92 PRINCIPAL FORBES ON AN EXPERIMENTAL INQUIRY INTO 



trate this, a portion of each curve near its origin has been drawn separately on 

 an exaggerated scale in a subsidiary figure, where its deviation from a straight 

 line is abundantly manifest. In each case it may be adequately represented for 

 the first 4° or 5° by an arc of a common parabola — more accurately perhaps 

 by a semicubical parabola. However, taking the former as the simplest, I 

 find the following equations to represent the part of the three curves nearest 

 their origin : — 



*o' 



Case I. ~ = -00830 v + 000615 v 2 

 at 



Case II d ^ = 01626 v + 00065*/ 2 

 at 



Case III. ^ = -01046 v + -00091 v°- 

 dt 



85. Secondly, The concavity upwards of these curves of the " rate of cooling" — 

 showing that the cooling increases faster than the temperature rises— gradually 

 diminishes; and in all the three curves we find between 110° and 120° (centigrade), 

 a space nearly straight, indicating a point of contrary flexure. Above 1 50' the 

 curve is in all the three cases slightly convex upwards, showing a rate of cooling 

 slower in proportion than the rise of temperature. 



86. Thirdly, This last circumstance appeared to me to be deserving of an 

 elaborate verification. , I therefore applied the same formula of interpolation 

 which I had used with success to represent considerable arcs of the statical curve 

 of temperature (see Art. 67, Eq. (1.) ), being what has been called Roche's formula, 

 to represent the temperatures of the cooling bar in the higher parts of the pri- 

 mary curve of cooling. 



87. In this I was successful, and I deem the matter of sufficient importance 

 to show the coincidence between the original thermometric observations and the 

 formulae employed in each of the three cases. The times (t) are in each case 

 reckoned from an arbitrary origin ; and v is the excess of temperature above that 

 of the air actually observed. [See Table VI.] 



88. Fourthly, It will be seen that, within the limits of these tables, the obser- 

 vations are, upon the whole, well represented by the equations. Moreover, they 

 confirm a result at which I had previously arrived from the projections, as to the 

 law of cooling at higher temperatures, namely, that above 140° or 150° there 

 is a gradual falling off in the rate of cooling, compared to the measure of tem- 

 perature. For it is to be observed, that the equations employed to represent 

 the primary curve of cooling coincide with the simple geometrical or logarithmic 

 law, when the co-efficient of t in the. denominator of the fraction (c of Art. 67) 

 vanishes. When this co-efficient is positive, the progression is faster than geome- 

 trical ; when negative, it is slower. Now, in each of the three cases c is negative, 



