154 EEPORT— 1889. 



blisTiing the relation above stated is to show that the capacity for cargo 

 bears from year to year a constant ratio to the space actually occupied by 

 cargo. In other words, we require to be assured that an average ship 

 (entering or clearing with cargo) is as fully loaded in one year as another. 

 Sir Rawson Rawson, whose sagacity and candour have anticipated every 

 objection, is satisfied that we may dismiss this scruple. 

 We may therefore write the postulated equation : — - 



Bulk of a in ?/+bulk of h in y + &c. 

 Bulk of a in a; + bulk of b in X + &C. 



Quantity of a in 7/ x normal price of a 4- &c. 



Quantity of a in x X normal price of a + <fcc. 



where ' bulk of a in 1/ ' is short for the total space, the volume in cubic 



yards, occupied by the whole mass of commodity a which is exported, or 



as the case may be imported, in the course of the year y. The relation 



of these two fractions may be better seen by putting each of them in 



the form of what may be called a ' weighted mean ' of the ratios of bulk ; 



(or, as implied in the last note, we might take as the ratios to be operated 



Quantity (in tons or gallons) of a in 7/ „ ^ m rr , ,1 • • . i i ri. 

 on : :^ ■i-^ .J — . 1 -1^ &c.) . To effect this m the left- 

 Quantity ot CD in a; 



hand member of the equation, we should leave the denominator as it is, 



and we should alter each term of the numerator thus : For Bulk of a in y 



write Bulk of a in a;x— !^- ^', and so on. The left-hand side of 



Bulk ot a in x 



the equation is now in the form of a weigbted mean of the ratios, 



.f-—- — - — : — -, &c., the weights being bulk of a in x, bulk of h in x, &c. 

 Bulk ot a in a; o o 



Treating the right-hand member in the same spirit, we obtain a weighted 



mean of the same ratios, each weight being of the form, bulk of a in 



iBxNo. of tons [gallons, pieces, &c.] in unit of bulk x normal price often 



[gallon, piece, &c.], or, as it may be more shortly written, value of Bulk 



of a in a; at standard prices — that is, assuming that the number of tons, 



&G., in a unit of bulk is constant from year to year. But if tbis cannot be 



assumed we must add a remainder, of which the numerator is made up 



of terms like the followina: : — 



Bulk of a in 2/ (No. of tons in unit bulk of a in 7/— No. of tons in unit bulk 

 of a in a;) X normal price of a ; and the denominator is the total value in x. 



Omitting this remainder for the present we have now to compare two 

 weighted means of the same set of quantities (the ratios above specified), 

 the weights being in the one expression each of the form, bulk of a in a; ; 



method, in so far as it is on the same footing with Drobisch's ; each admitting of 

 being regarded as an arbitrarily weighted mean of certain ratios, such as 



tons of commodity a in 1886 

 tons of same commodity in 1885 



(the" ratios of quantity described at p, 140 above). Whereas the theoretically correct 

 expression is the value of commodity a at normal (or corrected) prices ; Drobisch 

 puts tons avoirdupois of a, and Sir Kawson Eawson puts (in effect) tonnage (or 

 cubical volume) of a. 



From this point of ^^ew it will appear that both methods derive confirmation 

 from the experiment tried above, at p. 140, of taking an altogether unweighted mean 

 of the ratios between quantities. 



