Robert Baldwin Hayward. 271 



similar Quantities, with respect to Axes movable in any manner in 

 space." This was probably the first development, by direct vector 

 methods, of the general equations of motion of a body, or system of 

 bodies, referred to moving axes of co-ordinates, and marked a very 

 important step in the progress of the science of theoretical mechanics. 

 In this paper the subject was illustrated by an account of the theory 

 of Foucault's Gyroscope, involving a brief analysis of the problem of 

 the motion of Gyroscopic systems. 



This was followed, in 1860, by a paper in the third volume of the 

 " Quarterly Journal of Mathematics," giving a direct demonstration of 

 Jacobi's canonical formulae for the variation of the elements of a 

 disturbed planetary orbit. In the tenth volume, 1870, of the same 

 journal, Hayward produced an article on the interpretation and 

 proof of Lagrange's equations of motion, referred to generalised 

 co-ordinates, among other points giving a direct explanation of why it 

 is that the time can enter explicitly into the equations of constraint of 

 the system. 



In 1890 he published a short text- book, on original lines, on 

 Elementary Solid Geometry; and, in 1892, he produced a more 

 elaborate treatise on the Algebra of Coplanar Vectors and Trigono- 

 metry. In the " Mathematical Gazette " of February, 1897, there is 

 an article by Hayward on " Some Semi-regular Solids." 



Hayward was a real mathematician, and, throughout his life, had 

 great delight in mathematical study and in mathematical research. 

 He was a very careful reader, and he read extensively. His tone was 

 thoughtful and highly philosophical, and all that he produced was 

 worked out with the greatest possible care and precision. 



He took a great interest in the work of the Association for the 

 Improvement of Geometrical Teaching, the 'first annual report of 

 which was published in 1871. The late Prof. Hirst was the first 

 President of the Association, and Hayward was President from 1878 

 to 1889. In 1897 the Association changed its name, and became the 

 Mathematical Association, and Hayward was the first Vice-President 

 of the new Association. He had the reputation of being an exceedingly 

 courteous president, very much liked by the members, and he opened 

 up discussion on the papers read at the yearly meetings in a very 

 enlightened and interesting manner. 



He was a regular attendant at the meetings of the British 

 Association, and in 1884, accompanied by his eldest son and one of 

 his daughters, he -visited Canada, and attended the meeting held at 

 Montreal, under the presidency of Lord Rayleigh, in the autumn of 

 that year. 



He was an expert mountain climber, and was one of the original 

 members of the Alpine Club. 



