176 Mr Hargreaves, Examples illustrating the use, etc. 
‘It should be stated that though formulae (13) and (14) lead 
to the usual results, there is no gain but rather loss in facility of 
reaching them. But the form used is striking, and the failure 
to apply it in any advantageous way may well be due to my own 
shortcomings. 
EXAMPLE III. Clebsch’s form in Hydrodynamics. 
The integral form used p. 116 op. cit. was 
= Jude + vdy + wdz+ Tdt, | 
in which 7’ was found to be —f—4 wu, the hydrodynamical 
equations being 
ee Anes ie, f=* + V or \2 +V. 
If we quote the pressure equation in the form 
ftddwt 08 oH 0. (15) 
(cf. Basset’s 1 See then obviously 
rp) OD ty Od Om 
P= aa ee as well as w= ap tM Op? Re (16). 
Thus ©, is identified in respect to all terms with pray + d¢. 
