148 report — 1865. 



afforded through its measures of weight, capacity, square and cubic measure being 

 all directly and decimally derived from the metre (the measure of length). 



The paper was elaborately illustrated by diagrams, and numerous practical ex- 

 amples were given in proof of the great advantages of the system. To estimate 

 the number of figures that would be saved in consequence of the metric system 

 being decimal, the author stated that, " To judge of this advantage it will not do 

 to take any particular example, for particular examples may be found in favour 

 either of the English or the Metric System, or even in favour of the old Roman 

 numerals ; since CDM each expresses by one sign the quantity which in Arabic 

 numbers must be expressed by three or four signs, thus, 100, 500, 1000. It will 

 therefore be necessary to enter into some general calculation as to the number of 

 figures required under each system, and to set down and carry out a regular series 

 of figures in addition, multiplication, subtraction, and division, in order to see 

 with which of the two systems the advantage lies. I take the weights, and begin 

 with addition. I proceed with the metric system, and write down consecutively 

 every weight that can be expressed, proceeding by grammes from 1 to 1024 grammes. 

 1024 items can be expressed, and to express them either in grammes, deci- 

 hecto-, and kilogrammes, exactly the same figures, and therefore the same number 

 of figures are required — the number is 2986. 



" I proceed now to set down 1024 items in the English system, from the half 

 drachm (the approximate equivalent of the gramme) to 1 lb. 15| ounces. The 

 figures I must set down are — 



For the fractions 1024 



For drachms 1384 



For ounces 1384 



For pounds 512 



Total figures required for the English weights . . 4304 

 or nearly 50 per cent, more than are required for the metric system. 



" This is, however, only writing down data. Suppose we begin to add up the 

 items in each system, we shall find the gain to the metric system enormous. I 

 begin by adding 1 and 2 grammes, then 1, 2, 3 grammes, and so on ; adding up 

 every sum from one gramme till I have added from 1 to 31 grammes. 



I have to set down before I add up 758 figures ; and 



The sums of these would take 83 „ 



Making the metric total 841 



" Now I proceed to add up the English weights from half a drachm to 1 oz. (a 

 similar number of items to the metric). 



I have to set down before I add up 1027 figures. 



When added up, the number of figures required to express the 



sums in drachms is 92 „ 



But the sums of these drachms have to be brought in ounces and 

 pounds by calculation, and each addition involves a sum in 

 long division, which again involves multiplication and sub- 

 traction, and the number of figures I require to set down for 

 these calculations is 4096 „ 



To express the final result of my additions in pounds, ounces, 

 and drachms, I have to set down 89 „ 



Making a total (English) of 5304 



Against a total (metric) of 841 



or six figures English for one figure metric. 



" Were we to strike off the figures required for the fractions in the English 

 system altogether, still the English system would take 4277 



" While the metric system would require but 841 



or five figures English to one figure metric. 



