On " Random Scattering " of Points on a Surface. 439 



is established by my own experiments ; (2) the fact that 

 there is a sudden fall in rigidity at a temperature about red 

 heat — this is established by Mr. Tomlinson's Experiment I. 

 as well as by similar experiments of my own ; (3) the 

 assumption (? fact) that a wire of even 1 mm. diam. is not 

 heated uniformly throughout its thickness, but that the inner 

 part is hotter than the parts near the surface ; and lastly 

 that the rigidity of the iron at the high temperature of 

 reglow is less than the rigidity of iron at not so high a 

 temperature before reglow. 



A similar line of argument will explain the results recorded 

 in Experiments VI. and VII. 



I have made a great number of experiments on the return 

 of magnetic properties in cooling iron ; and can at present 

 only say with certainty that the matter is not so simple as 

 appears from Experiment IV. of Mr. Tomlinson's paper. 

 The relation between the reglow and return of magnetic 

 properties varies with the specimens of iron and steel used. 

 I have found some few specimens in which the reglow takes 

 place in the middle of the return of magnetic properties, so 

 that the galvanometer indication is two kicks, the first very 

 small, just before reglow, the second and main kick after 

 reglow, as if the metal was becoming magnetic, when the 

 rise of temperature, coincident with reglow, caused it to pause 

 for an instant. In general, however, the reglow precedes the 

 return of magnetic properties, though by intervals which 

 vary with the specimens observed. I hope to have more 

 definite results when I have tested the numerous specimens of 

 steel and iron which I have now in my possession. 



LVI. On u Random Scattering " of Points on a Surface. By 

 Joseph Kleiber, Privat-Docent in the Imperial Univer- 

 sity of St. Petersburg .* 



IN a paper published in the Philosophical Magazine [ser. 3], 

 vol. xxxvii. pp. 401-427 f, Prof. Forbes set forth some 

 objections against the application of the principles of the 

 mathematical theory of probabilities to the question of the 

 distribution of stars in the sky. Mr. Todhunter quotes this 

 paper in his well-known ' History of the Theory of Probabi- 



* Communicated by the Author. 



t "On the Alleged Evidence for a Physical Connexion between Stars 

 forming Binary or Multiple Groups, deduced from the Doctrine of 

 Chances." 



