1098 
Journal of Agricultural Research 
Vol. V, No. 23 
complete contraction in all cases. It also indicates that the value of 
such ratio should be greater than 7 in all cases, and that 15 probably 
would come nearer than 7 to meeting average conditions. 
effect of suppressing bottom contractions with a 90° trian¬ 
gular notch 
In order to throw more light upon the question of the effect of bottom 
contractions upon discharges through triangular notches (9, p. 114-116) 
experiments were made with a 90° triangular notch with the floor of 
the weir box at the same level as the vertex of the notch. The width of 
the weir box used was 10 feet, being the same as that in the standard 
test with complete contractions, but in the standard test the floor was 
about 4 % feet below the vertex of the notch. The discharges through the 
90° triangular notch with the bottom contraction entirely suppressed 
was found to be represented by the formula 0= 2.53/P* 496 , which varies 
but little from Thomson's formula for the flow through a 90° triangular 
notch having complete bottom contractions. It is probable that some 
part of the increased discharge obtained when the floor was level with the 
vertex of the notch was due to the increased velocity of approach. The 
increase in the discharges amounted to 1.6 per cent with a head of 1 foot, 
but gradually diminished as the head was decreased. The percentage 
of increase with heads of 0.3 foot or over is represented by the formula 
E— ioi.6// 0 - 016 — 100. • 
RELATION OF LENGTHS OF NOTCHES TO DISCHARGES 
The principal advantage claimed in irrigation practice for Cipolletti 
notches over other notches has been that the discharges are proportional 
to the crest lengths. This claim is not in accordance with the limitation 
put on the notch by Erancis and Cipolletti, but has been very generally 
made in irrigation practice. The failure of this theory is shown in 
Table XV, in which the discharges through Cipolletti and rectangular 
notches of different lengths are compared with the discharges through a 
i-foot Cipolletti and a i-foot rectangular notch, multiplied by the number 
of feet in length of the notches. The percentages in the table represent 
the failure of the larger notches to give discharges proportional to their 
lengths. It will be seen from the table that rectangular notches give 
discharges which are more nearly proportional to their lengths than do 
Cipolletti notches. The percentages of error increase with the head and 
length of the crest until the discharge through a 4-foot Cipolletti notch 
with a i-foot head is 9.2 per cent less than four times the flow through 
a i-foot notch with a i-foot head, and the discharge through a 4-foot 
rectangular notch is 4 per cent greater than 4 times the discharge through 
a i-foot rectangular notch with a i-foot head. Side slopes of 1 to 4 are 
therefore too flat and vertical sides are too steep to give discharges 
proportional to the length of the crest. 
