"It would be misleading and therefore irresponsible to try to claim that essential oils

are both powerful in their beneficial effects and totally harmless otherwise".

Please read these general safety precautions again and again:

Keep essential oils out of reach of children (and pets)
Do not use essential oils with babies under 6 weeks old and with children without confirmed knowledge
If you are pregnant or lactating always seek the advice of a qualified aromatherapist
Do not take essential oils internally unless properly trained in the safety issues of doing so. Internal use is the most hazardous method of application and is outside the scope of holistic aromatherapists.
Do not apply undiluted essential oils to the skin except in rare cases for very short period, we want to avoid sensitization which could prevent from using our cherished essential oils for the rest of our life
Keep essential oils away from the eyes
If you have a medical condition such as epilepsy, high blood pressure, heart conditions, liver or kidney disease or are taking medications, seek the advice of a professional aromatherapist.
Where possible always purchase essential oils that are 100% pure and organic.
Research and get to know the oil prior to using it on others.

Moreover, these are the factors that influence the safety of essential oils as well:

The method of application
How much of the essential oils is used: The more IS NOT the better. Stay safe with a maximum dilution of 5% for local application, preferably 1-2% for full body massage.
The person being treated: age, skin condition, health...
The potential toxicity of the essential oils used and any drug interactions
The purity and freshness of the essential oils

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