248 M.Viktor von LaDg on the Crystalline Form and 



straight line, or its perpendicular fall into the sun, would 

 therefore, under such conditions, be impossible. The observed 

 movement of all planetary bodies in closed curves agrees with 

 this. 



We shall now return to the example of the weight suspended 

 by a string and oscillating round a point towards which it is 

 attracted. The diameters of the orbits described by this weight 

 are observed to be nearly equal; continued observation, how- 

 ever, shows that these diameters gradually diminish in length, 

 so that the weight will by degrees approach the point in which 

 it can touch the floor. The weight, however, touches the floor 

 not in a mathematical point, but in a small surface ; as soon, 

 therefore, as the diameter of the curve in which the weight 

 moves is equal to the diameter of this surface, the weight will 

 touch the floor. This final contact is no accidental or improbable 

 event, but a necessary phenomenon caused by the resistance 

 which the oscillating mass constantly suffers from the air and 

 friction. If all resistance could be annihilated, the motion of 

 the weight would of course continue in equal oscillations, 



The same law holds good for celestial bodies. 

 [To be continued.] 



XXXV. On the Crystalline Form, and Optical Properties of Sul- 

 phate of Thallium. By Viktor von Lang*. 



THE crystals of sulphate of thallium (Th SO 4 ), on which I 

 made the following crystallographic and optical observa- 

 tions, were prepared by M. Lamy : their investigation was of 

 special interest to me, as, from measurements of other combina- 

 tions of thallium recently published by M. de la Provostaye, it 

 seemed to follow that this new element is in its combinations 

 isomorphous with potassium. Now the salts that are isomor- 

 phous with sulphate of potassium are remarkable on account of 

 the difference they exhibit in their optical properties, and it was 

 therefore interesting to me to get, if possible, a new salt of this 

 series for investigation. That the crystals of sul- 

 phate of thallium are really isomorphous with the 

 corresponding potassium-salt, will be seen by the 

 following crystallographic description of them. 

 The crystals are combinations of the forms 



10 0, 010, 110, 210, 101, 111; 

 they are elongated parallel to the axis c, the plane 

 (10 0) being generally very largely developed, as is 

 represented in the accompanying figure. Thepara- 



* Communicated by the Author. 



