of z may be determined in the fame manner, 
which will be found 
j,4_s a /'!_ J i/ r 37* 47 • 1 1 yAfTA 1 + 1 °f 6 a , 
- 9 ( a 4 f A ) 
If f — o, this value of £ — 0,537a; 
/= °> 2 5 * 
/— 0,3 
/ - 0,5 a r 
f~ 0,7 a 
/=■ 0.9 * 
/=« 
r CS 
a 
— 0,49 vu 
=. 0,486^ 
— 0,436a; 
r:~ 0,3Q0a; 
= °>353^ 
= °>333 rJ 
By the infpedion of thefe different values it ap- 
pears that this value of z diminifhes as the plunged 
part is greater, and that this velocity can never exceed 
the quantity 0,537x9 nor be lefs than L.v *. 
This value of z and of its fquare zz being fub- 
flituted in the general formula (§ II.) we fhall ob- 
tain from it the following equation : 
M * 6 -2 7 « 4 r*+i i/«+* («*-*//) v- r o tt 4; 4 nf-— 
8 I (a +— -f +) 
which for a given relation between f and a will fhew 
the breadth 0 for producing the greatefl efteft. 
* If in the value of z we make f — «, we have z — - 
which obliges us to take, according to the common method, the 
differentials of the numerator and of the denominator, confi- 
deringy as variable, and the relation of thefe differentials will 
give the value of z : but on account of the radical quantify, the 
calculus being fomewhat tedious, and, again bringing out 3 — ^ 
and that after fevcral fimilar operations, it is better to have re- 
courfe to the equation from which the value of z wu; deduces ; 
... 1 — r 
this eouation is | »vz.— — - 2 - axvv . — 
* cc / CC i 
■r * , « 4 + +/; 
by the above operation will be | zz'zz vz — } vv, and 
.. LV1I. c c c 
which 
: ' v. 
. i 
As 
