744 



Making use of (52) we get after integration : 

 ^^,^ T 1 + 3^ F-' 



In order to obtain a limiting value for 1.^;, we make use of the 

 results of an investigation b}- Hess ^j on the sagging of ice 

 crystals. He charged a crystal 2.9 cm long, 'i.O cm broad, and 1,2 cm 

 thick at its end with a weight of 5000 grams, without rupture taking 

 place. Let us assume by approximation that an ice cylinder of a 

 diameter of 1 cm could bear the same load. We can then derive a 

 limiting value of Yz from (51). 



If we introduce this into (52), we find finally, assuming that =: {, 

 which is about correct for a great many substances. — 1.19 X 10"* 

 degree for A 7', which quantity is probably not liable to measure- 

 ment. That this quantity is so small, is the consequence of the small 

 value of the maximum tangential tensions which ice can bear. 



We considered the point on the circumference for which .6' = R, 

 y = 0. If on the other hand we take the point for which x = 0, 

 y =z R, we get the formulae 



U 



^. = ^3 . Py X, = r, =: . 



jrZt!' ^ . 



If as before, we again assume that an ice cylinder of a diameter 

 of 1 cm. can bear a load of 5000 grams at its end, we find for iT^ 

 a value which appears to be greater than the value assumed by 

 RiECKE. If we calculate the lowering of the freezing point by means 

 of this, we find LT= — 0°.081, an amount that can be easily measured. 



We see at the same time that the lowering of the freezing point 

 has different values at difterent points of the surface ; a state of 

 equilibrium is therefore impossible. The rod of ice will diminish on 

 the upper surface and on the lower surface, and that much more 

 quickly than on the sides, which will also diminish a little. Further 

 this diminution will increase towards the end where the rod is loaded. 



3. Torsion. 



In this case only Qz -\- 0. From the formulae (51) follows then 

 for the point iv = 0, y ^ R 



z^z=o x. = — — rz = o. 



jiR' 

 Taking the small amount of the tangential tensions which ice can 



i) H. Hess Ann. d. Phys. 8 p. 405. 1902, 



