62 



Whence 





The exceptional cases are where 2i = 0. That is, ^ can be so chosen as to con- 

 vert any vector into any other except those lying in the plane of (a, /3), which is 

 converted into itself, the line x^a being converted into itself. The cubic of <j> is 

 (^ — ocY = 0. We may write <t> p=^x p -\- ( yy^ + zz^) a ~\- yz^ /3. 



Hence the effect of any o is to move the terminal point of p along its line 

 in either direction, and then slide this extremity along a plane parallel to ( a, 3 ). 

 Thus the infinite number of strains, which belong to this infinite group of strains, 

 and that have the same r, represent a group of shears. Space nor time permit a 

 fuller treatment of this interesting line of application of this algebra. The ap- 

 plication of the other algebras might similarly be deduced. 



I may say in closing that the natural classification of these algebras referred 

 to by Professor Benjamin Peirce, who regarded his own classification as Linnean, 

 is pointed to by these representations of the dlgebras. 



Illinois College, Dec. 23, 1895. 



Variation of a Staxpard Thermometer. By Chas. T. Knipp. 



During the term just past I made a number of observations on a standard 

 thermometer. The problem that presented itself was to observe the variations'in 

 a standard thermometer under given conditions, and the minimum limit of con- 

 ditions that would produce the same. 



Having a delicate cathetometer at hand, that reads directly to j^ and 

 accurately to yj^ of a mm., no hesitancy was felt in making the observations, 

 feeling assured that the slightest variations in the reading of the thermometer 

 could be detected. 



The thermometer that was in cj[uestion was one of Queen & Co's standardized 

 thermometers of the centigrade scale, graduated in tenths over a range of 100 

 degrees. The bulb, is cylindrical in form, thus having a maximum, or tending 

 towards a maximum surface and consequently increased sensitiveness. 



The thermometer was tested and standardized by the above named company 

 on the 10th of October. After standardizing it was put in a brass case lined with 



