832 
MR. G. H. DARWIN ON THE SECULAR CHANGES IN 
In order therefore to illustrate the rates of increase of log tan ]jJ and log tan \\ from 
the preceding numerical results, we must either refer the second sets of £’s to the same 
iuitial value c 0 as the first set, or (which will be simpler) we may take y/c as the 
independent variable. 
Then for the values between £=1 and ‘76, the ordinates of our curves will be the 
numerical values given in Tables IY. and XI., each divided by y/c 0 . By the choice of 
a proper scale of length, c 0 may be taken as unity. 
For the values in the second integration from £=l to '88, the y/c 0 is the final value 
of y/c in the first integration. Hence in order to draw the ordinates in the second 
part of the curve to the same scale as those of the first, the numbers in Tables VII. 
and XIV. must be divided by ‘76. 
Also the second set of ordinates are not spaced out at the same intervals as 
the first set, for the d y/c of the second integration is ‘76 of the d^/c of the first 
integration. 
Hence the ordinates given in the four Tables, IV., VII., XI., and XIV., are to be 
drawn corresponding to the abscissae 
0, 1, 2, 3, 4, 5, 6, 676, 7*52, 8*28. 
In fig. 7 these abscissae are marked off on the horizontal axis. 
The first integration corresponds to the part 00', and the marked points correspond 
to the seven values of £ from 1 to '76 inclusive. The second integration corresponds 
to the part O'O", and the values computed in Tables VII. and XIV. were divided by 
‘76 to give the ordinates. 
The value for £='76 of the first integration is identical with that for of the 
second. 
The integrations, which have been carried out, correspond to the determination of 
the areas lying between these curves and the horizontal axis, areas below being 
esteemed negative. 
The two curves for /log tan H/dy/c lie very close together, and we thus see that the 
motion of the earth’s proper plane is almost independent of the degree of viscosity. 
On the other hand, the two curves for d log tan \3/d^c differ considerably. For 
large viscosity the positive area is much larger than the negative, whilst for small 
viscosity the positive area is a little smaller than the negative. 
If the figure were extended further to the right, the two curves for the variation of 
I would become identical, and the ordinates would become very small. The two 
curves for the variation of J would separate widely. That for large viscosity would 
go upwards in the positive direction, so that its ordinates would be infinite at the 
point corresponding to ; the curve for small viscosity would go downwards in the 
negative direction, and the ordinates would be infinite at the point where \=1. 
In this figure 00' is 6 centimeters, 00' is 8'28 centimeters, and the point 
