14

The determination of the direction of the progressive movement being founded upon meanvalues, the result is essentially approximate. But there is still another source of inaccuracy. Theequation—

P-P^D,

P-P, D,

states that the decrease of atmospheric pressure from the outer limit of a typhoon to any twopoints within it is inversely proportional to their distances from the center. There can be no doubtthat this assertion is not rigorously true. Still in actual application the error is found to be suf-ficiently small to give results which have all the accuracy required for practical purposes.

Correction for daily oscillation.—Above we stated that the barometer readings, l 3 ! and P 2should be corrected for daily oscillation if necessary. For this purpose we give a set of tablescontaining the mean corrections to be added (algebraically) to these readings, if it is desiredto correct them. The tables (pp. 15-19) have been compiled from the records of the observatoriesof Manila, Hongkong, Zi-ka-wei, Tokio, and Nemuro, and consequently cover the seas most exposedto typhoons. From them the observer can select the one corresponding to his latitude.

Theoretically there can be no doubt that these corrections are required, because the formula—

P-P.^D,

P-P,

in which P is a constant mean value, supposes the differences P—P, and P—P 2 to express thebarometric fall due to the cyclone. The actual reading, however, gives the combined effect of thecyclone and the daily oscillation, though the latter may be hidden by the overwhelming influenceof the former.

But practically these corrections will rarely be of great importance. The tables give asextremes —1.8 millimeters (0.070 inch) and —1.4 millimeters ( — 0.050 inch). A glance at theformula makes it clear that whenever the differences P — P, and P —P 2 are rather large, theapplication or omission of the corrections will have little effect on the resulting value of D„.Moreover, we must not forget that the whole process is based upon mean values, hence in a concretecase it can not give rigorously exact results. Nor is this necessary. The discrepancy between thevalues of D 2 , as obtained with uncorrected respectively corrected readings, appears chiefly in zonesA and B, where the differences P — 1+ and P — P 2 are small; the nearer we approach the vortexthe less the value of D 2 is affected by slight corrections. Now it is easily understood that in theouter parts of the storm a small error in the determination of the direction of the storm’s trackis not likely to have grave consequences. Still it will be advisable to try the effect of the correc-tions in zones A and B whenever they have opposite signs for 1+ and P 2 , or even when they areof the same quality but the barometric fall between the two observations has been small. We willshow by an example the effect which the corrections can have in extreme cases.

Suppose, on May 15 at 9 a. m., the barometric reading on board a steamer in the latitudeof Manila is found to be 753.2 millimeters (for sea level). The wind having veered, anotherobservation at 4 p. m. gives 747.6 millimeters. Hence the total fall is 5.6 millimeters. Butis this due solely to the approach of the cyclone ? By no means. During May the' correctionfor oscillation is at Manila — 1 millimeter at 9 a. m. and —)—1.6 at 4 p. m. Fully 2.6 millimeters ofthe change are therefore due to the daily oscillation.

Applying Fournier’s rule to the original readings we have:

755—747.6 7.4 100

755—753.2 1.8 '%

x ~ (D 2 ) =24

But applying the same formula to the corrected readings we obtain:

9 a. m.: 753.2 —1.0=752.2) . 755—749.2_5.8_ 100

4 p. m.: 747.6 + 1.6=749.2) ' '-755 — 752.2 — 2~8 ~ y ' ' V