METHODS EMPLOYED IN CALIBBATION OF MERCDEIAL THERMOMETERS. 147 



by any method in wliicli the con-ections of the principal points are taken 

 as accurate, the points of subdivision are termed secondary iwints. 



The corrections for points intermediate to the principal or secondary 

 points may be determined either by interpolation formulae or, as is far 

 more convenient, by a graphic method. In the latter case the abscisste 

 are the nncorrected scale divisions, the ordinates are the corrections to 

 be applied to them, and the curves passing through the points thus deter- 

 mined are called correction curves. The curves employed in this inves- 

 tigation have been drawn on paper divided into millimetre squares. In 

 the line of abscissae two centimetres con-esponded to one degree, while an 

 ordinate of one centimetre represented a correction of 0°"01. In the case 

 of second approximations it was often necessary still further to magnify 

 the corrections and to represent 0°-01 by five centimetres. Time and 

 trouble are saved by using an open scale. In the plates the curves are 

 half the size actually used. 



If a thermometer has been corrected by several methods, it is neces- 

 sary in order to compare the results to transform the correction curves, 

 so that the corrections may be the same at two arbitrarily selected points. 

 These, which ai-e in general at the extremities of the scale, are called the 

 standard points, and a curve such that the corrections at these points are 

 zero is called a standard correction curve. 



(4) The transformation of a correction curve is exactly similar to 

 the conversion of a temperature from the Fahrenheit to the Centigrade 

 scale. On the corrected scale equal differences of scale readings corre- 

 spond to equal tube volumes. This condition will still be fulfilled — (1) if 

 all the corrected readings are increased or diminished by a given amount ; 

 (2) if the difference between any two readings is increased or diminished 

 in a given ratio. 



Let X be any point on the scale ^ {x) its correction. To make the 

 correction for the lower standard point I zero, we have to diminish all the 

 readings by ^ (I). Hence ^the reading for x becomes x + (l>{x) — f (I). 



Let U and 0(U) be the upper standard point and its correction, and let 



U + 0(U) -(I + </>(!)) = N + a, 



where U — I = N. 



Hence after the scale divisions are altered in the ratio necessary to 

 reduce the correction for the upper standard point to zero, the reading for 

 X becomes 



{. + *Ov)-*(I)}^„. 



For facility of calculation this is thrown into the more convenient 

 form — 



x + ^{x) -,p(I)-^^-i|_|a; +^{x) -./.(I)} 



= ^ + ^(^) _ ^(I)_ « ^1 _ I) |a; + <^ (a,) _ ^I) } 



approximately, 



= „. + ^,(3,) - ^(I) _ ^jo. + ^(x) - </,(!) -|a;} 



approximately, whence the transformation can, as shown hereafter, be 

 easily effected. 



L 2 



