**Proof spirit:** The proof spirit is defined as a mixture of absolute alcohol and water which has 57.1% v/v ethyl alcohol. The strength of alcoholic preparations is indicated by degrees ‘over proof’ and ‘under proof’ for excise purposes. Proof spirit is that mixture of alcohol and water which at 51° F weighs 12/13th of an equal volume of water. In India 57.1 volume of ethyl alcohol is considered to be equal to 100 volumes of proof spirit. This means that alcoholic solutions containing 57.1%v/v alcohol are a proof spirit which is said to be 100 proof. So any strength above proof strength is expressed as overproof (O.P.) and any strength below proof strength is expressed as under proof (U.P.).

**The formula for calculation of overproof and underproof:**

- 57.1% v/v alcohol = 100 volume of proof spirit. Therefore, 1% v/v alcohol = 100/57.1 = 1.753 volume of proof spirit.
- So multiply the given percentage strength of alcohol by 1.753 and deduct from the product
- If the result is positive it is known as overproof.
- If the result is negative, it is known as underproof.

**Conversion of percentage strength into proof strength:**

Multiply percentage strength v/v with 100/57.1 i.e. 1.753 and subtract the resulting product from 100.

**Example**

Find out the proof strength of alcohol which is 90%v/v and 30%v/v

**Solution:**

90% v/v = 90 x 1.753 = 157.77

Thus, proof strength = 157.77 – 100 = 57.77° O/P (Over proof) 30% v/v = 30 x 1.753 = 52.59.

Thus, proof strength = 52.59 -100 = – 47.41 i.e. 47.41° U/P (Underproof).

**Conversion of proof strength into percentage strength:**

Add 100 to overproof and subtract 100 for underproof spirit, and divide the resulting product by 1.753.

**Example**

Find out the percentage strength corresponding to 40° O/P and 25° U/P.

**Solution:**

40° O/P = 100 + 40 /. 1.753 = 79.86% v/v

25° U/P =100-25 /1.753 = 42.79% V/V.

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