1880.] 



J. F. Tennant — On Standard Weiglits. 



53 



P„ = 6 Pi — + "Ix,, + «3 + x.^ ± e v/lO 



'= 10 P, — 3i<;, + 3a;, + 1x^ + x^ + ± e \/ 24.. 

 While descending, we have 

 Po = T^o Pio — iV (2^0 - 2*'. + - + 6^ J ± e ^/fT 

 P3 = x% Pio — TO - ^4 — 4^3 + + ± c V^-^ij^ 



P. = T% Pxo - 1^0 (-1^5 - + + 2*'3 + 2*- J ± e 

 Pi = tV Pio + TO (3^-5 — 3«^,, — 2x3 - - a; J ± e y/f^ 

 Pi'= T^ Pio — 1^ (7^5 + 3^, + 2^3 + + ± e v% 



Section VII. 



I now proceed to the determination of the actual values of the weights 

 below Oi, and of the P set, in commercial grains. The equations have all 

 been determined in terms of the I'ider R,, in the balance Oertling No. 1, and 

 they are given in this way. Of coiirse the whole of the computations were 

 made with this unknown factor, but it has been determined (see page 56) 

 and the value has been substituted in the results to save repetition. 

 The differences between the two determinations of the constant term in 

 each equation are given, and from them is derived a probable error of one 

 equation. I had intended that the observations in each decad should be 

 separately valued, but when that is done the results are so nearly alike 

 that it seems unnecessary to adhere to this. The mode of determining the 

 probable error of each weight is the subject of the next section, but the 

 values are given in this. 



Value of Weiglits of W set hcloio W-^ witli Balance Oertling No. 1. 



I have here the following equations : 



Oi 





+ 0., 



+ 0., 



— 0-213325 R, 



Difference 





2600 



0. 



= 0.5 



+ 0.3 



+ 0,, 



— 0-238825 „ 



)) 





1450 



0.. 



= 0., 



+ 0., 





— 0-001800 „ 







350 



0.0 



= 0.3 



+ 0., 





— 0-124325 „ 



» 





500 



0... 



= 0.3 



+ 0., 





— 002913 „ 







825 



0.3 





+ 0., 





-0-011113 „ 



» 





275 



0., 



^0.0, 



+ 0.0. 



+ 0.0, 



— 0-033200 Rj 



Difference 





200 



0., 



^o.„. 



+ 0.03 



+ 0.0, 



— 042213 „ 



>i 





2925 



0.0, 





+ 0.01 





-0-020938 „ 



)> 





475 



0.0. 



^0.,3 



+ 0-03 





-0-032138 „ 



J) 





1475 



0.0,. 



^0.03 



+ 0.0, 





— 0-030838 „ 



)) 





775 



0-03 



^o.„. 



+ 0.01 





— 0-035763 „ 



7> 





475 



