Viscosity and Rigidity of Iron and of Steel. 181 



reversed when the helix is passed from the upper to the lower 

 wire. It follows, therefore, that <p is not influenced by errors 

 which in my apparatus might result from the increase of length 

 due to magnetization. In other words, in the mechanism 

 adopted magnetic elongation has no rotational effect. I and p 

 denote length and radius each in centimeters, r is in degrees, 

 (p in radians, as above. 



Table 4. 

 Showing the effect of sign of twist and of position of helix. 



Remarks. 



No. 



r 



0xlO 6 



Helix symmetrically on upper wire < 



17, 18 



2p=0-053 cm 



Z=30 cnl 



+ 6 

 -4-5 

 + 6 



-130 

 + 133 

 -139 



Helix symmetrically, on upper wire . 



" + eccentrically, " " 



" —eccentrically, " " 



19, 20 



2p=0-083 cm 

 ?=30 cm 



-3-0 



-3-0 

 -3-0 

 -30 

 -3-0 

 -.3-0 

 -3-0 

 — 3-0 



+ 93 

 95 

 93 



" + diagonally, " " .. 



95 



" —diagonally, " " . 



" high position, " " 



" low position, " " 



95 

 94 

 97 



" symmetrically, on tower wire 



88 







Helix, symmetrically, on upper wire -J 



15, IG 



2/)=0-110 om 



Z=30 cm 



-3-0 

 + 3-0 



+ 66 

 -68 



These sudden changes in the values of <p due to magnetiza- 

 tion are equivalent to an increase of the rigidity* of steel and 

 I shall therefore describe them as such. If T be the torsional 

 rigidity of a wire, i. e., the reciprocal of the amount of twist 

 per unit length per unit moment of twisting couple ; and if G 

 be the absolute rigidity of the material, i. e., the reciprocal of 

 the amount of shear per unit of shearing force, then 



Now if in the present apparatus r' be the rate of twist in 

 radians and <p the change of z' due to magnetization ; if more- 

 over G m and G be the rigidities of the magnetized and un mag- 

 netized wires respectively ; then since the radii (/>) are identical 



G m (r'-m) =G{r' + cp), 

 which if (p is small in comparison with x' may be written 

 G m 

 G 



* The retrograde motion formerly observed when the upper wire heated to a high 

 temperature (100° — 300°), is cooled to the temperature of the lower wire (this 

 Journal, xxxiv, p. 17), might in like manner be used to compute the variations 

 of rigidity due to temperature. In such a case, however, the variations of tem- 

 perature from the high value to the low value must be as nearly instantaneous as 

 possible, otherwise elastic and viscous detorsions will be erroneously confounded. 



2m 

 r 



