280 The Laws of Motion of a Cylinder, &é, 
firoke — —“— drawn into the fquare root of that 
is 
term of the progreffion laft mentioned, which corre- 
{ponds to the ftroke, and the fum of thefe quan- 
afx 
tities h Ae spittin ies == the whole time fpent 
Vitt—t1 
in penetrating the Obftacle. Now the fum of the 
three parts of time found above = the whole time 
° : : ¢ 
required for performing the operation = ae sts 
SAREE By 18 Fay Vl ahrae 
Ys Vitt-1 Avs Vit+t-1 
c ath oh be Pw . 
4 or xX Vv «x Pret ah% Lise 2 Buk, 
Vs eR 
Cor. I. Now, in this est for the whole 
: ‘ai +h 
time, the quantities ——— = and Yizi—1, 
c 
bear. iva 
are conftant, and have nothing to do with the va- 
riation of the time, the maximum and minimum 
of which depend on the variable part Yx % 
c 
Wie? but x» = eae therefore by fqua-~ 
2 
y 
ring, we have * X vi +t-1— M— 
cx Viper = Viskaesd xe 
; pit Now, fince 
Mi as ee Vitis 
the 
