.6

2

Coefficient of discharge C.

6.

The values of C, for the different orifices were carefully determined, and are shown by the curves of fig. 3.

With the turbulent jets, the recorded pressure is very unsteady, and to obtain consistent readings of the manometer it was necessary to damp out the oscillations by using a long connecting tube of small bore.

Fig. 3.

1.0

the turbulent jets are shown in fig. 4, and for the steady jets in fig. 5. From these curves it appears that so long as the ratio A/a is less than about 3.9 for the steady jets and from 34 to 37 for the turbulent jets, the value of is sensibly constant and approximately equal to unity. This is a critical value of the ratio and is practically identical

f

with the critical ratio found in the case of impact on a hemispherical cup. As Ala is increased beyond this. point, k falls rapidly. Its values are shown in the curves of fig. 6.

(6) The exact value of the critical ratio is very easily determined in any series of experiments. For values of the ratio smaller than and up to the critical, the water escaping around the periphery of the impact tube takes the form of a continuous clear glassy film, forming a conical surface (fig. 7) whose conical angle diminishes as A/a is increased until it attains a minimum value of 20° for a steady jet and 40° for a turbulent jet *.

The attainment of the critical area-ratio is marked by the breakdown of the film into a series of isolated drops (fig. 8), accompanied by much splashing, while whether with a steady or turbulent jet the pressure in the impact tube becomes very unsteady.

* With the vertex of the cone downwards.

(7) With the object of determining the form of the boundary between the moving and dead water within the impact tube, experiments were carried out with two glass. tubes initially filled with aniline dye solution. With a stream-line jet a well-defined boundary between clear and

coloured water is soon established (fig. 8), and this is maintained for a considerable time. If I be the distance from the top of the tube to this boundary, and if D be the diameter of the tube and d the diameter of the jet, the value of 1/D increases slightly as d increases and also as D increases. If d/D=0.66 its value is approximately 3.9 with a 0-4 inch

tube and 42 with a 0-56 inch tube, while if d/D=0.75 the values are respectively 4.25 and 4:45.

XX. On a Simple Derivation of the Lorentz Transformations. By H. M. DADOURIAN, M.A., Ph.D., Associate Professor of Physics, Trinity College, Hartford, Conn.*

ΟΝ

N account of the important position which the Lorentz Transformations have come to оссиру in modern physics it is desirable to make their derivation as direct and simple as possible, to give it a physical rather than a *Communicated by the Author.