. The London, Edinburgh and Dublin philosophical magazine and journal of science. fixed intervals we can by numerical interpolation findintermediate terms conformable to the law of the series ; so, be-tween fixed and determined points of our thermometer, we can,by using the interpolating-engine, so divide the interveningspaces that they shall conform to the varying nature of the series,or, in other words, that the divisions shall increase in magnitudeas we ascend the scale in such proportions as are demanded bythe expansion of the alcohol and the bore of the tube employed. To illustrate this n
. The London, Edinburgh and Dublin philosophical magazine and journal of science. fixed intervals we can by numerical interpolation findintermediate terms conformable to the law of the series ; so, be-tween fixed and determined points of our thermometer, we can,by using the interpolating-engine, so divide the interveningspaces that they shall conform to the varying nature of the series,or, in other words, that the divisions shall increase in magnitudeas we ascend the scale in such proportions as are demanded bythe expansion of the alcohol and the bore of the tube employed. To illustrate this new method I have invented, let us supposewe have ascertained the fixed points, P, Q, R, S, of a thermometercorresponding to equal differences of temperature. And let J? Q K S It is desired to divide the intervening spaces each into ten divi-sions, so that each division shall occupy its true position. ?H Intelligence and Miscellaneous Articles. 157 . To do this, take any right-angled triangle, A B C, and divide theside A C into ten equal parts by straight lines drawn from Then, if a straight line, as A C, be drawn parallel to A C, itwill 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 lawgoverning the series, and we can in the same manner, by usingthe same formula, divide any number of spaces with equalaccuracy. It remains, therefore, mechanically to transfer such divisionsto our thermometer, previously marked off at equal intervalsof temperature, in order to secure its correctness to even seconddifferences. This mechanical copying can be done by the dividing-enginebefore referred to; and it is worthy of note, that th
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