1896-97-] COUNTING AND TIME RECKONING. 



COUNTING AND TIME RECKONING. 

 By John Thorburn, LL.D. 



(Read April 2ph, i8gy). 



N.B.— As some of the letters and characters meant for this paper are not in common use, it has been- 

 found necessary to use others approximately like them. 



The system adopted by different nations for recording events prior to 

 the introduction of what are generally known as the Arabic numerals 

 varied greatly, and, as might naturally be expected, was in most cases 

 extremely primitive, and not unfrequently complicated, especially when 

 the art of writing was unknown, or but partially practised. Nor can we 

 wonder at this, for in comparatively recent times, we find uncivilized 

 tribes whose knowledge of numbers is so limited that it is difficult to 

 imagine how, except for a very brief period, they can keep trace of past 

 events. The faculty of counting seems to be one of the last to be 

 exercised and developed, and hence we find that, even among nations 

 well advanced in civilization, and with a considerable amount of 

 intellectual advancement, their range of using numbers is comparatively 

 restricted. As has been well said, the power of accurately estimating 

 and correctly expressing any considerable numbers is one of the most 

 striking evidences of civilization, and complications of words in the 

 expression of small amounts must be deemed evidence of great 

 intellectual inferiority. 



Sir John Bowring, whose work on the decimal system contains a large 

 amount of curious information, and to whom I am largely indebted for 

 matters relating to this subject, mentions that the method of employing 

 the fingers, hands and feet can be traced in the numerals of many of the 

 aboriginal tribes, both on this continent and elsewhere, and that, owing 

 to the complex and cumbrous character of their languages, they were 

 prevented from extending their numerical calculations beyond a very 

 limited range, and we are not surprised, therefore, when we are told that 

 one of the tribes on the Amazon break down when they come to 3, 

 which they call paettarrarorincoaroac. Probably the main reason why, 

 among rude and uncultured nations, so much use is made of the fingers 

 and toes, and why they play so important a part in expressing numbers* 

 is because they are at all times ready at hand and available to make 



