We visualized a curvature path as a portion of irregular arc during the motion of particles with velocity v which is comparable to the speed of light c. This is slightly conflicts with the calculations of Lorentz's time dilation and reflects a new considered type of movement for the motion of objects without falling under the influence of other forces but under the impact of the movement of the body itself. We succeed to modify Lorentz's relativistic coefficient
ɣ
for time dilation in terms of
Khbh

224
formula for obtaining the length of irregular arc, where b and h are their base and height, and K is a constant. The relativistic Lorentz's coefficient
)221(1
cv

becomes
)221(2)]221)(24(2[
cvcv K K K


. The calculated values of relativistic time t, Lorentz's relativistic coefficient
ɣ
and path length
ℓ
for muons are 17.29 µs, 7.92 and 5135.13 m, which are higher than that of Lorentz's (15.574 µs, 7.09 and 4625.48 m). Our results are discussed in terms of the mechanism of spiral path motion and understand a new meaning of speed changing spatially not temporally.