296 PROCEEDINGS OF THE AMERICAN ACADEMY. 



ta <■ + *>= (I).- 



This derivative is well known from the work of Holborn and Henning. 48 

 Also 



tan /3 = (dp/dt) v . 



This is the derivative given by Knoblauch, Linde, and Klebe, as just 

 explained. Along OB, v is constant ; along OD, which is perpendicular 

 to OB, v increases most rapidly. The following equations can then 

 be verified, " Grad. v " being the space rate of v'a increase along OD. 



n , 1 Va — v n 



(jrad. v = — 



(?''\ _ lim Vc 



sin a (J\ 

 ~ v o _ lim W ' Grad. v ■ sin B 



— A' = 



A* «*-" A* 



sin /? OC lim v A — v 

 sin a (Ja a ' = A£ 



sin 8 , ~ fdv\ 



= ~ --— COS (a + /8) ( jt- ) 

 sin a J \ot J x*. 



The last term of Planck's equation can then be written in the form 



^'/Vi " \dt)^\dt) p \ct J sat . sin a 



In this transformation use has been made of the familiar Clapyron 

 equation and of the definition of tan (a + B). The computations are 

 carried through by determining (a + B) and B from their tangents and 

 getting a by subtraction. The necessary values of the differential 

 coefficient (dv/dt)^ were formed from the values of v in the Steam 

 Tables of Marks and Davis by the usual finite difference formula 



dv = Av — \ A 2 v + 



The results of the computation are summarized in the first part of 

 Table VI., and are plotted as black dots in Figure 12. 



48 Wied. Ann., 1908, 26, 835. 



