282 



SCIENCE. 



[N. S. Vol. XVIII. No. 452. 



sends a tongue northward from Eincon to the 

 Vento on the Almendares Eiver in the north- 

 ern watershed. Aside from the ' Ojos de 

 agua ' along the edge of the eienegas skirting 

 the southern coast there are two notable 

 places where undergTound rivers find an exit; 

 the one at Vento, as already mentioned, sup- 

 plies the entire city of Havana with its water, 

 the other serves to make the region about 

 Guines a garden, its waters being used for 

 irrigation. Other subterranean rivers in all 

 probability have a subaqueous exit to the 

 south. 



The large spring at Vento is the only one 

 on the northern slope as far as I know. The 

 .exact origin of the supply issuing from the 

 Vento Spring has not been traced. But the 

 region north of the Almendares Eiver, being 

 shut out from a possible contributing source, 

 it undoubtedly derives its water from the 

 tongue of the system of underground streams 

 thrust into the northern slope. An examina- 

 tion of the best available map and the levels 

 of the Western and United Havana Eail- 

 roads makes it seem, quite certain that the 

 Vento Springs derive their water from the 

 region immediately south of Vento and north 

 of Eincon and Bejucal. This region contains 

 various sinks without surface outlets, as well 

 as dry sink-holes. A notable sink -hole in this 

 region is that at Aquada on the United Havana 

 Eailroad. This is very broad, shallow and dry 

 during the dry season but the water rises to 

 stand over ten feet deep on the railroad track 

 during some of the wet seasons. All of these 

 probably drain into the Vento Springs. 



It behooves the health authorities of the 

 city of Havana to exercise the strictest guard 

 over the region between Vento on the north 

 and Eincon and Bejucal on the south. Any 

 contamination of sink-holes in these regions 

 is sure, during the wet season at least, to 

 contaminate the underground streams leading 

 to Vento. An examination of the under- 

 ground channels in the Lost Eiver region of 

 Indiana has shown the main underground 

 channels to be provided with numerous smaller 

 tributary channels which in ordinary weather 

 do not carry water, but which do carry water 

 into the main stream after a long rain. At 



such a time any filth that may have accumu- 

 lated in any of the sink-holes over one of the 

 tributary streams is sure to find its way into 

 the main stream. The same is very probably 

 true of the Vento supply, although on ac- 

 count of the nature of the region it is not 

 possible to follow the underground channels. 

 At present some of the sink-holes between 

 Eincon and Vento are used as cess-pools and 

 receivers of sewage. 



C. H. ElGENMANN. 



NOTES ON PHYSICS. 



GROUP AND WAVE VELOCITY. 



The question was raised at the Pittsburg 

 meeting of the American Association, in a 

 private discussion of Professor Brace's 

 scholarly vice-presidential address, as to 

 the physical distinction between wave and 

 group velocity of light. Undoubtedly the 

 best physical discussion of this matter is 

 to be found in the remarkable chapter on 

 plane electromagnetic waves in Chapter IV., 

 Vol. I., of Heaviside's ' Electromagnetic 

 Theory,' especially in his discussion of the 

 generation of tails. A simple conception of 

 the distinction between wave and group ve- 

 locity is as follows : Imagine a stretched rubber 

 tube with a series of equidistant weights sus- 

 pended from th^ tube by helical springs and 

 imagine a train of say one hundred equidistant 

 similar waves to be started along this tube. 

 The head of this wave train, as it runs out at 

 full speed (wave speed) upon the previously 

 stationary portion of the stretched tube, exerts 

 upon each element of the tube a series of pe- 

 riodic forces, and because of the suspended 

 weights these periodic forces require some 

 perceptible time, ten or fifteen cycles, say, to 

 establish the full oscillatory motion corre- 

 sponding to the full amplitude of the wave 

 train. Therefore, although the head of the 

 wave train runs out on the tube at full speed, 

 there is a gradual rise in amplitude from the 

 extreme head backwards towards the middle 

 of the train. Furthermore, as the main por- 

 tion of the wave train leaves a portion of the 

 tube this portion of the tube persists for an 

 appreciable time in oscillations of diminish- 



