1880.] 



J. F. Tennant — On Standard Weir/Jifs. 



55 



I shall for convenience write M for 47'999997 grains and place tlie equations so far as 



are necessary to determine the weights down to Pj in 



a form suitable for use thus — 











Diff. 







— M + 0020194 



= 0-275 R, 



p * 

 -'-2 4, 







— 0064138 „ 



= 0-475 „ 



P P P 



-■-10 -^2 





— 012913 „ 



= 0-1125 „ 



P * p P 



-^■24 -^20 -^-3 







+ 0-000125 „ 



= 0.650 „ 



P P P 







+ 010138 „ 



= 0-900 „ 



P P P P 



-Px 





— 008500 „ 



s 25 „ 



P p P 







— 0.018400 „ 



= 1700 „ 



P P — P 



-Px 





— 004813 „ 



= 0-775 „ 



P P P P 



^ a 3 2 1 





+ 0-018908 „ 



= 0-375 „ 



p — p — P 





+ 015463 „ 



= 0-1075 „ 



I 



'2-Px 



-P\ 



+ 009388 „ 



= 01175 „ 





Px 



-P'x 



— 0-005838 „ 



= 1275 „ 



I have tried various ways o£ dealing with these equations but, when 

 the probable errors are wanted, the method of least squares is the easiest. 



I thus get — 



















grs. 









grs. 





P2. 





23-999999 — 



0-006997 Ri 





23-999296 p. 



e. = 0-000042 



P * 





23-999999 — 



0-003185 



)! 





23-998679 



„ 0-000042 



P 



2 





19-999999 — 



0-014515 



)J 





19-998541 



„ 0000050 



PXG 





15-999999 — 



0006007 



?J 





15-999396 



„ 0-000049 



Pxo 





9 999999 — 



0-009026 



)) 





9-999092 



„ 0-000043 



Pa 





6-000000 — 



0-015531 



)J 





5998440 



„ 0-0U0013 



Pa 





3-000000 — 



0-006360 



)) 





2-999361 



„ 0-C00035 



P2 





2-000000 + 



0-001371 



)) 





2-000137 



„ 0-000050 



Px 





1-000000 + 0-008077 



)) 





1-000811 



„ 0-000039 



P'x 





1-000000 + 0-002461 



)> 





1-000247 



„ 0-000043 



Further 



P, 



^ P.„ + P.3 + P., 



+ 0-000038 R, 



Diff. 725 R 





P. 



, S P.3 + P., + P., 



+ 0-005525 „ 



„ 





P- 



S = P-2 + P-1 



— 004675 „ 



500 „ 





P. 



= P + P' 



+ 006963 „ 



„ 1325 „ 





P. 



= P' 

 1 — • 1 



+ 0-005813 „ 



„ 525 „ 



ence P.,. 





grs. 



0-600000 + 002673 Rj = 0-600269 p.c. = 0-000056 



P-3 





0-300000 + 0-005647 



„ = 300567 



„ 0-000035 



P-2 





0-200000 + 0002832 



„ = 0-200285 



„ 0-000042 



P-x 





0-100000 + 0-000842 



„ = 0-100085 



„ 000028 



P'x 





0- 100000 — 0-004971 



„ = 0-099501 



„ 0-000045 



