time that the red is a yellow red, they become quite as distinct to the colour-blind as to the normal-eyed.

The colouring of geological maps is very perplexing to the colourblind, and it is recommended that engraved marks, to distinguish the different strata, should always be added to the colours.

In conclusion, the author gives hints which he considers useful for the examination of colour-blind persons, and states the importance of collecting further evidence on the subject, of an accurate and definite

nature.

II. "Researches on the Velocities of Currents of Air in Vertical Tubes, due to the presence of Aqueous Vapour in the Atmosphere." By W. D. CHOWNE, M.D. Communicated by JOHN BISHOP, Esq., F.R.S. Received May 22, 1856.

(Abstract.)

This was a paper supplementary to one presented June 14th, 1855, an abstract of which was published in the Proceedings of the Royal Society' for June 21st, 1855. The author having ascertained that an upward current of air becomes established in a vertical tube placed in as quiescent an atmosphere as can be obtained, and having demonstrated its existence by means of anemometric discs placed in tubes as described in that paper, proceeded to ascertain the velocity of the currents by which the discs were moved.

In order to estimate the velocity of the currents, one of the anemometric discs was placed within a short zinc tube three inches in diameter, the lower end of which was accurately fitted into an aspirator capable of containing thirty-six gallons of water. By drawing off in a given time a quantity of water equal in bulk to the cubic contents of one of the tubes described in the former paper, the velocity of a current required to produce a given number of rotations of the disc was determined.

The experiments were varied by altering the height of water in the aspirator, and thereby changing the velocity, while the exitorifice remained unaltered.

By ascertaining the number of rotations of the anemometric disc,

caused by currents of air of different velocities thus produced, he was enabled to arrive at a measure of the velocities in tubes placed in a still atmosphere, as described in his former paper.

The author in that paper pointed out a correspondence between the variations of force in the upward currents of atmospheric air in the tubes and variations in the humidity of the atmosphere, and expressed his belief that the variations were attributable in great measure to the varying hygrometric conditions of the atmosphere.

In further proof of this position, he has appended two tables, showing that both natural and artificial increase of atmospheric humidity are accompanied by increase in the velocity of the rotations, and that in each case increase of humidity is attended by increase of velocity, independent of temperature.

III. "On the Thermal Effects of Fluids in Motion." By J. P. JOULE, Esq., F.R.S., and Professor W. THOMSON, F.R.S. Received May 23, 1856.

On the Temperature of Solids exposed to Currents of Air.

In examining the thermal effects experienced by air rushing through narrow passages, we have found, in various parts of the stream, very decided indications of a lowering of temperature (see Phil. Trans. June 1853), but never nearly so great as theoretical considerations at first led us to expect, in air forced by its own pressure into so rapid motion as it was in our experiments. The theoretical investigation is simply as follows:-Let P and V denote the pressure and the volume of a pound of the air moving very slowly up a wide pipe towards the narrow passage. Let p and v denote the pressure and the volume per pound in any part of the narrow passage, where the velocity is q. Let also e-E denote the difference of intrinsic energies of the air per pound in the two situations. Then the equation of mechanical effect is

since the first member is the mechanical value of the motion, per

pound of air; the first bracketed term of the second member is the excess of work done in pushing it forward, above the work spent by it in pushing forward the fluid immediately in advance of it in the narrow passage; and the second bracketed term is the amount of intrinsic energy given up by the fluid in passing from one situation to the other.

Now, to the degree of accuracy to which air follows Boyle's and Gay-Lussac's laws, we have

pv = +PV,

ift and T denote the temperatures of the air in the two positions reckoned from the absolute zero of the air-thermometer. Also, to about the same degree of accuracy, our experiments on the temperature of air escaping from a state of high pressure through a porous plug, establish Mayer's hypothesis as the thermo-dynamic law of expansion; and to this degree of accuracy we may assume the intrinsic energy of a mass of air to be independent of its density when its temperature remains unaltered. Lastly, Carnot's principle, as modified in the dynamical theory, shows that a fluid which fulfils those three laws must have its capacity for heat in constant volume constant for all temperatures and pressures,‚—a result confirmed by Regnault's direct experiments to a corresponding degree of accuracy. Hence the variation of intrinsic energy in a mass of air is, according to those laws, simply the difference of temperatures multiplied by a constant, irrespectively of any expansion or condensation that may have been experienced. Hence, if N denote the capacity for heat of a pound of air in constant volume, and J the mechanical value of the thermal unit, we have

E-e JN (T-t).

Thus the preceding equation of mechanical effect becomes

q2 2g

=

PV (1-4)+JN (T−1).

Now (see "Notes on the Air-Engine," Phil. Trans. March 1852, p. 81, or "Thermal Effects of Fluids in Motion," Part 2, Phil. Trans. June 1854, p. 361) we have

where k denotes the ratio of the specific heat of air under constant pressure to the specific heat of air in constant volume; H, the product of the pressure into the volume of a pound, or the "height of the homogeneous atmosphere" for air at the freezing-point (26,215 feet, according to Regnault's observations on the density of air), and to the absolute temperature of freezing (about 274° Cent.). Hence we have

Now the velocity of sound in air at any temperature is equal to the product of ✔k into the velocity a body would acquire in falling under the action of a constant force of gravity through half the height of the homogeneous atmosphere; and therefore if we denote by a the velocity of sound in air at the temperature T, we have a2 = kg PV.

Hence we derive from the preceding equation,

which expresses the lowering of temperature, in any part of the narrow channel, in terms of the ratio of the actual velocity of the air in that place to the velocity of sound in air at the temperature of the stream where it moves slowly up towards the rapids. It is to be observed, that the only hypothesis which has been made is, that in all the states of temperature and pressure through which it passes the air fulfils the three gaseous laws mentioned above; and that whatever frictional resistance, or irregular action from irregularities in the channel, the air may have experienced before coming to the part considered, provided only it has not been allowed either to give out heat or to take in heat from the matter round it, nor to lose any mechanical energy in sound, or in other motions not among its own particles, the preceding formula will give the lowering of temperature it experiences in acquiring the velocity q. It is to be observed that this is not the velocity the air would have in issuing in the same quantity at the density which it has in the slow stream approaching the narrow passage. Were no fluid friction operative in the circumstances, the density and pressure would be the same in

the slow stream flowing away from, and in the slow stream approaching towards the narrow passage; and each would be got by considering the lowering of temperature from T to t as simply due to expansion, so that we should have

by Poisson's formula. Hence if Q denote what we may call the "reduced velocity" in any part of the narrow channel, as distinguished from q, the actual or true velocity in the same locality, we have

and the rate of flow of the air will be, in pounds per second, wQA, if w denote the weight of the unit of volume, under pressure P, and A the area of the section in the part of the channel considered. The preceding equation, expressed in terms of the "reduced velocity," then becomes

The second member, which vanishes when t=0, and when t=T, attains a maximum when

t = ·83T,

the maximum value being

⚫578.

α

Hence, if there were no fluid friction, the "reduced velocity" could never, in any part of a narrow channel, exceed 578 of the velocity of sound, in air of the temperature which the air has in the wide parts of the channel, where it is moving slowly. If this temperature be 13° Cent. above the freezing-point, or 287° absolute temperature (being 55° Fahr., an ordinary atmospheric condition), the velocity of sound would be 1115 feet per second, and the maximum reduced velocity of the stream would be 644 feet per second. The cooling