BALL-DRY-BULB AND WET-BULB THERMOMETER READINGS 47

A RAPID METHOD OF FINDING THE ELASTIC FORCE OF AQUEOUS VAPOUR AND THE RELATIVE HUMIDITY

READINGS.’ FROM DRY - BULB AND WET - BULB THERAIOMETER

BY JOHN BALL, PH.D., B.Sc., Assoc.3I.Inst.C.E.

[Read December 20, 1905.1

IN the course of some investigations on atmospheric humidity, tho author has been led to devise a simple and rapid method of finding the elastic

of Aqueous Vapour.

force of aqueous vapour2 and the relative humidity of the air on the basis of the well-known formdoe of Glaisher. The essential feature of

Communicated by permission of Capt. H. G. Lyons, Director-General of the Survey

I have adhered t o Glaiuher’s terminology ; “ vapour tension,” or prefe;fbly “ vapour but the olil

bepartment, Miuistry of Finance. Egypt.

pressure,” would be a better term than “elastic force of aqueous vapour, nomenclature has become familiar by long usage.

48 BALL-DRY-BULB AND WET-BULB THERMOBIETER READINGS

the method is the use of a special form of diagram in place of the ordinary tables.

In the calculator for dew-point and elastic force in Fig. 1 there are four scales, representing respectively dry-bulb thermometer readings, wet-bulb thermometer readings, dew-points, and elastic forces, the last two scales being arranged along a single line. These scales are so placed and graduated that if a straight-edge be laic1 across the diagram so as to

FIO. 2.-Relative Humidity Cnlcolntor.

pass through any given dry-bulb and wet-bulb readings on their respective scales, the dew-point and elastic force of aqueous vapour mill be at once given by the point where the straight-edge cuts the remaining double scale.

Similarly in the hnmiclity-calculator in Fig. 3, the relative humidity can be a t once read off by aligning a straight-edge through any given dry-bulb and wet-bulb readings.

The figures are considerably reduced from the originnl diagrams, But they will be found large enough to enable the method to be tested. If

BALL-DRY-BULB AND WET-BULB THERMOMETER READINGS 49

the diagrams be redrawn on the original scale (about double that of the figures) by the method given below, they will be found to yield results of about the same accuracy as the usual tables, whilst presenting some advantages over the latter. The calculation being made directly from the thermometer readings themselves, it is unnecessary to take out their difference ; no interpolation is required in any case ; the elastic force is obtained without the necessity of first calculating the dew-point ; and the whole range is presented at one view instead of on several pages. Further, it may be noticed that the graduations on the enlarged diagrams will be of about the same degree of openness as those on the instruments themselves, so that the degree of accuracy of the result will be equal to that of the readings, and the effects on the resnlt produced by sm:ill variations in the observed data can be readily studied.

The diagrams open up a simple means of applying Glaisher's results to the centigrade system. For it is easy to rrgnduate thc temperature scales in centigrade degrees, and the elastic force scale in millimetres, leaving the positions of the scales unchanged ; and the hygrometric state of the air can then be directly read off without any convcrsion from one system to the other. The humidity scde is of course the same in both systems.

In practice it will be found convenient to draw the diagrams on a stout card to avoid any distortion by the unequal shrinkage to which ordinary paper is liahle. A strip of transpnrcnt celluloid, bearing a straight line scratched on its under surface, is an improvcmcnt on the ordinary woodcn straight-edge in malting the alignment.

Theory of tlie Dew-point nud Blaslic Force Calctilutor.

Let a number of equidistant horizontal lines (Fig. 3) be drawn, each of the equal intervals between them representing 1" of temperature. Let AB and CD be two vertical lines cutting the horizontal ones, and called the clew-point scale

WET n u n C

DEW -POINT A

I

D N I L 3.

I

B

and wet-bulb scale respectively. Considering now the 40' horizontal line, it is clear that if we take a point X on it such that tlie distances of X from AB and

E

50 BALL-DRY-BULB AND WET-BULB THERMOMETER HEADINGS

CD are in the ratio of 2.29 to 1 (2.29 being Qlaisher's fiLctor for 40"), then a straight line, passing through X and say 38" on the wet-bulb scale, will cut the dew-point scale a t 40" - (2" x 2.29), or 36'-4, which is the dew-point correspond- ing to dry-bulb niid wet-bulb readings of 40" and 38". And by similar triangles any other straight line drawn through X will give the dew-point corresponding to a dry-bulb reading of 40", and that red ing of the wet-bulb represented by the point on CD through which the line passes.

Let a series of points similar to X be taken, using the proper Qlaisher'e fnctom, on each of the other horizontal lines, and let theni be numbered with degrees like the other two scales. The locus of X will be a peculiar curve, which approaches nearer to CD the lower the temperature. The result gives a dew-point calculator, from which the dew-point corresponding to any given dry- bulb ant1 wet-bulb readings can be instantly found by aligning a straight-edge through the given readings.

To convert the cnlculator thus formed into a siniultaneous calculator for elastic force, a11 that is necessary is to graduate the other side of the scale AB with the elastic forces corresponding to the vnrious dew-pointa Thus the -250 inch mnrk will be placed at 40"*3, the -240 inch niark at 39O.3, and so on. This results in the complete diagram as shown in Fig. 1.

Construction of th Humidity Calculator.

The humidity calculntor is constructed from Table VIII. in Ninfs to ilfeteoro- Let A13 (Fig. 4) be u, vertical scalc loyicnl Observers by the following piocess.

C

70h

Yl-.\

PIO. 4.

of equal parts representing degrees of the wet-bulb thermometer. Let CD be n pnrallel straight line, and S any convenient point on the other side of AB.

1 For a list of these factors Ben Table I., p. iv., in Glaisher's €Iygro~ncf&ul Tables, Ninth Edition. London. 1902.

3 Iliitls lo'Jleleorologiual Observers, by W. Marriott, F.R. Met.Soc.,!Fifth Edition, London, 1902, p. 50.

BALL-DRY-BULB AND WET-BULB THERMOMETER READINGS 61

Taking X to represent 100 per ceut of relative humidity, draw radii frornit through say 50", 60°, and 70" on the weLbulb scale. The intersections of these radii with CD will give the corresponding divisions 50", 60", and 70" of the dry-bulb scale, because when the humidity is 100 per cent the readings of the two bulbs are of course equal. (The three selected divisions should not be more than 10" apart, because the dry-bulb scale will not be a straight line for more than a short distance.)

Now from the table we take, for humidity 90 per cent, dry-bulb 50", wet- bulb 48O.6 ; dry-bulb 60", wet-bulb 58O.4 ; dry-bulb 70", wet-bulb 68O.8. Lines drawn through these pairs of points will intersect in the 90 per cent division of the humidity scale, which is thus fixed. Proceeding in a similar way, we fix the 80 per cent point, then the 70 per cent point, nud so on, always considering only from 50" to 70" of the dry-bulb. (For very different readings of the two bulbs, the three lines may not intersect precisely in a point, but in n very small triangle, the centre of figure of which is taken as the point.) We thus get the complete humidity scale.

I t remains to complete the dry-bulb scale by reversing tlie above process. For instance, to find the 30" mark of the dry-bulb scale, we know that it must lie on the straight line which passes through 100 per ceut on the humidity scale and 30" on the wet-bulb scale ; we also see from the tables that it inunt lie on the lines passing respectively through 50 per cent and 20 per cent on the humidity scale and through 26O.3 and 21O.4 on the wet-bulb scale. The inter- section of these lines therefore fixes tlie 30' division. By n similar process we find the remaining divisions of the dry-bulb scale ; these will be found to lie on a curve which bends rather sharply near the freezing-point. The degree of accuracy of the scale depends on the closeness with which the divisions are found geometrically ; near the freezing-point, on account of the rapid chaiige of curva- tiire of the scale, the individual degrees should be fixed by the process just described; but a t higher temperatures than 40" every fifth degree is close enough, the single degrees being found by subdivision after drawing a curve through the main points

I t is well to take three or four humidities for each point localised on the dry-bulb scale ; for although two are generally sufficient, yet a single pair may not give a very accurate result, owing to the fact that the table gives the humidities only to the nearest whole number per cent.

The convenience of the diagram depends largely on the relative positions selected for the scales ; the positions shown in Fig. 2 will be a guide as to what has been found suitable in practice. The aim in calculators of this type is always to get the scales of a fairly uniform degree of openness, while avoiding excessive obliquity of the aligning straight-edge with respect to the scales.

DISCUSSION. Mr. U'. MARRIOTT remarked that this was the second paper which Dr. Ball

had communicated to the Society on subjects relating to the reduction of observations. Mr. H. C. Russell, about 1877, published a diagram for finding the relative humidity a t a glance from the dry-bulb and wet-bulb readings. Dr. Spong devised an instrument called the '' Dew-Point Calculator " (which he showed at the Society's Exhibition in 189.i), in which, by placing the adjustable rule in a line with the top of the mercury in the dry-bulb and wet-bulb thern~ometers, the clew-point and elastic force of iqueous vapour were immediately read off.

Dr. W. N. SEAW remarked that, besides the instruments and apparatus referred to by hlr. blarriott, they had a slide-rule for the same purpose, designed

Dr. Ball's method was by no means new.