254 The Theory of Immersion. 



case for illustration, the aperture of 170^ in the first table. The 

 first column we may here reject entirely as useless in the high angles, 

 because we must use a cover unless we have thick glasses specially 

 constructed. Looking, then, at the other two columns, there does 

 not seem to be a great difference between the numbers 769 and 606 ; 

 nothing, at least, very starthng to lead us to expect much gain. 

 But then this way of comparison by totals may be wrong, or 

 rather is certainly wrong. For in applying to the resolving of 

 tests it may be the more oblique rays that do the resolving work, 

 or most of it. Now let us look, not for the whole gain, but for the 

 gain at the extremity, e.g. in the last ten degrees. We may, in 

 fact, suppose the inside of the glass stopped ofi", all except the 

 interval from 160^ to 170^. Theii to get the proportion we 

 subtract each number from the preceding one in the column, and 

 we find that for this ring the immersion has about four times the 

 light of the other. Therefore, to test experimentally where our 

 real strength hes, we must be able to divide our glasses by rings ; 

 that is, we must have stops not alone like those usually made, but 

 such that we can stop out the inside and preserve any ring of any 

 magnitude we wish. To carry out this comparison by " exclusions 

 and rejections " of course needs skill and patience, and appliances. 

 I have attempted it myself on a limited scale, but failed to go on 

 for want of these appliances, and of the necessary mechanical skill. 

 It is only those who are near opticians, and can have their ideas 

 carried out at any time by skilled labour, who can arrive at trust- 

 worthy results. It is perhaps worth observing that in such com- 

 parisons great care would have to be exercised in determining 

 apertures truly ; remembering such things, e. g. as the difference 

 we may be bringing in, without thinking, by adding on water and 

 a covering glass which changes the true front or first refracting 

 surface to another one altogether. And other such precautions ; 

 for in measuring apertures, notions are still very loose, and results 

 sometimes given which are wholly untrue. 



So much is plain, that the cause thus assigned is a vera causa 

 in Newton's sense of the phrase ; that is to say, the thing assigned 

 as the cause is a really existing thing. And on the face of the 

 calculation it is also clear that some difierence is truly accounted 

 for by its action. Whether the whole is accounted for by it is the 

 question to the answer of which this investigation supphes only the 

 first of two steps. If on dissecting the apertures for comparison it 

 should be found inadequate, then some other cause will have to be 

 sought for, not instead of this but in addition to it. 



