This section is from the book "A Text-Book Of Pharmacology, Therapeutics And Materia Medica", by T. Lauder Brunton. Also available from Amazon: A text-book of pharmacology, therapeutics and materia medica.
The circumstances which affect dosage have already been discussed (p. 37). In practice we reckon the dose according to age, making allowances, however, for the size and sex of the patient. Various tables have been drawn up for this purpose. One in common use is Dr. Young's. It is to convert the age into a fraction by adding twelve to it and using the number thus obtained as the denominator, the age itself being the enumerator. Thus, if a child's age be three years, the denominator will be 3 + 12 = 15, and the enumerator will be 3. The dose for the child will therefore be 3/3+12 = 3/15=1/5 that for an adult. For a child five years old it will be 5/5+12 = 5/17, which is between one-third and one-fourth of that for an adult. If the child is large for its years, we would give one-third; if small, we would rather give one-fourth.
Another rule, proposed by Dr. Cowling, is to divide the number of the patient's next birthday by twenty-four. Thus, for a child three years old, the fraction representing the dose would be 4/24=1/6; for a child five years old, 6/24=1/4
The rule which I should propose as being more convenient for the metric system is a modification of Dr. Cowling's. If we assume that the body has attained its full growth at twenty-five years of age instead of twenty-four, we get the proportion by dividing the number of the next birthday by twenty-five. Thus, for a child three years of age, the proportion would be fa = nearly 1/6; for a child five years of age, -fa = between 1/5 and 1/4. This number does not lend itself readily to fractions such as the preceding, but it is very easy to divide by twenty-five by simply multiplying by four and dividing by 100. When the metrical system is used, all that is necessary is to multiply the full dose by the number of the child's next birthday, then by four, and remove the decimal point two places to the left. Thus, if the full dose for an adult be 1 gramme, the dose for a child of three will be 1x4x4/100 =.160 gramme or 16 centigrammes. If the full dose for an adult be .3 gramme, the dose for a child of three will be x4x4/100 = .048, or 48 milligrammes. If the full dose be 1 gramme, the dose for a child of five will be 1x6x4/100 = .240 gramme or 24 centigrammes. If the full dose be .3 gramme, the dose for a child of five will be .3x6x4/100 = .072 gramme or 72 milligrammes. To put this rule shortly, the number of grammes in the full dose multiplied by the child's next birthday and by four, gives the result in centigrammes. The number of decigrammes multiplied in the same way gives the result in milligrammes.