HEAT FROM SMALL CYLINDERS IN A STREAM OF FLUID. 
.399 
in each compartment of the table. The theory of Part I. suggests that these results 
be examined in the light of the formula 
W = Bv/V + C,.(67) 
where B and C are functions of the temperature and of the dimensions of the wire. 
If W is plotted against ^/Y for each temperature, we should, according to (67), obtain 
a family of straight lines, and figs. 4 and 5 show this conclusion to be justified within 
the limits of experimental error. By determining the line of closest fit through the 
observed points, we are enabled to calculate the constants B and C. The position of 
this line can be found by calculating for each system of observed points the position 
of the major axis of inertia of the corresponding system of material points of equal 
weight.( 37 ) It was, however, found to be extremely tedious to make use of this 
method and it was deemed sufficiently accurate to adopt the simpler method of 
dividing the observations into two groups, finding the centre of gravity of each and 
taking the position of the line joining these two points as an approximation to the 
line of closest fit. The constants B and C were found in this way directly from the 
tabulated values of W and x/V. The accuracy of the observations was tested by 
plotting for each wire the family of approximately straight lines corresponding to the 
various temperatures, and in this way a check was obtained on the determination of 
the constants B and C. 
The constants B and C obtained in this manner are set out with the temperature 
and diameter of the wire in Tables V. and VI., and will now be discussed separately. 
(i.) Analysis of the Convection Constant B. 
The theoretical investigations of Sections 4, 5, and 6 suggest that the constant B 
be examined in the light of the formula B = f3(0 — 9 0 ). The third entry in each 
compartment of Table Y. gives the value of 8 = B/($—ffi) for Q 0 = 17° C., from which 
it is seen in fact that (3 is very nearly independent of the temperature; the slight 
increase in its value with increasing temperature may be represented by a small 
temperature coefficient b such that j3 = (3 0 [l+b ($ —0 (J )] and which may be interpreted 
as due to the combined variation with temperature of the diameter of the wire, and 
the specific heat, density, and heat conductivity of air. The variation of /3 with 
temperature is very little greater than that due to the errors of experiment, and the 
coefficient b was roughly determined by plotting (3 against the temperature, drawing 
in the line of closest fit and hence determining /3 U and b, giving a mean value 
b = (T000080. 
Theory further requires that (3 0 be given by the expression (3 0 = 2 \/irS^K^a^a^ where 
the suffix 0 refers to the temperature 17° C. That the ratio / 3 0 /va 0 is constant is 
( 37 ) Formulae for the determination of this straight line are given by Karl Pearson (‘ Phil. Mag.,’ 2, 
November, 1901, p. 559), and also by Snow, E. C. (‘Phil. Mag.,’ 21, March, 1911, p. 367). 
