80 PRINCIPAL FORBES ON AN EXPERIMENTAL INQUIRY INTO 



of figures in Case II. of Table I. The observations of April 16 were made with 

 melted solder as a source of heat, which fuses at a much lower temperature than 

 lead. The result is, that the temperatures in the 3, 6, 9 inch holes and those 

 which follow, are intermediate between the temperatures shown in those holes in 

 the other experiment. Thus, by varying the temperature of the source of heat, 

 we may multiply indefinitely points in the curve without increasing the number 

 of holes with which the bar is pierced, which is evidently undesirable. It would 

 have been very serviceable for the interpolation of the numbers in Case I., had the 

 temperature of the origin been expressly varied for this purpose. 



59. The general agreement of the independent interpolated observations has 

 been highly satisfactory, as may be seen from Plate III., where the several sets of 

 temperatures belonging to Case I. are distinguished by marks. 



60. A continuous curve was next to be drawn through the extremities of the 

 ordinates, so as best to conciliate the whole of the observations. To draw this 

 curve was a matter requiring great nicety and judgment, owing to the limited 

 number of ordinates disposable. It is well known to every one who has used 

 such projections, that to draw an interpolating curve advantageously requires 

 that the rate of increment of the two variables shall not be excessively unequal. 

 In curves like those of Plate III., which rise very rapidly at one end, and become 

 almost or quite asymptotic at the other, it is indispensable to make subsidiary 

 projections of different parts of the curve, in which the relative scale of the vertical 

 and horizontal co-ordinates shall be altered. For the part of the curve between 

 and 2 feet, the temperatures had to be contracted in scale and the abscissae 

 expanded : while for the right-hand branch of the curve the contrary was done, 

 even to the extent of magnifying the vertical scale of degrees tenfold, whilst the 

 horizontal scale of feet was diminished fourfold, compared with the first pro- 

 jection. For each of the three Cases (Art. 48), the statical curve was thus sub- 

 divided and partially projected on four different scales, three of which are exhi- 

 bited on the engraved Plate. The result of this close analysis and comparison 

 has been highly favourable to the assurance of accuracy in the final results, since 

 the interpolated temperatures for any abscissae are the result of two, if not 

 three, projections of the observations on different relative scales. No numerical 

 or other casual error could thus possibly escape detection. 



61. I believe that these curves, as now obtained with the ordinates immediately 

 to be given, are favourable specimens of numerical accuracy and geometrical 

 definition, considering the difficulties attending the experiments. Throughout a 

 great part of the curves (and that by far the most important for the results), the 

 temperature excesses of the bar, or vertical ordinates, may, I hope, be esteemed 

 correct within a very small fraction of their amount. The following table (which 

 may be regarded as summing up the whole Statical data) contains the ordinates 

 of the curves corresponding to the three Cases of Art. 48. 



