ON LINES OF INDUCTION IN A MAGNETIC FIELD. 
311 
In order to find C', we notice that v = 0 when x — ^ t , the velocity at the boundary 
vanishing. This gives 
The volume flowing through per second per unit width ot the layer of thickness 
t is 
r + it r\t 
q = vdx = 2 vdx 
' - it J 0 
f* 
l'2r) 
The rate of flow of a viscous liquid in a thin layer between parallel plane walls is 
thus, for a given fall of pressure along the layer, seen to be proportional to the cube 
of the thickness of the layer. 
An examination of the curves obtained experimentally shows a satisfactory 
agreement with this theoretical law. 
The data contained in the curves also enable us to calculate approximately the 
coefficient of viscosity. The apparatus is not, however, well adapted for exact 
measurements, since, in addition to the great difficulty in measuring accurately the 
thickness of the liquid film, it is doubtful if the glass plates are either sufficiently 
true or sufficiently rigid (notwithstanding their great thickness) for refined measure¬ 
ments. Since the formula 
v — 
fd 
12 2 
for the coefficient of viscosity involves the cube of the thickness of the liquid layer, 
a comparatively small error in the determination of t will give rise to a large error 
in Taking the water curve (fig. 2), we find for the coefficient of viscosity in C.Ct.S. 
units (using the point on the curve corresponding to a thickness of ’012") the value 
•0092, a value which is considerably too low, and which may be accounted for either 
by an error in estimating the thickness, or by slight irregularities in the containing 
walls, or slight bulging of the walls in the centre—all of which causes combined might 
easily account for the error. # 
The glycerine curve (fig. 3) gives a value of the viscosity equal to 2*5 ; the density 
of the glycerine being l - 23. This value is in fair agreement with the results of 
previous experimenters, f 
As, however, our object was not to carry out careful absolute measurements, but 
to find relative values which would enable us to apply the method to two-dimensional 
problems in magnetic induction, and, as the curves obtained (figs. 2 and 3) were 
* It must also be remembered that the water used in these experiments was ordinary tap water, which 
had not been freed from dissolved gases.—July 18, 19 DO, 
t See p. 131 of ArcHBUTT and Mountford’s ‘ Lubrication and Lubricants.’ 
