HARMONIC ANALYSIS AND PREDICTION OF TIDES 151 
introduced. This factor, which depends upon the velocity of the cur- 
rent, is selected with the view of obtaining a reasonably large working 
scale without exceeding the limitations of the predicting machine. The 
following scale factors are suggested: 
' Average velocity of current at time of strength: Scale factor 
WessithamnOcocknO tee Sie) ae) a a eee Mees ee Ess See 20 
ERROTIAN Os nUON Oso UKeIn Olle atone as WS erat pee UE VOR ey ae ee yee 10 
FROMMAOF OS FOw le OFM O beete ed eyes SB ke hee Seperate. 5 
Brome Oktomle sok Ot se. esis on pigdh oa ely ee oR Ss 3 
EOE LOWS. Os KT OGS ay eh peach ee ee ee ee cake ee 2 
romeo OtoOrs Oy KO tse oo ee ee aes ae Fee We Oe emcee! ee 1 
romeo OrtovaOsknotsies lee tis Oe Bye! Se ae, shee ae 0.5 
BromeavOntor a OV Knots 205 ke ei in eh blondy Eee Bin ai 0.25 
Brom o-OstowliQvOvknotssefi ss: s2ns8 see eke eee et eee ee 0.1 
In practice, the scale factor is usually combined with the factor (C) 
and the product applied to each of the constituent amplitudes in the 
expression for difference in head. i 
445. Using the harmonic constants, modified in the manner de- 
scribed above, in the predicting machine, the resulting dial readings 
will represent the square of the current velocity. In order to avoid 
the necessity of extracting the square root of each individual reading, 
a square-root scale may be improvised and substituted for the regu- 
lar height dial on the machine. From a consideration of the con- 
struction of this machine, it can be shown that with a scale factor of 
unity the angular position of a velocity graduation as measured in 
degrees from the zero point will be 9° (velocity)?.. Thus the 1-knot 
graduation will be spaced 9° from the zero, the 2-knot graduation at 
36°, the 3-knot graduation at 81°, etc. For any scale factor (S), the 
formula for constructing the square-root scale becomes 
Angular distance from dial zero=9° XS (velocity)? (478) 
446. To take account of any nontidal current not attributed to 
difference in head at the two entrances to the strait, a special -gradu- 
ation of the square-root scale is necessary. Let V, represent the 
nontidal current velocity, positive or negative according to whether it 
sets in the flood or ebb direction, and let V represent the resultant 
velocity as indicated by any scale graduation, positive or negative 
according to whether it is flood or ebb. The angular distance of any 
scale graduation as measured from an initial point, usually marked by 
an arrow, may then be expressed by the following formula: 
Angle in degrees=9 x SX (V —V,)? (479) 
The required angle is to be measured to the right or to the left of the 
initial point according to whether the angle (_V—YV,) is positive or 
negative. When setting the predicting machine the velocity pointer 
must be at the initial point marked by the arrow when the sum of 
the harmonic terms is zero. 
447. In the graphic representation of the summation of the har- 
monic terms by the predicting machine, the scale of the marigram 
depends upon the marigram gear ratio as well as upon any scale factor 
which may have been introduced. With a gear ratio of unity, the 
scale of the marigram is 0.1 inch per unit of machine setting. In the 
summation for the hydraulic currents, the marigram read by a natural 
