By St. John C.E.

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**Extra resources for A Search for an Einstein Relativity-Gravitational Effect in the Sun (1917)(en)(3s)**

**Example text**

Sometimes a suffi x to iJ denote s the independent variable. A shear defo r mation. with only the compo nent e u = oysx/ 2, prod uces a shear stress P12 = IlOySx . 51) The rigidity Il expresses the resistance to shear. 52) where Pet is the e ffective pressure generated by elasticity. 53) is the compre ssibiiity and K = A + 21113 the bulk m odul us. equal to abo ut 51113 in the Earth's interior. 45) of the strain energy. 47") whieh clearly shows the role of K . Dynamics of a solid body. The inertial acceleration is the second Lagrangian derivative of the displacement s: the displacement , and not the fluid veloc ity.

Say, PijlljdS. T he stress tensor has the d imension of a pressure, or an energy den sity. 40 ) Pij = - Po ij (or P = - P I): the scalar P is the pressure (note the minus sign. corresponding to the fact that pre ssure tends to expa nd the volum e eleme nt d V) . In ge neral, how ever, there is also a fo rce parallel to the surface eleme nt (shear stress). From the conser vation of ang ular mom entu m it ca n be show n that Pij is symmetric. T he total stress force exe rted upon a vo lume elemen t V bounded by a surface S by the s urround ing medium is given by J,r liS /li Pij , 1 or.

Zr 2' = sin (Jcos ()cos q,. "1 "1 . 2 = sm- O(cos- q,- sm 4'), ,,2 ? "I _Z - x-- y. ---"-- = 3 cos ()- I . rThe last function is independent of the longitude. One of the possible realizations of spherical harmonics. often used in mathematical physics, uses the Legendre polynomials p ( u) . Their importance in gravitation physics stems from their definition: p( u ) is the coefficient of ,/ in the power expansion of the function (llIl ~ I and a < 1) r I (I - 2au + (y2 1f2 ~ = (2, 1) p {(u ) a t .

### A Search for an Einstein Relativity-Gravitational Effect in the Sun (1917)(en)(3s) by St. John C.E.

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