Statistical mechanics 



21 



As further 



cos 



so 



dd- 



dA 



sin , 



T2 cos ^ 



sin sin sin ^ ' 



sin 'B 



Is - ^ (Y2^ + Tb^) 

 sin ^£ 



But 



Ï2''l + Ï3^ = — sin ß sin {)■ sin i}* + cos ß cos d 

 = cos jB 



as is found from fig. 3. The sphaerical triangle between the Z-axis, the asymptote 

 (= Z-axis) and the hne of symmetry (/, m, n), has indeed the elements shown ni 

 the accompanying figure 4. 



We thus have ^ 



dA _ Y3 — 'CcosB 

 ^ sin ^B " 



We had found before 



dB Y2 cos sin 4" — T3 sin d- 

 sin B ' 



or, multiplying nominator and denominator by sin è, 



dB sin Q- cos d- sin ^ — Yg (1 — cos 



90" + 7 



dd- 



sin B sin è 

 cos d (cos ßcos ■& — sin ß sin ^ sin — Y3 



sin B sin d- 



Y3 — C cos 



sin B sin d- 



Our values of the differentialcoefticients are now 



Y3 — C cos B 



Fig. 4. 



8^ 



d>!^ 



dA 



dd- 



d_A 

 d<!^ 



sin 5 sin à)- 



sin j5 



sin ^i? sin t)- ' 



Y3 — C cos B 

 sIîâTB 



