406 Mr. T. Proctor Hall on New Methods of 



the weight of liquid displaced by the cylinder, the increase in 



Fis-. 7. 



weight over the weight of the frame in air is, for this central 

 part, 



(l—2r—jrr/2)p< f|- + 2rz/Jsin u + r 2 (u — it) — r 2 sin a cos a 



To this is to be added the surface-tension around the vertical 

 ends, and also the weight of liquid supported under them 

 above the level of the surface ; making as a very close ap- 

 proximation the whole increase of weight to be W, where 



W/p= {l-2r-TTr/2){{c*/2 + 2ry) sm* + r\a-7r) 



— r 2 sin a cos «} + 7rrc 2 + 27rr 2 (A — k). . . (9) 



In the following table are given the observed weights 

 with a somewhat irregular glass frame, along with the calcu- 

 lated values of the four terms on the right of equation (4) 

 for the same height h, in grams per centim. The liquid was 

 water, whose density is assumed as unity. 



r = *0375 (mean); l = 9'76; T = *07395 gram per centim. 



A(mm.). 



w, obs. 



a. 



2T sin «. 



2 ry sin a. 



r 2 a. 



— r 2 sin a cos a. 



w, calc. 



1 



•0109 



13° 47' 



•0352 



•0012 



0003 



-•0003 



•0364 



2 



•1042 



41° 4' 



•0972 



•0149 



•0010 



-•0007 



•1124 



3£ 



•1547 



69° 16' 



•1383 



•0217 



•0017 



-•0005 



•1612 



4 



•1724 



84° 29' 



•1472 



•0273 



•0021 



-•0001 



•1765 



4* 



•1755 



92° 49' 



•1477 



•0298 



•0023 



+ •0001 



•1799 



4£ 



•1763 



97° 9' 



•1468 



•0304 



•0024 



4- -0002 



•1798 



t 



* 



99° 42' 



•1458 



•0307 



•0025 



4- -0003 



•1793 



4f 



•1755 















4f 



•1739 















5 



•1722 















&h 



•1579 















5f 

 6 



•1547 



•1520 

 •1520 





•1458 



2r sin a(y—c/ \l'2) 



•0025 



+•0003 



•1509 



•0023 X 



* During the next five weighings the balance was in unstable equilibrium. 



t The numbers in this row are calculated from the value of y found from 

 equation (8), and are for the point at which the two liquid surfaces meet below 

 the bar. 



I See the paragraph following equation (8). 



