and to the general characters of the oily acid produced. Since then we have compared the reactions of pyruvic acid prepared by us with those of the acid obtained from cystine, and we have no doubt of their identity.

Pyruvic acid was discovered by Berzelius as one of the products of the dry distillation of racemic and tartaric acids, and has been called pyroracemic acid. To prepare it, tartaric acid is distilled at a temperature gradually rising to 300° C., and the oily acid distillate thus obtained is repeatedly fractionated. The portion distilling between 160° C. and 170° C. is found to have the composition C ̧H ̧ ̧.

4

Pyruvic acid is a liquid of a yellowish colour smelling of acetic acid, slightly viscid, boiling at 165o C., always with some decomposition. It is soluble in water, alcohol and ether.

This acid differs from lactic acid in containing a molecule less of hydrogen, and has been shewn by Wislecenus and Debris to be easily transformed into lactic acid by hydrogening agents, such as nascent hydrogen and hydriodic acid. It also unites directly with a molecule of bromine.

The following are the molecular formulæ of ordinary lactic acid, and pyruvic acid: to the right is exhibited a probable molecular formula of cystine:

It is obvious that the above molecular formula of cystine exhibits only one of at least four possible isomers.

One of the peculiarities of pyruvic acid is the ease with which it is transformed by heat into a non-volatile syrupy acid which is undoubtedly a polymeric modification. This new acid is also produced when pyruvic acid is separated from its salts; salts are not crystallizable, and they are of a peculiar yellow colour.

A greal deal more might be said touching the theoretical relations of pyruvic acid to acetone and its derivatives; but this would be quite out of place here.

The relation which we believe we have shewn to exist

between cystine and pyruvic acid, and consequently between cystine and lactic acid, is not without interest to the physiologist. The juice of muscle has long been known to be rich in an isomer of lactic acid, viz. sarco-lactic or paralactic acid, and we now know that this acid is one of the products which are formed in muscle during muscular work. The living and inactive muscle has an alkaline reaction, but when it is made to contract it gradually becomes acid, and evolves carbonic acid; the sarco-lactic and carbonic acids being developed by the splitting up of a substance whose presence in muscle is apparently essential to the production of mechanical work. When a muscle passes into the condition of rigor mortis the same changes occur, and we know that at the same time heat is evolved.

Sarco-lactic acid is, as we have said, merely an isomer of ordinary lactic acid, and readily passes into it. We cannot but think that in all probability cystine is a product of the splitting up of an albuminous constituent of muscle-that it represents an imperfect oxidation in muscle, by which a portion of the sulphur residue of an albuminous body leaves the muscular fibre in an unoxidized condition.

NOTES OF SOME EXPERIMENTS ON THE RATE OF FLOW OF BLOOD AND SOME OTHER LIQUIDS THROUGH TUBES OF NARROW DIAMETER. By J. MATTHEWS DUNCAN, M.D., F.R.S.E. and ARTHUR GAMGEE, M.D., F.R.S.E.1

THE experiments, of which the results are recorded in the present communication, were undertaken in order to determine the rate at which blood flows through tubes of moderately small diameter, with a view to the study of the mechanical theory of dysmenorrhæa; they were afterwards extended to blood-clot serum, milk, and urine, &c.

In a memoir inserted in the ninth volume of the Mémoires des savants Etrangers, M. Poiseuille stated the results of an investigation on the flow of water and other fluids through capillary tubes, showing how this is influenced by pressure, by the length and diameter of the tube, and by temperature. A committee of the French Academy, of which M. Regnault was the reporter, corroborated the results of M. Poiseuille's researches. Subsequently this observer published a still more extended series of observations, including the determination of the rate of flow of serum and defibrinated blood3.

The method employed by Poiseuille in his researches, and which is described at length in his Memoir, consisted essentially in causing air under a known pressure to force a known quantity of the fluid to be experimented upon through tubes of known diameter and length, and determining the time employed.

The following are the general results at which he arrived concerning the influence of the length and diameter of tubes of smaller diameter than a millimetre on the rate of flow of any liquid at a constant pressure and temperature:

1st. The volumes of liquid flowing in equal times through capillary tubes of equal length, but of different diameters, are amongst themselves as the fourth powers of the diameters.

1 Communicated to the Royal Society of Edinburgh, May, 1870.

2 Recherches expérimentales sur le mouvement des liquides dans les tubes de très-petits diamètres. Commissaires MM. Arago, Babinet, Piobert, Regnault rapporteur. Académie des Sciences, séance du 26th Décembre 1842.

3 Recherches expérimentales sur le mouvement des liquides de natures diffèrentes dans les tubes de très petits diamètres par M. le Dr Poiseuille. Annales de Chimie et de Physique. Troisième série, t. xxi. 1847.

2nd. The volumes of liquids which flow in equal times. through capillary tubes of the same diameter, but of different lengths, vary inversely as the length of the tubes.

With regard to the influence of pressure, it was found that the rate of flow increased directly as the pressure; and with regard to the temperature, that, as a general rule, the rate of flow of solutions increases as the temperature rises.

With regard to the influence of various substances held in solution by a fluid, on the rate of flow no general law was arrived at, connecting it either with chemical constitution, density, capillarity, or viscosity'.

The following are some of the results, extracted from M. Poiseuille's Memoir :

Tube employed (B) is 64 millimetres long; its diameter is 0mm.249; capacity of receiver, 6 C. C.; pressure, 1 metre; temperature, 145 C.

Time of flow.

S.

535.2

169.0

1184.5

1029.0

M. Poiseuille made a single determination of the rate of flow of blood-serum; of blood-serum plus a small and unknown quantity of corpuscles, and of defibrinated blood, the same animal's blood (an ox's) having been used to furnish the three liquids. The following are the results:

Temperature and pressure stated to have been kept constant during all the experiments; length of tube, 110 millimetres; diameter, 0mm.256; capacity of receiver, between 5 and 6 cc.

1 We may merely allude to the fact that M. Graham succeeded in showing a decided connection between the rate of flow of the different hydrates of sulphuric acid and their chemical constitution. His very interesting results are to be found in a paper "On liquid transpiration in relation to chemical composition." (Philosophical Transactions, 1861, p. 373.)

Poiseuille points out that the aggregation of blood-corpuscles, which always takes place in defibrinated blood, leads to a choking of the tubes employed, especially when these are of narrow diameter (0mm-1), or to an irregular flow, and that consequently defibrinated blood cannot readily be injected through the capillaries of the lungs of animals which have been bled to death. The recent experiments of Dr J. J. Müller', carried on under the direction, and according to the method, of Professor Ludwig, in the Physiological Institute of Leipzig, are opposed to the statement of Poiseuille, for he succeeded in keeping up for long periods a flow of defibrinated blood through the lungs.

Method employed in the present research.

All our experiments were conducted according to a method suggested by, and under the direction of, Professor Tait, in the Physical Laboratory of the University of Edinburgh. The liquids to be experimented upon were allowed to flow through tubes of known diameter and length, into a large air-pump receiver exhausted to a partial and known extent, the fluid being thus subjected to the pressure of the atmosphere, minus that of the air in the receiver.

Before enumerating our experiments, it may be well to point out certain fundamental differences which exist between them and those of M. Poiseuille. 1st, our tubes had a much wider diameter-those used by the French observer varied in diameter from 0mm.1949-0mm 256, whilst our tubes were from 0mm.845-1mm.259; 2dly, by our tubes being much longer than those of Poiseuille; and, 3dly, by the liquids being allowed to flow, not into water, but into empty vessels placed in the partially exhausted receiver.

I.-Influence of the Shape of the Tubes employed on the

Rate of Flow.

It was considered advisable to determine, in the first place, whether bends in the tubes through which the liquids were made to flow would exert any influence on the rate. Accordingly, a tube 1129 millemetres long was bent twice at right

1 "Ueber die Athmung in der Lunge von Dr J. J. Müller." Arbeiten aus der Physiolog. Anst. zu Leipzig Mitgetheilt durch C. Ludwig. Leipzig, 1870, pp. 37--76.