to the speed V., with which it traverses the ouïe and penetrates between the spaces of the wings. There is then to the debit of the depression the height generative of this speed

V2
2g

Second, the air once drawn between these vanes has a double movement, the movement relative to the dragging after the surface of the vanes, and the movement of drawing produced by the rotation of the machine, but theory requires that the total depression should be the sum of the elementary depressions due to each of these movements. Let us look first at the relative movement.

The interval between two consecutive vanes forms an évasée canal which the air enters with a certain speed V1, and leaves with a less speed V2. From this slowing action results, according to Bernouilli's theory, a gain of depression expressed by the difference—

1

But the speed of entry V, is the resultant of two rectangular speeds, the one V, following the radius, the other wr equal and opposite to the tangential speed of the wings. In the ideal ventilator which I have here supposed, the interior surface of the wings is directed exactly in accordance with this result, so that the composition of the speeds is produced without' obstacle, and the air slides without shock on the cutting surface of the vanes; I may, then, replace in the preceding expressions V2 by the sum V.2 + w2 r2, and bring to the gain of the depression the algebraic sum

Third, the movement of drawing in, which is a uniform rotation, creates the centrifugal force, which in its turn produces a gradual increase of pressure from the ouïe to the exterior circumference. If I isolate in imagination a prismatic element of the air drawn in, placed at a distance a from the centre and presenting a height da in the direction of the radius, a base S in the perpendicular direction, and a density 8, the mass in this element will be

The increase of depression per unit of surface from one base to the other of this little prism will be got by dividing the preceding expression by S. We will divide again by 8, to have this pressure expressed as usual in the column of air, and we shall have finally for the differential increase of the pressure due to the centrifugal force

a value to be carried to the credit of the depression produced by our ventilator.

Our analysis is now complete, and we may make the

addition. Many terms, some positive and some negative, cancel themselves, and there will only remain, when designating by the letter u the tangential speed w R, the simple expression

an expression which subsists whatever may be the curve given to the wings and the inclination under which they reach the exterior circumference.

The ventilator which we are now studying is in reality a very bad machine. Although it responds sufficiently well to the first of the two conditions which every machine must fulfil in which fluids circulate, that is to say it receives the air without shock, it is still far from realising the second, the escape without speed. The air extracted from the interior is thrown into the atmosphere with considerable speed, resulting from the tangential speed u and the speed relative to the outlet V2.

This important defect has not escaped constructors, who have generally sought to provide a remedy. The first means which they have employed, and which presented itself naturally, consists in giving a large inclination to the wings, so that they arrive in an angle more or less sharp at the periphery. In opposing in this way the relative speed of outlet to the speed at the extremity of the vanes, they hope if not to annul at least to diminish to a great extent the absolute speed of expulsion into the atmosphere, and so to improve the result. This arrangement was adopted by Combes, who carried things to an extreme, making his vane tangential to the exterior circumference, that is to say, at an angle of 0°. We reproduce (Fig. 3) the curve of his ventilator, but success has not responded to this theoretical view. To understand the cause it is sufficient

to reduce to its value the depression expressed by the difference

This difference constitutes in effect a veritable antithesis. To weaken in a sensible degree the absolute speed of expulsion by opposing to the tangential speed u the relative

FIG. 3.

speed V2, we must admit for this last a considerable value

approaching u, but then the negative term

2g

increases,

the depression weakens, and the machine loses its power. If to recover it we have recourse to an increase of the speed of rotation, we increase at the same time the passive resistance of the machine and its motor, and that which we gain on one side we lose on the other.

Such is certainly the principal if not the only cause of results so little satisfactory as those given by the experiments of M. Glepin on the Combes ventilator, the tangential speed being almost three times that which is required under

the same conditions by the Guibal ventilator, and the proportion of useful work to the motive power measured by Prony's brake has never exceeded 29 per cent. There exists, happily, a very efficient means for improving the resultant of ventilators-it is that connected with the name of M. Guibal.

The ventilator is inclosed in a cover, more or less eccentric, which does not permit of the exit of the air except by a narrow passage a b, Fig. 4, regulated according to the yield

FIG. 4.

of the machine. This passage is continued into the long évasée chimney. The speed of expulsion existing in the orifice a b is extinguished little by little, just as the air rising in the chimney fills larger areas, until it becomes inactive at the moment when it is expelled into the atmosphere. This extinction of speed occasions, as theory requires, a considerable depression, which is added to that produced by the centrifugal force, increasing in a marked manner the power of the machine.

This effect, so remarkable in the Guibal chimney, has