GOLF BALL TRAJECTORY, ETC. 117 



path of a pulled or sliced golf ball will be very approximately portions of 

 this spiral. The introduction of gravity acting constantly in one direction 

 greatly complicates the problem, which cannot be solved, even to a first 

 approximation, except on the supposition that the path nowhere deviates 

 greatly from the horizontal. To obtain forms of paths at all like those 

 observed, somewhat lengthy numerical calculations require to be made. The 

 method by which Tait builds up the curve is very instructive and is a good 

 example of his insight into the essence of a physical problem and of his 

 capacity in working out a sufficient solution. The practical details will be 

 found in the article on Long Driving reprinted below. 



In addition to the greater efforts of his mathematical powers, Tait 

 contributed to the Messenger of Mathematics, to the Proceedings of the 

 Royal Society of Edinburgh, and latterly to the Proceedings of the Edinburgh 

 Mathematical Society, a variety of small notes, many of which he incorporated 

 in the successive editions of his books. These notes were always interesting 

 in themselves and frequently presented old truths from new points of view. 

 In not a few of them his skill as a geometrician comes strongly into evidence. 

 Tait, in fact, was no juggler with symbols ; and when taking up a new subject 

 he invariably tried to make of it a geometrically tangible creation ; otherwise 

 he would have none of it. Maxwell expressed this view of Tail's mental 

 habitude in a letter in which, replying evidently to a demand of Tail's to 

 consider a problem in conduction of heat, he wrote : 



" O T' If a man will not read Lam6 how should he know whether a given thing 

 is v? Again, if a man throws in several triads of symbols and jumbles them 

 up, pretending all the while that he has never heard of geometry, will not the 

 broth be thick and slab ? If the problem is to be solved in this way by mere 

 heckling of equations through ither 1 I doubt if you are the man for it as I observe 

 that you always get on best when you let yourself and the public know what you 

 are about." 



Of those casual things which Tait threw off largely as mathematical 

 recreations, about a dozen were communicated to the Edinburgh Mathematical 

 Society. The subjects treated of are nearly as numerous as the papers, 

 including plane strains, summations of series, orthogonal systems of curves, 



1 " Through ither," an expressive Scottish phrase, meaning lack of method so that things get 

 tangled up one with the other higgledy-piggledy comes near it. It is often used with reference to 

 a thriftless housewife who has no method but drives through her work anyhow. "Heckling of 

 equations through ither" means assorting the equations in a random manner in the hope that they 

 will be disentangled and simplified. 



