20 



by the lake. The international exposition of 1893 will epitomize in ma- 

 terial form the progress of the world for the centuries, and to no Mecca 

 can the devotee of science turn with more reverent steps. 



The interdependence of the liberal pursuits there will have practical 

 illustrations of the most instructive character. The best thought of the 

 centuries will be realized on canvass, in marble, in bronze, in exquisite 

 fabrics, in jewels and ornaments of silver and gold, in the whirr of ma- 

 chinery and the flashes of electricity. 



There may we study things, and there may we in profitable intercourse 

 meet men. This will be the academy of science of the world. 



PAPERS READ. 



< K Till: CONSTRUCTION OF A SENSITIVE GALVANOMETER. I'>V BeN.I. W. S> 



Tests oi the torsional strength of \ steel shaft. By Thos. Gray. 



Analytk \l, and quaternon treatments op the problem of sun \\i> planet. 

 By A. S. Hathaway . 



introduction. 

 The object of the paper is to show the greater simplicity of quaternions 

 over analytics. For the purpose of comparison, the most condensed 

 analytical treatment possible is adopted. This turns out to be precisely 

 analagous to the quaternion treatment. Three equations, such as m a=a', 

 m b=b / , m c=c' are written m (a, b, c)=(a', b', c'i. By multiplying 

 these equations by (x, y, z) is understood the result of multiplying 

 the first by x, the second by y. the third by z, and adding, giving 

 m (a x+b y+c z)=(a / x-fb' y— c' z). This corresponds to scalar multi- 

 plication in quaternions. By forming corresponding determinants with 



