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Intelligence and Miscellaneous Articles. 



157 



. To do this, take any right-angled triangle, A B C, and divide the 

 side A C into ten equal parts by straight lines drawn from B. 



Then, if a straight line, as A' C, be drawn parallel to A C, it 

 will be divided into ten equal parts ; but if it be drawn not paral- 

 lel to A C, it will be divided into ten unequal parts. 



To apply this to the thermometer to be divided, draw a trans- 

 versal L M N cutting A C produced in L, at an angle </>, so that 



tan (j>= -3_ — i- tan A, 



and 



CC^-j- X-^ 



MK=j, 



On doing this, it becomes evident that such a line, so placed, 

 will be divided into ten unequal parts, proportionate to the law 

 governing the series, and we can in the same manner, by using 

 the same formula, divide any number of spaces with equal 

 accuracy. 



It remains, therefore, mechanically to transfer such divisions 

 to our thermometer, previously marked off at equal intervals 

 of temperature, in order to secure its correctness to even second 

 differences. 



This mechanical copying can be done by the dividing-engine 

 before referred to ; and it is worthy of note, that the formula and 

 engine equally apply to the more correct dividing of mercurial 

 thermometers having unequal or varying diameters of bore, as also 

 to the construction of hydrometers of absolute accuracy. 



I can easily understand that whilst the mathematician may ap- 

 preciate the formula thus introduced, and also its successful applica- 

 tion, those accustomed to the construction of thermometers would 

 hesitate to adopt it, from the fact that the plan involves a series of 

 calculations for each thermometer, which would involve consi- 

 derable loss of time and risks of inaccuracies, if these computa- 

 tions were hastily done ; hence my first idea was to compute a 

 series of tables ; but this was attended with only partial success. 

 My attention was then directed to the mechanical solution of 

 these problems, the result of which was the invention of a little 



