WELCOMES MATHEMATICAL ASSISTANCE. 1 37 



Had the clouds not lifted — had Joule still found his 

 work unrecognised — he might have felt himself, however 

 ill-qualified for the task, compelled to continue, the develop- 

 ment he had already commenced of the several mathematical 

 sciences which directly followed his discovery of the 

 definite relations between the physical and mechanical 

 sources of heat. But the assurance that such mathematical 

 powers as were evinced by Sir William Thomson, Rankine, 

 and Clausius, were inevitably directed to the subject, besides 

 the fact that the work itself was already in great part accom- 

 plished by the two latter, before Joule had become aware 

 of their assistance, not only relieved him from all necessity 

 to continue it, but in a great measure took it out of his hands, 

 and carried it into a region where the language was such 

 that Joule, with his scant mathematical education, was ill- 

 qualified to follow, much less to lead the advance. I 



That Joule resented this does not appear in the slightest, 

 rather that he welcomed it with enthusiasm. He evinced 

 an admiration which almost amounted to reverence for the 

 mathematical powers displayed, himself looking on until 

 demand was made for further experimental work on in- 

 cidental points, when he again lent his unequalled powers 

 to the mathematicians. 



For the next two years, while Thomson, Rankine, and 

 Clausius were performing mathematical feats, which not 

 only secured them the front place amongst the mathema- 

 ticians of their time, but raised the Universities of Glasgow 

 and Zurich above all others as seats of the most advanced 

 mathematical and physical philosophy, Joule had little 

 to do but enjoy the rest he had earned, r and the 

 gratification which he must have felt in the chivalrous 

 and enthusiastic honour which these men paid to his work. 



