To compute the magnification given by a microscope it is necessary to multiply together the separate magnification due to the eyepiece and objective. Practically manufacturers use the following formula (not entirely accurate for calculating the magnification*): Divide 100 by the product of what are called the focal length of objective and eyepiece expressed in inches. For example: Two-inch eyepiece and objective. To find the magnifying power: Applying the above rule, 2X; 100 ÷ % 250 diam., the magnifying power.

The manufacturers send with their instruments cards referring to the magnifications of the lenses, of which the following is an abstract :—

It will be seen from the above that the eyepieces are sometimes lettered instead of numbered.

The Microscope and the Pharmacopoeia.-Generally in descriptions of crude drugs it is sufficient to indicate the distinctive

* See paper by W. LeConte Stephens, American Journal of Science, vol. XL, July, 1890,

characteristics that are visible to the naked eye, "and, when necessary, such as are visible under an ordinary good pocket lens magnifying about ten diameters." Ex.-Unguentum Hydrargyri, Amylum, Aloe, Lycopodium, etc. For expert work the compound microscope is invariably called into requisition. The microscopical unit of measurement is the 1000th of a mm., known as the micromillimeter (mkm).

Alligation in Pharmacy.

Alligation is the process of mixing substances of different values to produce a mixture of given mean value.

1 Problem.-Given 2 lbs. of a certain powder at 7 per cent., 3 lbs. of another powder at 8 per cent., 5 lbs. of another at 16 per cent. and 6 lbs. of another at 18 per cent.; to find the average per cent.

Rule.-Multiply the percentage of each kind by the number of it. Add the products. Divide the sum of the products by the sum of the numbers.

2 Problem.-Given 4 lbs. of powder at 7 per cent., to be mixed with three other kinds at 8 per cent, 16 per cent and 18 per cent., so that the mixture shall average 14 per cent. To find the amounts of the 8, 16 and 18 per cents. that must be used.

Explanation. The 7 per cent. and 16 per cent. kinds when used in certain quantities will give an average of 14 per cent. That is 7 per cent. put into a 14 per cent. average gains 7 per cent. The 16 per cent. put into a 14 per cent. average loses 2 per cent. In a similar manner the 8 per cent. gains 6 per cent. and the 18 per cent. loses 4 per cent.

Therefore, for the average of the 7 and 16 the difference between 14 and 16 gives the proportional part of the 7 per cent. kind, and the difference between 7 and 14 gives the proportional part of the 16 per cent. kind. In the same manner for the 8 and 18. The sum of the parts is equal to 19. Then, by proportion, find the amounts of the other kinds. Thus::

Rule. Find the proportional parts according to the above explanation. Then, by proportion, find the amount of each kind.

3. If the problem be to find the ratio of the ingredients to be used, in order to make a certain definite amount, then the method of solution as given in No. 2 is to be used.

2

Suppose the mixture to contain 19 lbs., as in No. 2, then

4 7 6

15, 15, 15, 15, of 19 lbs. will be the results required.

PROBLEMS IN ALLIGATION AND SPECIFIC GRAVITY.

In alligation.

(1) How shall samples of powdered opium be mixed (the opium being 6, 8, 10, 15, and 17 per cent. of morphine respectively) to make a mixture containing 12 per cent. of the alkaloid?

(2) How shall one mix 150 lbs. of jalap, containing 14 per cent. resin, with lots containing 9 and 11 per cent. to make an average of 122 per cent.?

(3) How many pounds of 14 per cent. can be made from 9 pounds of 16 per cent. by diluting with sugar of milk? (4) How much glycerine shall I mix with water to make 25 pounds of solution having a specific gravity of 1.16?

(5) Wishing to make 150 gallons of 50 per cent. alcohol, how shall one mix lots containing 60, 65, 35, and 20 per cent. respectively ?*

(6) How shall I make a solution of KOH, sp. gr. 1.036, from solutions having the sp. gr. of 1.2, 1.25, and 1.4? Use water as 1.

Rules of the U. S. P. for making an alcohol of any required lower percentage from an alcohol of any given higher percentage:

I. BY VOLUME.-Designate the volume-percentage of the stronger alcohol by V, and that of the weaker alcohol by v.

Rule.-Mix v volumes of the stronger alcohol with pure water to make V volumes of product. Allow the mixture to stand until full contraction has taken place, and until it has cooled; then make up any deficiency in the V volumes by adding more water.

Example.-An alcohol of 30 per cent. by volume is to be made from an alcohol of 94 per cent. by volume.-Take 30 volumes of the 94 per cent. alcohol, and add enough pure water to produce 94 volumes.

II. BY WEIGHT.-Designate the weight-percentage of the stronger alcohol by W, and that of the weaker by w.

Rule.-Mix w parts by weight of the stronger alcohol with pure water to make W parts by weight of product.

Example.--An alcohol of 50 per cent. by weight is to be made from an alcohol of 91 per cent. by weight.-Take 50 parts by weight of the 91 per cent. alcohol, and add enough pure water to produce 91 parts by weight.

(7) How many gallons of official ammonia can be made from 35 gallons of 28 per cent. ammonia? In this example water must be figured at 0 (zero).

(8) How many ounces of scammony containing 80 per cent. resin can be made from 54 ounces, assaying 57 per cent., by mixing with lots containing 85, 90, and 92 per cent. of resin?

(9) How much water will be required to make 5 lbs. of solution of soda, sp. gr. 1.12, from a solution having the sp. gr. of 1.40?

(10) How shall one make 240 gallons of bay rum containing 60 per cent. of alcohol from lots containing 70, 62, 58, and 50 per cent.?

(11) How much 96 per cent. sulphuric acid must be mixed with 20 ounces at 15 per cent., and 30 ounces at 45 per cent., to make 60 per cent. acid?

(12) How much hydrochloric acid, sp. gr. 1.16, 1.12, and 1.10, must be mixed to make 1000 ounces, sp. gr. 1.15?

(13) I have 7 kilogrammes of 60 per cent. and 9 kilos of 80 per cent. alcohol. How shall these be mixed-all into 60 per cent. and how much will the mixture make? Water is used for dilution of course.

(14) How shall one make 250 gallons of dilute alcohol from official alcohol?

(15) If tincture of capsicum is made from 19 parts by weight of official alcohol to 1 of water, what is the per cent. of absolute alcohol in the menstruum?

(16) How shall I make 32 ounces of salt bath, sp. gr. 1.15, from solutions having sp. gr. of 1.30, 1.27, and 1.20?

Problems in specific gravity.

Rule. Divide the weight of the substance in air by the weight of an equal bulk of distilled water.

This rule is very simple, is easily comprehended, but to apply it in every case is difficult. In practice the operator is often puzzled to know how he shall best determine the