FOREST AND STREAM. 

are shown as broken heavy black lines. It is 
obvious that the difference in length of any two 
‘ordinates of the curve is the difference in seconds 
that the two corresponding vessels take to go one 
nautical mile, and is, therefore, the number of 
seconds for such distance that the larger vessel 
should allow to the smaller in order that the 
larger vessel should have no advantage due solely 
to her size.- In practice this allowance would 
seldom be correct because there are several modi- 
fying factors; yachts seldom get an opportunity 
of showing their full speed in a race and the 
actual distance sailed is a quantity which is in- 
dependent of the stated length of the course. To 
cover these uncertainties the present time allow- 
ance tables have been calculated at various per- 
centages at different times, the present tables be- 
ing calculated at 70 per cent. of the full theo- 
retical allowance. 
In constructing the time allowance tables a ves- 
sel of 150 rating was taken as standard. The 
time per mile corresponding to this rating is 
203.9s. If now we take a line through 293.9s. per 
mile as base, the ordinates measured from it to 
the broken heavy black line will represent the full 
100 per cent. allowance that vessels of corre- 
sponding rating should receive from a vessel of 
150 R. M., and 7o per cent. of these ordinates 
will represent the allowance as set forth in the 
- 




standard tables. The full heavy black line in the 
diagrams represents this 70 per cent. curve. Tak- 
ing Y as the ordinate of this curve to the 293.9 
base we have for the equation of the curve 
Y= Fe(Y — 2030) 
7 (3,600 — 293.9) 
VX 
or referred to the o base 
Y” 293.9 + Y’ 
= 293.9 + .7 (3,600 — 293.9) 
Woe 
= .3 x 203.9 + .7 x 3600 
XxX 

cy 
= 88.17 + 2520 
Veg 
The diagrams show the actual conditions for 
1905, the boats are taken in classes as far as pos- 
sible, reduced to an average rating and to an 
average elapsed time over the course. For the 
sake of uniformity this average elapsed time is 
reduced to seconds per mile. These seconds per 
mile are plotted for the average of each class on 
each day and fair curves passing as nearly as 
possible through the spots have been drawn for 
271 
each race day, as shown on the accompanying 
diagrams. 
To avoid confusion of lines the material has 
been grouped on two sheets; one devoted exclu- 
sively to the New York Y. C. races and _ the 
other to the races of the Long Island Sound 
organization. Where there were but two spots 
for any day, they were not deemed worthy of 
much consideration and, the character of the 
curve being indeterminate, the two spots were 
joined by a straight line. 
The coefficient of the curve was then obtained 
for each race day. This coefficient is the differ- 
ence in the ordinates of any two points of its arc 
divided by the difference of the corresponding 
abcissa. The corresponding coefficient for the 
standard 100 per cent. curve was also obtained, 
and the ratio of these coefficients taken. This 
ratio shows the proportionate amount of the 
standard 100 per cent. allowance that would have 
put boats of the different sizes upon an equal 
basis. 
If the two curves were of similar character any 
two points could be taken. But inspection shows 
that the curves are only similar in a very general 
way so that two points at about the center of the 
length of the curves were chosen as best approxi- 
mating the general character of the curve. These 
ratios are shown tabulated on the diagrams. 

TIME ALLOWANCE CURVES. 
NEW YORK YACHT CLUB RACES 
HELQ IN 1905. 









Classes Courses Wert 
C.D.W. 

Others 

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Sloop Classes 
— Class Gr — 
_ |. Cass K. — —-| Cass A- 



















. Class E — Clas\s D. aie 
5o 53 60 465 
Rating Measurement 

