On the Fundamental Principles of Mathematics. 329 



Mount 



nu- 



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merous little conical crater-like hillocks, each probably (like those 

 on the flanks of Etna) once in action. Lofty ice cliffs, probably over 

 1000 feet in thickness, solid without a fissure, and presenting ver- 

 tical walls to the waves which dashed their foam high against them, 

 stretched away interminably to E.S.E., and the ships sailed alon 

 them more than 100 miles without any prospect of passing 

 around them. The latitude was now 77° 46' S., longitude 

 176° 43' E. 



The magnetic dip had diminished to 87° 22' S., proving that 

 they had passed beyond the magnetic pole, and the variation was 

 104° 25' E. Soundings were obtained in 410 fathoms with two 

 feet of soft green mud ; temperature at 300 fathoms, 34° 2', in 

 the air 28° ; in summer the air and the water seldom differ more 

 than three or four degrees. 



A petrel wounded by a shot, falling in the water, was immedi- 

 ately torn to pieces by its companions. 



At midnight the lat. was 78° S., in 180° E. long. 



Magnetic irregularities.— In lat. 77° 6' S., long. 189° 6' E., 

 the dip had diminished to 86° 23', the variation decreased from 

 96° E., to 77° E., and then again increased to 16°. It appeared 

 to be one of those extraordinary magnetic points first observed 

 during Sir Ed. Parry's second voyage to the Arctic seas near the 

 eastern entrance of the Hecla and Fury straits. 



an 



progress farther south was prevented by a barrier of ice 160 feet 

 high, and extending in one unbroken line 250 miles. 



(To be continued.) 



Art. XXVIII. — On the Fundamental Principles of Mathe- 

 matics ; by Stephen Alexander, Professor of Mathematics 

 and Astronomy in the College of New Jersey. 



(Continued from p. 187.) 



Of Positive and Negative Signs, and a Particular Case of 



aginary Values. 



(17.) The consideration of the algebraical signs of quantities 

 seems to be next in order, after what has already been exhibited, 

 with regard to their division ; for the relative greatness of the por- 

 tions obtained, and the manner in which the greatness of the 

 quantity will be affected by that of another in any given case of 

 combination, will depend upon their respective signs; while nei- 

 ther the absolute, nor yet even the relative greatness of the quan- 

 tities, will be affected by those signs. 



Sjboosd Series, Vol VII, No. 21.— May, 1840. 42 



wm 



