88 



A Simple Proof That the Medians of a Triangle Concur 



John C. Gregg. 

 Theorem.— The three medians of a triangle are concurrent. 



DfiiMONSTKATION. 



Let AD and BE be two of the medians; 

 they will meet in some point G. Join CG 

 and extend it to meet AB in F. Extend AD 

 to H, making DH = DG, and join HB and HC. 



Since BC and GH bisect each other, BGCH 

 is a parallelogram. In the triangle ACH, 

 since GE is drawn through E, the middle 

 point of AC and parallel to HC, G is the 



3/^ I X\ ^ middle of AH. And in the triangle ABH, 



\ ^^» ^ since G is the middle of AH and GF is paral- 



lel to BH, F is the middle of AB and CGF is 

 the third median, and the theorem is estab- 

 lished. 



On the Density and Surface Tension of Liquid Air. 

 C. T. Knipp. 



[Ab.<tract. PubHshed in the Physical Review, February, 1902.] 

 The variation of the density of liquid air with time was determined. 

 The li(jnid was contained in a given Dewar bull). The sinker method 

 was used, and it was assumed that the coefficient of expansion holds at 

 the temperature of liquid air. A curve was platted which indicates that 

 .933 is the density of l](iuid air when first made. 



In the determination of the surface tension two methods were em- 

 ployed—the capillary tube method and the maximum weight method. 

 Owing to the distortion due to the bulb, also to the agitation of the liquid 

 surface, the first was not considered reliable. The second method, how- 

 ever, worked very Avell. The variation of the surface tension with time of 

 the liquid contained in the above bulb was determined. A curve was 

 platted. From the curve the surface tension of li(iuid air when first made 

 was found to be 9.4 dvnes. 



