NOTE ON THE INTERSECTION OF TWO CURVES. 359 



M'ith // -|- goes through the common focus. In tlie figure / -|- is 

 not produced to the lower point of intersection. 



/ /' 



Note. — Idiat the hyperl)olas — ^^ i -\- c cos 0, — = i -{- e' 



r r 



sin intersect in four points and each branch of the one cuts each 

 branch of the other, the necessary condition (I give it without the 

 working out) is independent of / and /', and is e"^ e'~ > c- -\- c'- 

 In Figure i, ^- ^ 3, e'- = 4, and the conchtion is satisfied, but 

 in Figure 2, r = 3. 8^'- = 9, and the condition is not satisfied. 



Fossil Man. — The Hriti'^li Afuseum has recently issued a 

 guide to the fossil remains of man in its Geological and I'akeon- 

 tological Department. After explaining the significance of the 

 various specimens comprising the exhibits, the author states the 

 general conclusion that man, having a skeleton essential!}- iden- 

 tical with the existing one. lived in Western Europe long before* 

 the British Isles were separated from the mainland. His imme- 

 diate jiredecessor. the Neanderthal or Mousterian man, more 

 nearly approached the apes in the retreating forehead and other 

 features. The still earlier Heidelberg man had a much more 

 retreating bony chin, and the Piltdown man, probably older than 

 the Heidelberg race, had both lower jaw and front teeth as nearly 

 on the ape-pattern as was compatible with their working on a 

 human skull of normal width: thus, the furtlier that liuman 

 remains are traced back in geological time, the more marl<s tliey 

 retain of an ape-like ancestry. 



Isotopes. — While the British Association was at Mel- 

 bourne in August, 1914, Sir Ernest Rutherford, in opening a 

 discussion on the structure of atoms and molecules, drew atten- 

 tion to the remarkable fact that radium B, with an atomic weight 

 of 214, and lead, with an atomic weight of 207, were identical 

 in respect of their cliemical pro]:)erties : chemically they were 

 inseparable, and their gamma ray spectra were also identical, and 

 he concluded that difi:'erent varieties of lead exist, identical in 

 every respect except in their atomic weigiits. Such varieties of 

 an element have been designated " isotopes," and in the case of 

 lead there appear to be several of tliem. Soddy, for instance, 

 found that lead derived from thorite possessed a greater density 

 and a higher atomic weight than common lead. It has recently 

 been announced by Richards and Wadsworth* that lead derived 

 from certain Australian radioactive minerals falls below ordinary 

 lead both in atomic w^eiglit and in density ; the density of ordinary 

 lead being 11.337, while that of the Australian lead is 11.288. 



'^Journ. Amer. Cheni. Soc. 38 [2]. 



