1880.] 



J. F. Tennant — Oji Standard Weiglits. 



59 



Also ». <?. P. , . =— >/20G-l-6 + 169'5 + 13'6 = -i- .'s/22l7'7 = 000047 

 10° 10" 



^. ^. p.^ ^ - 1^ v^l032-3 + 81-2TTjr3 = i _ \/ll29-8 = 0'000034 



P. , = - V'2061'6 + 84-2 + 70-0 = — \/2218-8 = 000047 

 r 2 10° 



Section IX. — Determinations of the Wei(/Jits to O^g and also Prinsep's 



Bronze Troy Pound. 



The comparisons of the weights from to O^o have been made with 

 the balance Oertliug No. 2. Three complete comparisons were made in 

 each case, and the weight P.^g has been always used for valuing the scale. 

 I have deduced the following equations of condition : — 



grs. 



O3 =03+0, -0-37200 P.03 s O^+Oi OOO0000-037200P.O3 



O., =03 + Oi+P.oo+0-74.542P.„3 = O3+O1 +0-060769 + 0-74542 P. „ 3 

 0, sOg+O.+P.i +0-37867 P.03 s 03 +0^ +0-100085 + 0-37867 P.03 

 = 0., +O1 + P.O. +0-60467 P.„3 = O., +0, +0-019881 + 0-60467 P-^g 

 0,„sO, + 0,+0, -P., - P.O. + 0-45742 P.„3 ^ 0, + 0, +0,— 

 0-160854 + 0-45742 P.^, 

 Whence I deduce by the Formulie in Sec. VI. 

 O, s 20,+ P.oG + P.i +0-97142 P.o 3 = 960-011294 grs. 



j?. c. = 0-000757 „ 



O3 =30,+ P.oo + P.02— P.1+ 0-59942 „ = 1440-000584 „ 



e.= 000900 „ 



0., =40,+2P.o„+ P.02— P.1+ 1-34484 „ = 1920084613 „ 



p. e. =0-001194 „ 



O, = 50,+2P.o, + 2P.0,— P., + 1-94951 „ = 2400123435 „ 



p. e. =0-001438 „ . 

 0,0=100, +3P.0, + 3P.o,—3P., + 3-75167 „ =4800-061736 „ 



i?. e. =0-002795 „ 

 In the last Section, I have given a general formula for finding a 



p. 



probable error of observation. In this case, I have S (o) = 3941-2 , 



whonec the probable error of one equation of condition will be 



on 1,1.0 p 



= 0-8454 --^^^--fl = 0-000413-5 

 V3-2 10^' 



The probable error of each determination of a weight de^^ends — 



1st, on its error derived from 0, of which it is nearly a multiple, 

 2nd, on the error derived through the weights of the P set used to 

 nearly counterbalance, 



