82 



PRINCIPAL FORBES ON AN EXPERIMENTAL INQUIRY INTO 



be seen farther on (Art. 71) that a formula, however empirical, enables us to 

 execute promptly and with confidence the otherwise tentative and uncertain 

 process of drawing tangents to the curve in its higher part, in other words, of 



obtaining values of -j- upon which the final deductions mainly depend. (See 



Arts. 6 and 31.) 



63. It had been acutely perceived by Lambert nearly a century ago,* that 

 the temperatures of a bar heated in the manner of our experiment would diminish 

 in a regular geometrical progression. A more rigorous analysis led BiOTf and 

 FourierJ to the same result, according to the physical assumptions with which 

 they started. Biot and Despretz§ subjected various metallic bars to experi- 

 ment, but they assumed the logarithmic law to be true, and endeavoured 

 to accommodate their numerical results to it, as well as they might. Biot, 

 in particular, applied to his (apparently excellent) observations, the method 

 of least squares to enable him to draw a logarithmic curve through his points of 

 observation, giving no attention to the fact, that the temperatures found did 

 not conform themselves by any means to the a priori geometrical law, and that 

 the laws of Probability could not be applied to them without ascribing extra- 

 vagant and improbable errors to a large part of the curve of observation. || 



64. That the temperatures deviate systematically from the law of continued 

 progression, will appear from the following table of the ratios of successive ordi- 

 nates, taken three inches apart in the three Cases of Table II. 



Mean Ratio!! between Two Consecutive Ordinates 3 Inches apart, from the 



Numbers in Table II. 



Intervals. 



Case I. 



Case II. 



Case III. 



3 to 6 inches, 



•707 



•650 





6 to 9 



•722 



•673 



■687 



9 inches to I. foot, . 



•733 



•690 



■690 



I. foot to I. foot 6 inches, 



•753 



•707 



•719 



I. foot 6 inches to II. feet, 



•770 



•727 



•728 



II. to III. feet, . . . 



•787 



•735 



•750 



III. to IV. „ . . . . 



•809 



•762 



•755 



IV. to VI. „ . . . . 



•830 



•774 



•731 



* Pyrometrie. Berlin, 1779, p. 185. 



f Traite de Physique, vol. iv. p. 669. 



J Theorie Analytique de la Chaleur. 1822. 



§ Traite Elementaire de la Physique. 1836, p. 197. 



|| Compare Note to Art. 3 of this paper. 



*fT By " mean ratio," I intend to express, that where more than one 3-inch space is included 

 in the Interval specified in the first column, the number which follows is the average decrement 

 throughout that space. Thus, in Case I. the whole interval from II. to III. feet, shows a decrement 

 from 24° - 2 to 9°33, which would result from the mean ratio of 0787, four times multiplied into 

 itself. 



