PROCEEDINGS 
OF THE 
MATHEMATICAL SECTION. 
1888 to 1891. 
36th Meeting. January 25, 1888. 
The Chairman presided. 
Present, thirteen members. 
The minutes of the 35th meeting were read and approved. 
An election of officers of the Section was held, resulting in the 
choice of Mr. H. M. Doolittle for Chairman and Mr. R. S. 
Woodward for Secretary. Thereupon Mr. Doolittle was called 
to the chair and presided during the subsequent proceedings of 
the evening. 
Mr. A. S. Christie presented a communication on What is a 
Quaternion ? 
[Abstract.] 
A quaternion, according to the point of view from which it is regarded, 
is either, 1st, The product of a tensor and a versor; or, 2d, The sum of a 
scalar and a vector; or, 3d, A power or a root of a vector; or, 4th, Any 
combination by sum, difference, product, quotient, power, or root of tensors, 
versors, scalars, vectors, or quaternions—where the underscored words 
must be taken in the peculiar but not perverted sense assigned them by 
Hamilton. 
Tensors, versors, scalars, vectors, and quaternions are reals, easily com¬ 
prehensible and combined by methods always rationally explicable. It 
is a mistake to suppose that either the ideas or the methods of the qua¬ 
ternion calculus are based upon or are affected by any “ curious quasi¬ 
metaphysical speculation.” Tait’s employment of that phrase (North 
British Review, September, 1866, page —; Quaternions, 2d edition, § 64) 
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