82 MANUAL OF CURRENT OBSERVATIONS - 
197. In order that the magnitude of the constituent amplitudes may be adapted 
for use with the predicting machine, a scale factor (S) is mtroduced. This factor, 
which depends upon the velocity of the current, 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 
Tbe ss ib lsum (OY Siakery oh eee See ee I aS a wd ope are 20 
From: 3 ito Oorknothtc @8 es. pe ake ese ae eee ee ee eee 10 
SaRoya owl Opgrand TO) Sa Voy rege yee ee ee ee es er et ee ee ee sh ee 5 
Proms ONC gl Sek O tS a she EA ee re 2 et a Sen a alle ih 3 
MO me ob OVA O SKN O GS saa i es aS ce ee ae 2 
TserOpe Oe AAO TOR as ON sa aKON AS cs ee cae I ET a ees eae eees 1 
LUT TIN 3. On OAS Osean oS tee ps sr are OE CR ED we SU eg a erp 0. 
Mrome4# OS tOs5" OMksn Obs eee ee st ake dA a i age ON ee ee ae ee 0 
Brom ORC Ow Ol OKs’ ts eee ea ee ee can eee 0. 
re bh Oo 
Or 
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. 
198. Using the harmonic constants, modified in the manner described 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 
regular height dial on the machine. From a consideration of the construction 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° X (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 con- 
structing the square-root scale becomes 
Angular distance from dial zero=9° x S (velocity)?______________ (22) 
199. To take account of any nontidal current not attributed to difference in head 
at the two entrances to the strait, a special graduation of the square-root scale is neces- 
sary. 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: 
Atne:/emimbcl eee es 9S) GVA V5) i aa (23) 
The required angle is to be measured to the right or to the left of the initial point 
according to whether the angle (V—V,) is positive or negative. When setting the 
predicting machine the velocity pomter must be at the initial pomt marked by the 
arrow when the sum of the harmonic terms is zero. 
200. In the graphic representation of the summation of the harmonic 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 scale 
