PROCEEDINGS OF SECTION A. 365 
produced when the intensity of twist rose beyond a certain 
point. From the experiments it is deduced that a good margin 
for safety will be left if a fibre ‘01 cm. in diameter is not twisted 
at a greater rate than one-third complete turn per centimeter, 
and in other fibres at a rate simply inversely as the diameter. 
The claims of quartz fibres for suspension purposes are established 
beyond criticism by the above researches. 
Notre.—Further experiments have shown that the tempera- 
tive coefficient of total torsional rigidity is more nearly ‘00012 
than -00013; also that the amount of nachwirkunk exhibited 
appears to depend on the thickness of the threads in a manner 
probably related to their rate of cooling during manufacture. 
2,—CLOUD OBSERVATIONS. 
By W. W. Cuucuetru, M.Inst.C.E. 
3.—_SOME REMARKS ON THE TEACHING OF ELE- 
MENTARY MATHEMATICS AND PHYSICS. 
By Rev. W. L. Bowpitcu, M.A. 
4._-NOTE ON THE EULERIAN EQUATIONS OF 
HYDRODYNAMICS. 
By ALExANDER McAutay, M.A. 
| Adstract. | 
Mr. Larmor (Proc. Lon. Math. Soc., March, 1884) has from 
general dynamical principles deduced the Lagrangian equations 
of hydrodynamics by the principle 
ho BPS O07) Lo 0 * a2 GLY. 
[ Z the Lagrangian function of a system, g a co-ordinate, Q the 
external force corresponding to 7, the initial and final positions 
and times of the motion, invariable.] We may, by considering azy 
finite portion of a fluid, deduce the Eulerian equations, and also 
the fact that the stress is a hydrostatic pressure. Here by a fluid 
is understood a substance, the potential energy due to whose- 
strain is a function of the density only. For the finite portion 
we have with usual notation 
