84 



PRINCIPAL FORBES ON AN EXPERIMENTAL INQUIRY INTO 



throughout the whole extent of the experimental curve.* But in order to follow 

 the observations more closely, it seemed desirable to divide the curve into two 

 parts, one between and 1*5 feet, and the other beyond 15 feet, and to employ dis- 

 tinct constants for each. A like process was applied to the numbers of Table II., 

 for Cases II. and III. In these, the variations of temperature along the bar being 

 more rapid, the approximation of the formulae was less exact than in the first case, 

 and a formula with three constants was insufficient to represent the curve through- 

 out its whole extent. I found it advisable, in the case of the bar covered with 

 paper (No. II.), to use modified formulae for the upper, middle, and lower part 

 of the curve. I may add that it was found convenient to adapt the formula 

 (Eq. (1.) of this article) to the calculation of the lower temperatures, by changing 

 the origin to an arbitrary point some feet to the right, and by reckoning the 

 abscissae in the opposite direction, thus rendering the second term of the equation 

 positive instead of negative. To this end the equation was written, — 



log v = A + 



1+cc' 



when 



68. The coincidence of the various formulae with the experimental numbers of 



Table II. is shown in the foregoing Table. 



* The formula in this case would be, — 



log v— 272.7- 



•63374 x 

 1 + -0956 a:' 



The following adaptation of Young's formula also represents the observations in Case I. very 

 approximately. 



v= (-43027 + -09539 a)-"*"'. 











v by Formula 





x in feet. 



o by Experimental 

 Curve. 



v by Formula 

 (a -\- bxf. 



Difference. 



log v — 



, bx 

 log a- — — 



\-\-cx 



Difference. 









o 



o 



o 













272-66 



. • • 



272-7 





0-25 



190-5 



190-5 



00 



1910 



+ 0-5 



0-5 



134-7 



135-5 



+ 0-8 



135-9 



+ 1-2 



0-75 



97-3 



9804 



+ 0-74 



98-23 



+ 0-93 



1-0 



72-0 



72-0 



o-o 



72-0 



0-0 



125 



53-6 



53-6 



00 



• •■ 



... 



1-5 



40 l 8 



40-41 



-0-39 



40-21 



-0-59 



2-0 



24-2 



23-75 



-0-45 



23-53 



-0-67 



2-5 



148 



14-52 



-0-28 







3-0 



9-33 



9-18 



-0-15 



9-08 



-0-25 



4-0 



4-0 



40 



0-0 



4-0 







50 



1-8 



1-91 



+ 0-11 



1-96 



+ 0-16 



60 



0-9 



1-00 



+ 0-10 



• •■ 



. . • 



80 



0-28 



0-31 



+ 0-03 



0-36 



+ 008 



