298 Proceedings of the Pioyal Society 
known as Rankine s method. He was much loved and respected 
by his numerous fellow-pupils, several of whom have attained 
high professional status. His pupilage ended, Eankine returned 
to Edinburgh, and was occupied for some time in the preparation 
and publication of an “ Experimental Inquiry into the Advantages 
attending the Use of Cylindrical Wheels on Railways.” 
The theoretical investigation, and the deductions from the 
results of the experiments, conducted by his father and himself, 
are characterised by the same completeness in every respect as 
his more important and more famous writings of maturer years. 
But cylindrical wheels never came into use. It was “ too late ” 
to begin an obvious improvement, or there was no time to think 
of it ; and yet, taking everything into consideration, the wheels 
would he better cylindrical, so formed that they should retain that 
shape for the longest time. 
In 1842-43 various papers were sent to the Institution of Civil 
Engineers, and prizes were granted for them. There is one on 
“ The Fracture of Axles,” in which the importance of continuity of 
form and fibre was first shown, and the hypothesis of spontaneous 
crystallisation disproved. The conclusions of this paper were gene- 
rally accepted and acted upon in the construction of axles. 
In 1844-45, and afterwards till 1848, Rankine was employed 
under Messrs Locke and Errington on various railway projects 
promoted by the Caledonian Railway Company, of which his father 
had become secretary. But from 1842 onwards his mind had 
been much occupied in perfecting himself in the use of the higher 
analysis and in its application to the mechanics of molecular 
vortices. 
Rankine’s first investigation of the principles of the mechanical 
action of heat appeared in a paper received by the Royal Society 
of Edinburgh in December 1849, and published in their Trans- 
actions, vol. xx. It is based on what he calls u the hypothesis 
of molecular vortices ; ” that is to say, the supposition that the 
motions of which Davy showed thermotic heat to consist are of 
the nature of vortices — whirls or circulating streams. This is 
the part of the hypothesis that is specially connected with the 
phenomena of the mechanical action of heat ; but in order to 
connect these with some other phenomena, Rankine makes the 
