1G0 Intelligence and Miscellaneous Articles, 



Has it ever been noted that, whereas in polyhedrons the three 



\ t cos 116° 33'54"=-i 

 3 V ° 



peculiar angles are cos 109° 28' 16"= -,cos 116° 33 f 54"=—, and 



cos 138° 11' 23"= - V5, these must form the hypothenuse and legs 

 o 



of a spherical triangle, with the respective angles of 90°, 

 tan- 1 (-3) = 106° 26' 06" and 135°=90 + 45. 

 The second angle = 225°-116° 33' 54". Further, 



cos 109° &c. : cot 116° &c. : sin 138° &c. : : 2 : 3 : 4. 

 London, January 8, 1863. 



FRESH-WATER LAKES WITHOUT OUTLET. 



To the Editors of the Philosophical Magazine and Journal. 



Linfield, Belfast* 

 Gentlemen, January 21, 1863- 



In your Number for April 1858, Mr. Jennings mentions two lakes 

 near Damascus as being without an outlet and yet fresh, which he 

 regards a unique exception to the rule that lakes without an outlet 

 are salt. I think the lake of Tacarigua, or Valencia, in the north of 

 South America is another instance of the same kind. Humboldt, 

 in his ' Personal Narrative,' vol. iv., gives a description of the lake, 

 which be distinctly states to be without outlet ; and though 1 cannot 

 find any statement in so many words as to whether it is salt or fresh, 

 I infer the latter from the following circumstances : — 



Were it salt, an observer like Humboldt would mention its degree 

 of saltness. 



He compares it with the alpine lakes without mentioning saltness 

 as a point of contrast. 



Its vegetation is that of fresh water. " The banks, shaded by tufts 

 of Coccoloba barbadensis, and decorated with fine liliaceous plants 

 (Pancratium undulatum, Amaryllis nervosa), remind us, by the appear- 

 ance of the aquatic vegetation, of the marshy shores of our lakes in 

 Europe. We find there pond weed (Potamogeton), Char a, and cat's- 

 tails 3 feet high." 



Its fishes are those of fresh water. It contains three kinds, " the 

 guavina, the vagra, and the sardina; the two last descend into the 

 lake by the streams that flow into it." 



Humboldt also remarks, " It is somewhat remarkable that the 

 lake of Valencia, and the whole system of small streams which flow 

 into it, have no large alligators, though this dangerous animal abounds 

 a few leagues off in the streams that flow either into the Apure or 

 the Oroonoko, or immediately into the Caribbean Sea." 

 I remain 



Your obedient Servant, 



Joseph John Murphy. 



' 



