8 Astronomy and Geology compared. PT. T. 



7 times 7 make 49 as that 2 and 2 make 4, and the 

 whole multiplication table must be as correct in the 

 star Arcturus as in any national school in the three 

 kingdoms where it is painfully drubbed into the 

 heads of puzzled ploughboys. The multiplication 

 table is one of the first stages in arithmetic ; 

 logarithms are amongst the most refined and the 

 most subtle, yet it is as impossible that the logarithm 

 of the tangent of the angle of 44 should be any- 

 thing less than 9-984837, or that the logarithm of 

 the number 365 should be anything but 2-562293 

 as that 2 and 2 should not make 4. Where the 

 principle is true the results must be always the 

 same. Eelying upon the correctness in the prin- 

 ciples of logarithms, mathematicians use them to 

 facilitate their most abstruse calculations. What 

 is true in arithmetic is equally true in every descrip- 

 tion of pure mathematics. When the young student 

 has mastered the pons asinorum in his Euclid, he 

 knows absolutely that the two angles at the base of 

 an isosceles triangle are equal ; he does not require 

 to seek for a confirmation of this in the evidence of 

 fact; it is not necessary for him to measure 100 or 

 1,000 or 10,000 isosceles triangles in corroboration 

 of. the demonstration of the fifth proposition of 



