The divergence formulas we have obtained (differential conservation
laws) of the form div * F* = 0 for an arbitrary smooth field of unit vectors

**τ**(x; y; z), for a family of spatial curves as well as {

*L*τ} for a family of surfaces {

*S*τ} continuously filling a certain domain. The solenoidal vector field

*in these formulas is expressed, respectively, through the field*

**F****τ**(x; y; z), the characteristics of the curves

*L*τ and characteristics of the surfaces

*S*τ. Also, we have found the formulas connecting the surface characteristics and those of the curves orthogonal to them. In the case when the curves

*L*τ and the surfaces

*S*τ are vector lines of the vector field

**υ**= |

**υ**|

**τ**with the direction τ and the surfaces orthogonal to them, the conservation laws found are equivalent to divergence formulas for the field

**υ**. With these general geometric formulas the divergent identities (differential conservation laws) for the solutions of the eikonal equation |grad τ|2 = n2(x; y; z), the Poisson equation uxx + uyy + uzz = –4πρ(x; y; z) and for solutions of Euler's hydrodynamic equations are obtained. In the plane case, these formulas transform to the conservation laws obtained earlier.