people who succeed in anything admit that they practice visualizing their success, with optimism, before actually attaining their goal.

10 Don't Tell Everyone.

When we begin something new, we are very vulnerable. It is like a little seedling which needs to be protected from the elements until it is strong enough to withstand the forces of wind, sun, water, etc. If we tell the wrong people about what we are doing too soon, we will sabotage the results. Only discuss your intentions to seriously lose weight with people you know for sure are there for you and who are completely supportive.

Where is the sun when you see a rainbow?

What makes the bow?

He writes:"Considering that this bow appears not only in the sky, but also in the air near us, whenever there are drops of water illuminated by the sun, as we can see in certain fountains, I readily decided that it arose only from the way in which the rays of light act on these drops and pass from them to our eyes. Further, knowing that the drops are round, as has been formerly proved, and seeing that whether they are larger or smaller, the appearance of the bow is not changed in any way, I had the idea of making a very large one, so that I could examine it better.

Descarte describes how he held up a large sphere in the sunlight and looked at the sunlight reflected in it. He wrote "I found that if the sunlight came, for example, from the part of the sky which is marked AFZ

and my eye was at the point E, when I put the globe in position BCD, its part D appeared all red, and much more brilliant than the rest of it; and that whether I approached it or receded from it, or put it on my right or my left, or even turned it round about my head, provided that the line DE always made an angle of about forty-two degrees with the line EM, which we are to think of as drawn from the center of the sun to the eye, the part D appeared always similarly red; but that as soon as I made this angle DEM even a little larger, the red color disappeared; and if I made the angle a little smaller, the color did not disappear all at once, but divided itself first as if into two parts, less brilliant, and in which I could see yellow, blue, and other colors ... When I examined more particularly, in the globe BCD, what it was which made the part D appear red, I found that it was the rays of the sun which, coming from A to B, bend on entering the water at the point B, and to pass to C, where they are reflected to D, and bending there again as they pass out of the water, proceed to the point ".

This quotation illustrates how the shape of the rainbow is explained. To simplify the analysis, consider the path of a ray of monochromatic light through a single spherical raindrop. Imagine how light is refracted as it enters the raindrop, then how it is reflected by the internal, curved, mirror-like surface of the raindrop, and finally how it is refracted as it emerges from the drop. If we then apply the results for a single raindrop to a whole collection of raindrops in the sky, we can visualize the shape of the bow.

The traditional diagram to illustrate this is shown here as adapted from Humphreys, Physics of the Air. It represents the path of one light ray incident on a water droplet from the direction SA. As the light beam enters the surface of the drop at A, it is bent (refracted) a little and strikes the inside wall of the drop at B, where it is reflected back to C. As it emerges from the drop it is refracted (bent) again into the direction CE. The angle D represents a measure of the deviation of the emergent ray from its original direction. Descartes calculated this deviation for a ray of red light to be about 180 - 42 or 138 degrees.

The ray drawn here is significant because it represents the ray that has the smallest angle of deviation of all the rays incident upon the raindrop. It is called the Descarte or rainbow ray and much of the sunlight as it is refracted and reflected through the raindrop is focused along this ray. Thus the reflected light is diffuse and weaker except near the direction of this rainbow ray. It is this concentration of rays near the minimum deviation that gives rise to the arc of rainbow.

The sun is so far away that we can, to a good approximation, assume that sunlight can be represented by a set of parallel rays all falling on the water globule and being refracted, reflected internally, and refracted again on emergence from the droplet in a manner like the figure. Descartes writes

I took my pen and made an accurate calculation of the paths of the rays which fall on the different points of a globe of water to determine at which angles, after two refractions and one or two reflections they will come to the eye, and I then found that after one reflection and two refractions there are many more rays which can be seen at an angle of from forty-one to forty-two degrees than at any smaller angle; and that there are none which can be seen at a larger angle" (the angle he is referring to is 180 - D).

A typical raindrop is spherical and therefore its effect on sunlight is symmetrical about an axis through the center of the drop and the source of light (in this case the sun). Because of this symmetry, the two-dimensional illustration of the figure serves us well and the complete picture can be visualized by rotating the two dimensional illustration about the axis of symmetry. The symmetry of the focusing effect of each drop is such that whenever we view a raindrop along the line of sight defined by the rainbow ray, we will see a bright spot of reflected/refracted sunlight. Referring to the figure, we see that the rainbow ray for red light makes an angle of 42 degrees between the direction of the incident sunlight and the line of sight. Therefore, as long as the raindrop is viewed along a line of sight that makes this angle with the direction of incident light, we will see a brightening. The rainbow is thus a circle of angular radius 42 degrees, centered on the antisolar point, as shown schematically here.

We don't see a full circle because the earth gets in the way. The lower the sun is to the horizon, the more of the circle we see -right at sunset, we would see a full semicircle of the rainbow with the top of the arch 42 degrees above the horizon. The higher the sun is in the sky, the smaller is the arch of the rainbow above the horizon.

What makes the colors in the rainbow?

The colors of the rainbow arise from two basic facts:

• Sunlight is made up of the whole range of colors that the eye can detect. The range of sunlight colors, when combined, looks white to the eye. This property of sunlight was first demonstrated by Sir Isaac Newton in 1666.
  
• Light of different colors is refracted by different amounts when it passes from one medium (air, for example) into another (water or glass, for example).

Descartes and Willebrord Snell had determined how a ray of light is bent, or refracted, as it traverses regions of different densities, such as air and water. When the light paths through a raindrop are traced for red and blue light, one finds that the angle of deviation is different for the two colors because blue light is bent or refracted more than is the red light. This implies that when we see a rainbow and its band of colors we are looking at light refracted and reflected from different raindrops, some viewed at an angle of 42 degrees; some, at an angle of 40 degrees, and some in between. This is illustrated in

Ana excellent laboratory exercise on the mathematics of rainbows is here, and F. K. Hwang has produced a fine Java Applet illustrating this refraction, and Nigel Greenwood has written a program that operates in MS Excel that illustrates the way the angles change as a function of the sun's angle.

What makes a double rainbow?

It is possible for light to be reflected more than twice within a raindrop, and one can calculate where the higher order rainbows might be seen; but these are never seen in normal circumstances.

Why is the sky brighter inside a rainbow?

What are Supernumerary Arcs?

Mikolaj and Pawel Sawicki have posted several beautiful photographs of rainbows showing these arcs.

The "purity" of the colors of the rainbow depends on the size of the raindrops. Large drops (diameters of a few millimeters) give bright rainbows with well defined colors; small droplets (diameters of about 0.01 mm) produce rainbows of overlapping colors that appear nearly white. And remember that the models that predict a rainbow arc all assume spherical shapes for raindrops.

There is never a single size for water drops in rain but a mixture of many sizes and shapes. This results in a composite rainbow. Raindrops generally don't "grow" to radii larger than about 0.5 cm without breaking up because of collisions with other raindrops, although occasionally drops a few millimeters larger in radius have been observed when there are very few drops (and so few collisions between the drops) in a rainstorm. Bill Livingston suggests: " If you are brave enough, look up during a thunder shower at the falling drops. Some may hit your eye (or glasses), but this is not fatal. You will actually see that the drops are distorted and are oscillating."

It is the surface tension of water that moulds raindrops into spherical shapes, if no other forces are acting on them. But as a drop falls in the air, the 'drag' causes a distortion in its shape, making it somewhat flattened. Deviations from a spherical shape have been measured by suspending drops in the air stream of a vertical wind tunnel (Pruppacher and Beard, 1970, and Pruppacher and Pitter, 1971). Small drops of radius less than 140 microns (0.014 cm) remain spherical, but as the size of the drop increases, the flattening becomes noticeable. For drops with a radius near 0.14 cm, the height/width ratio is 0.85. This flattening increases for larger drops.

Spherical drops produce symmetrical rainbows, but rainbows seen when the sun is near the horizon are often observed to be brighter at their sides, the vertical part, than at their top. Alistair Fraser has explained this phenomenon as resulting from the complex mixture of size and shape of the raindrops. The reflection and refraction of light from a flattened water droplet is not symmetrical. For a flattened drop, some of the rainbow ray is lost at top and bottom of the drop. Therefore, we see the rays from these flattened drops only as we view them horizontally; thus the rainbow produced by the large drops is is bright at its base. Near the top of the arc only small spherical drops produce the fainter rainbow.

What does a rainbow look like through dark glasses?

Other Questions about the Rainbow

• "What is the rainbow's distance?" It is nearby or far away, according to where the raindrops are, extending from the closest to the farthest illuminated drops along the elements of the rainbow cone.
  
• Why is the rainbow so frequently seen during summer and so seldom during winter?" To see a rainbow, one has to have rain and sunshine. In the winter, water droplets freeze into ice particles that do not produce a rainbow but scatter light in other very interesting patterns.
  
• "Why are rainbows so rarely seen at noon?" Remember that the center of the rainbow's circle is opposite the sun so that it is as far below the level of the observer as the sun is above it.
  
• "Do two people ever see the same rainbow?" Humphreys points out that "since the rainbow is a special distribution of colors (produced in a particular way) with reference to a definite point - the eye of the observer - and as no single distribution can be the same for two separate points, it follows that two observers do not, and cannot, see the same rainbow." In fact, each eye sees its own rainbow!!
  Of course, a camera lens will record an image of a rainbow which can then be seen my many people! (thanks to Tom and Rachel Ludovise for pointing this out!)
  
• "Can the same rainbow be seen by reflection as seen directly?" On the basis of the arguments given in the preceding question, bows appropriate for two different points are produced by different drops; hence, a bow seen by reflection is not the same as the one seen directly".

What are Reflection Rainbows?

What is a Lunar Rainbow?

Rainbows and Proverbs

The meteorological discussion Humphreys presents is appropriate for the northern temperate zones that have a prevailing wind, and also for a normal diurnal change in the weather.

Experiments

In Minnaert's excellent book Light and Colour in the Open Air you can find a number of experiments on how to study the nature of rainbows. Here is an illustration of one of his suggestions. Other demonstration projects are listed here .

Meg Beal, while a seventh-grader, prepared a science fair project that illustrated the nature of rainbows. The Beal family provided a photograph (1MB) of her excellent demonstration.

For those wanting to try to demonstrate the nature of a rainbow in a classroom, here are examples.

An informative tutorial on optics can be found here.

I am indebted to William C. Livingston, astronomer at the National Optical Astronomy Observatory in Tucson Arizona for his expert assistance in preparing this paper, and to Seth Sharpless for his critical reading of the manuscript. Charles A. Knight, an expert on rain at the National Center for Atmospheric Physics, provided valuable guidance on the interesting properties of raindrops.

References

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Magie, W.F. ed, A Source Book in Physics 1935

Minnaert, M., The Nature of Light and Color in the Open Air, Dover 1954

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Pruppacher, H. R. and Beard, K. V., 1970, Quart. J. Royal Meteor. Soc. 96, 247

Pruppacher, H. R. and Klett, J. D. 1978, Microphysics of Clouds and Precipitation, Reidel Publishing Company

Pruppacher, H. R. and Pitter, R. L., 1971, Atmos. Sci. 28, 86

Science Universe Series (David Jollands, ed) Sight, Light, and Color Arco Publishing Inc. 1984 ISBN 0-668-06177-4

Strom, Karon; 1994 Rainbows

van Beeck, J.P.A.J., 1997, Rainbow Phenomena: development of a laser-based, non-intrusive technique for measuring droplet size, temperature, and velocity CIP-Data Library Technische Universiteit Eindhoven (ISBN 90-386-0557-9)

Wicklin, F.J. and Edelman, P. Circles of Light The Mathematics of Rainbows