they have no provision for expansion of liquid without overflowing, and therefore it may not be useless to represent one or two of a construction that is convenient for attaining very accurate results easily. Figure 1 of the cut is an ordinary 500 c. c. measuring flask, selected with a narrow neck and the mark low in the neck. A section of the neck just above the mark but including it is then heated in the lamp and drawn out so as to contract it to about one-half the original diameter. This is chemically cleaned, dried and tared, and the tare marked upon the glass. It is convenient to have a counterpoise for such a bottle, and this is easily made of a small vial and shot, the vial being closed by a rubber stopper which does not change in weight by hygrometric moisture. Such a counterpoise is illustrated by Fig. 3. It is sometimes convenient that this counterpoise should not only counterpoise the bottle, but also the standard volume of water. Then 500 grammes of recently boiled distilled water is carefully weighed into the flask at the temperature of the room and weights. This at room tempera. tures should fill the flask to near the top of the narrow portion of the neck. The flask is then corked and placed in a large bath of ice and water immersed to the upper end of the neck contraction. The bath is to be kept supplied with a moderate stratum of pieces of floating ice during two hours, being occasionally stirred. A corrected thermometer in the bath should indicate about 3° C. during the first hour, and should then be allowed to gradually reach 4°C. by a diminished supply of ice. At the end of the two hours, when the bath has been kept at 4° C. for at least half an hour, the flask should be raised just enough above the surface of the full bath to get the surface of the water in the neck on a level with the eye. A dot is made on the glass with a small file at the lower or lowest part of the crescent-like meniscus, so that when seen horizontally the lowest part of the curve just touches the dot. A slender thermometer, Fig. 2, whose error is known, is then passed down into the flask, still in the bath, and is moved around until it remains without change, and is then read. It will always be found to be within 0.2° C. of the required 4° C., and this is sufficiently accurate, as the water does not perceptibly expand within a degree each way from 4° C. The volume of 500 grammes of water at 4°C., or at its maximum density, is now obtained, and the 500 multiplied by 2 gives 1000. Place a decimal point after the 1, and the standard of unity is complete by which to measure all other liquids.

The dot on the neck of the flask is afterward to be extended around the neck to form a ring, so that in reading, the front and back part of the mark may be made to coincide, thus securing a horizontal position for the adjustment in filling.

It is convenient to have one or more smaller flasks for smaller quantities of liquid, and a flask of 100 c. c. is represented by Fig. 4, made very much in the same way. In such, the bath alone must be depended upon for temperature, as the contraction of the neck necessary for accurate reading is too small to admit a thermometer. Still smaller flasks down to 10 c. c. may be made in the same way, but with such, great care and skill are needed to obtain accurate determinations.

Returning now to the large flask, if the bath be brought to 15° C. 59° F., and the water inside be stirred with the thermometer until it also reaches 15° C., and the thermometer be removed, the water will be found expanded considerably, so as to stand much above the ring mark. With a pipette take out water until the meniscus is again adjusted to the mark, remove the flask from the bath and allow it to attain the temperature of the room and then weigh it. The water will now weigh 499.72 grammes, which multiplied by 2 gives 99944. A decimal point placed before this makes it 99944, which is the apparent s. g. of water at 15° C., as compared with water at 4° C., as unity or as 1.00000. But this is the apparent and not the true s. g., for in raising the temperature of the water from 4° C. to 15° C., or 11° C., the flask has expanded so as to hold more water up to the ring mark than it did before, and therefore the volume of water is not exactly the same as before, but is greater by the amount of the expansion of the glass. The amount of this expansion of glass vessels by temperature has been frequently determined by good observers, and for a 500 c. c. flask it has been found to be about '00002 c. c. for each 1°C. Then, as the temperature was raised 11°C. the total would be 00002 multiplied by 11, which is equal to 00022 c. c., and this, for the purposes of this correction, may be taken as grammes. Then the flask being 00022 gramme larger at the second weighing than at the first or standard weighing, this amount must be subtracted from the apparent to get the true s. g. Then 00022 subtracted from 49972 gives 49950, and this multiplied by 2 gives 99900 as the true s. g. of water at 15° C. as compared with water at 4° C., as unity. In this way the following specific gravities for recently boiled distilled water were obtained by actual experiment with the 500 gram. flask.

In using a 100 gramme flask, of course the correction is just onefifth of the fraction above given; that is (000020÷5=).000004 gramme for each 1°C.

Apparent s. g.

At 4° C. 39.2° F. 1.000000. corrected for 0° C.= '000000.

True s. g.

1,000000.

This is intended to illustrate the error through expansion of glass vessels, and the rule and method of correcting it; and also the effect of temperature on the expansion of liquids, the observations being made with a large flask, weighed to milligrammes, thus extending the figures to six decimal places. This is far beyond the sphere of other errors, such as those of filling, reading the mark, pressure, etc., but it illustrates the necessity for a uniform standard, which is not yet attained, in general usage, and the nature and extent of the principal difference between apparent and true specific gravity; and it shows that the error for expansion of glass in the ordinary range of specific gravity determinations, that is up to 25o C., is always beyond the third decimal place, and hence it is that it is commonly and properly disregarded in every day practice. The specific gravities stated in medicine and pharmacy are always apparent, and it is supposed that the pharmacopoeias and their commentaries always express apparent specific gravities, though this is nowhere stated, nor even do they state the temperature of the standard volume of water. They have a stated temperature, which is not uniform, but leave it to doubt whether the standard volume of water is to be weighed at their stated temperature or at some other.

There is reason to believe that many of the published tables of specific gravities are corrected for all the errors, small and great, and that these tables are often adopted and quoted in pharmacopoeias and dispensatories, and that this is the reason why the apparent or uncorrected specific gravities of every day practice so rarely agree with them. Therefore, it may be said, as a general deduction or inference, that whenever an apparent specific gravity agrees with authorities such as the pharmacopoeias, within one or two units of the third decimal place, it is practically and sufficiently correct. But when different temperatures are adopted for the

unity standard, the difference is liable to be greater, especially in the specific gravity of heavy liquids. For example, in the case of Sulphuric Acid, where s. g. is relied upon as the principal indication for strength, and where small differences of strength are often important to be known, the differences in the temperature of the standard volume give an error of just about one unit in the third decimal place. That is, a concentrated Sulphuric Acid compared with water at 4° C., and weighed at 15.6° C., gave a s. g. of 1.83689, and the same acid compared with water at 15.6° C., and weighed at 15.6° C., gave a s. g. of 1.83781.

In light liquids such as Ether, however, the difference is removed to the fourth decimal place, or beyond the usual reading limit. The U. S. P., of 1880, directs that the s. g. of its stronger Ether must be "not higher than 0.725 at 15° C. (59° F.), or 0.716° at 25° C. (77 F.)," and it does not give a temperature for its standard volume of water. This Ether, when compared with an equal volume of water at its maximum density, the Ether being at 15° C. 59° F., has an apparent s. g. of 0.7246, and when compared with an equal volume of water at 15.6° C.=60° F., the Ether being at 15° C. = 59° F., the apparent s. g. is 0.7255, a difference which, under ordinary circumstances, is unimportant, though it is easily recognized by ordinary good management. The same Ether weighed at 25°C.=77°F. compared with the standard volume at maximum density gave an apparent s. g. of 0.71449,-compared with the standard volume at 15.6° C.=60° F., the apparent s. g. was 0.71481.

The s. g. of distilled water not boiled, nor very recently distilled, compared with recently distilled and boiled water, and both at 4° C., was found to be 1.000006, or a difference of only three milligrammes in a 500 gramme bottle. Water of excellent quality, in its natural condition, namely, the Ridgewood water of Brooklyn,containing about 7 grains of solid matters to the gallon,―gave a difference of 8 milligrammes in the 500 grammes. Its s. g. therefore, compared with an equal volume of recently distilled and boiled water, both at the same temperature, is 1.000016. Well water containing about 30 grains of solids to the gallon gave in the same way a s. g. of 1.000570.

These observations are made and given to show that the ordinary small specific gravity bottles as sold, used with ordinary scales, may be easily tested without the refinements required for accurate critical work, since they are rarely weighed more closely than to the