being placed under the free surface of the water contained in a vessel at a lower level; when the discharge takes place the water is seen to rise in the glass tube, to about ths of the charge, affording a measure of the degree of vacuum formed in the adjutage.

33. TABLE showing the Increase in the "Coefficient of Contraction" by the Cylindrical Adjutage.

34. The mean of these coefficients gives 0.817, its value is generally taken as 0.82, so that we have the following formulæ :

Q = 0.82 S√ 2gH = 6.56 S √H ;

and if d be the diameter of a circular orifice—

35. In the case when the jet issues with the tube full, in threads parallel to the axis of the orifice, and when, consequently, the section is equal to that of the orifice, the diminution of the discharge can only occur from a diminution of the velocity; and the ratio of the actual to the theoretic discharge is the same as that of the actual to the theoretic velocity.

TABLE showing the Identity of the "Coefficients of Discharge" and Velocity, with the Cylindrical Adjutage.

The three quantities measured were the "charge" on the centre of the tube, the velocity computed by measuring ordinate and abscissa, as in § 8, and the volume discharged. The velocity due to the charge, compared with that so computed, gives the second column, and the product of the area of the tube into the velocity due to the charge, compared with the discharge, gives the third; that is

V (= √2gH): computed Velocity, : : 1 : 0.824, and

Sx V: Discharge

:: I: 0.822.

We must, therefore, conclude that the velocity of a jet of water at the extremity of a cylindrical adjutage is equal to 0.82 of that due to the charge, and that the head due to that velocity is but 0.67 of the actual head of the reservoir; that is (0.82), because the heads or charges are as the squares of the velocities.

36. As to the cause of this increase of the coefficient from 0.62 to 0.82, D'Aubuisson ascribes it to the attraction of the sides of the tube and the divergence of the fluid threads: after they have come in contact with the sides they are forcibly retained by some such attraction as that which causes the rise of fluids in capillary tubes : by this same force the outer threads draw after them the inner, and so all the vein issues with a full tube, and passes with an increased velocity through the contracted section. The immediate cause is the contact; and every circumstance which favours that tends to produce an augmentation of the coefficient.

37. Flow of Water through Conical Converging Adjutages.—Conical adjutages, properly so called, that is, those which are slightly converging to a point exterior to the reservoir, augment the discharge still more than the preceding. They give jets of great regularity, and throw the water to a greater distance or height, and are hence frequently used in practice: the effects vary with the angle of convergence of the sides.

Two distinct contractions of the fluid vein take place with this adjutage-one internally, or at the entrance of the adjutage, which diminishes the velocity due to the charge; the other at the exterior; in consequence of which the true section of the fluid vein is slightly less than the area of the external mouth of the adjutage.

If, therefore, we put S for the section of the external orifice, V for the velocity due to the charge, the actual discharge will be expressed by nSx n' V= nn'SV, the two coefficients n and n' must be found by experiment, n being the ratio of the section of the fluid at its least diameter to that of the orifice, or the coefficient of the exterior contraction, and n' that of the actual velocity to the theoretic, or the coefficient of the velocity, and nn', their product, is the ratio of the actual discharge to the

theoretic, or the coefficient of the discharge. The knowledge of these two last is of practical importance in the case of jets of water, as in fountains and fire-engines.

38. In order to determine the coefficients above mentioned, and especially to ascertain the angle of convergence that gives the maximum discharge, experiments were undertaken with a number of adjutages

Fig. 14.

successively, in all of which the diameter of the orifice of final issue cd, in the wood engraving, and the length of the adjutage ab, remained constant; but in each experiment the diameter of entrance, and consequently the angle of convergence, were altered. The flow of the water was produced under different charges with each of these varied adjutages.

At every experiment the discharge was determined by actual gauging, and the velocity of issue by the method of the parabola given above (§ 8). The discharge, divided by SV, gave the product nn' and the observed velocity divided by V (= √2gH), gave n'.

The series of the numbers nn' showed the discharge corresponding to each angle of convergence, and consequently the angle of maximum discharge, and the

series of n', marked the progression by which the velocities increased.

39. The same adjutage, under charges which varied from 0.69 feet to 9.94 feet, or from 1 to 14, always gave discharges proportional to ✔H, and therefore the coefficient, or nn', has been, q, p, the same also. A very small increase may be observed with the higher charges. With respect to the coefficients of the velocity, they also should have been found constant but for the resistance of the air. Now, this resistance diminishing the throw of the jet, and that in proportion as the charge is greater, we should expect in the coefficients calculated from it a decrease augmenting with the charge-although, at the same time, there was no actual diminution in the velocity with which the fluid issued, or tended to issue.

TABLE showing the "Coefficients with Conical Converging Adjutages," the Angle of Convergence being that giving the maximum Discharge, as determined in the next Table.