70 Mr. J. F. W. Herschel on the action oj 
reckoning from these points approximate in a general way 
to the Newtonian scale. In fact, the periods of the more 
refrangible rays being performed more rapidly than those of 
the less, if we suppose the coincidence above spoken of to 
take place at any point (the minimum for instance), of the 
n th r ing, the intervals between the n lh and (» + i)' fc minimum 
will be greatest for the red and least for the violet, &c. 
Consequently, when the violet next disappears totally from 
the extraordinary pencil, there will remain yet a little of the 
red, less of the orange, and so on, and this difference in- 
creasing at every succeeding minimum on either side, will 
produce a succession of colours approximating in a general 
way to Newton’s scale. This approximation will however 
be much less close on the side of the virtual pole towards the 
nearest axis, because the disturbing influence of the separa- 
tion of the axes on the figure of the rings and the law of 
their successive intervals, is much more sensible than at a 
distance from the pole. This will be evident if we consider 
that in the interval between the extreme coloured axes, the 
tints will be regulated entirely by the law of their distribu- 
tion. Now this is perfectly corroborated by the succession of 
tints in the foregoing tables, as well as by numerous experi- 
ments made on other bodies. 
Our equation (6) gives room for a remark of some conse- 
quence, as it affords a striking verification of the theory here 
delivered. It will be observed that this equation does not 
involve t, and in consequence, the angle Q determined from 
it, at which the coincidence takes place, is the same for all 
values of t, or for all thicknesses of the plate. The obser- 
vations of the tints in the tables given above, afford us ample 
