for Calibrating Thermometer s. 297 



as the starting- or reference-point of the computation, should 

 now be selected. In general the extreme ends of the tube are 

 to be avoided, as more likely to have been rendered irregular 

 or rapidly tapering in the process of making or joining on the 

 bulbs. If the zero of the numbering is placed one or two 

 centimetres from the bottom of the tube, it forms a desirable 

 starting-point. 



Find upon the curve the ordinate u' corresponding to the 

 abscissa A ; then with abscissa A + u' find the corresponding 

 ordinate u" ', with abscissa A + u' ' + u" find the corresponding 

 ordinate u'", continuing to the upper limit of the graduation. 

 If A is at a sufficient distance from the lower end of the gra- 

 duation, find a similar series below the point A. These points, 

 A, A + u', A + u' + u", &c, upon the graduation are separated 

 by equal volumes of the capillary. Select any one of these 

 as the second point of which the error is to be arbitrarily 

 assumed as zero, and call this B. Then 



A + v! + u" + . . . + «nth=B. 



There are thus n spaces of equal volume between A and B ; 



and these correspond each to -th of the interval B —A. Hence 



the true reading (which, however, it is not necessary to com- 

 pute numerically) at the point 



A is A, 



A + u' is A+- (B-A), 



A+u'+u" is A+?(B-A), 



B is B. 



And the error obtained by subtracting the true readings, as 

 given in the right-hand column, from the corresponding actual 

 readings, given in the left-hand column, at 

 A i» 0, 



A+t*' is A + w'j A+ i(B-A) \ =«'-* (B-A), 



A+u'+u" is u'u"- + -(B-A), 



B is 0. 



In selecting B it might have been assumed equal to A + u' , 

 thus making w = l. This would somewhat simplify the calcu- 



