Angle of Aperture of Object-glasses. Bg F. II. Wenhavn. 189 
properties of angles is in proportion to the sines, or more compre- 
hensively as the chord of the arc ; the difference of value between 
170° and 150 ' is only about three per cent., and the importance of 
the first is lessened by the distortion due to increased obliquity. 
With Colonel Woodward, I have no wish “ to provoke ill-tempered 
discussion on the merits of individual makers.” Microscopists have 
seen enough of this. If we are to come to what I believe to be 
rational, or more correct apertures, all alike must be reconciled to 
the reduction. I have known common sense in simple wonder- 
ment ask, What object can be properly seen at incidences claiming 
to near an aperture of 180 J ? — with every part foreshortened and 
distorted, even on the thinnest subjects, such as scales and diatoms 
— try and read a line of this page, at an incidence of five or ten 
degrees, and see what a confused muddle it appears to be. I think 
that microscopists should be glad if it could be proved that such an 
enormity does not exist. 
A tiresome paper war, on doubtful apertures, has so far ended 
in nothing, that the whole might as well be consigned to the waste- 
paper basket. The question now is, whether the ultra rays belong- 
ing to the oblique pencils are to be measured in addition to the 
central cone or true aperture, in order to garnish up the now 
diminished substance, and to serve as lateral props against a case of 
would-be unstable equilibrium, and for the support of apertures 
that have not been reached. 
Though Colonel Woodward and myself hold a difference of 
opinion, 1 do not at all wish to insinuate that he has any prejudice 
or bias in the question. The hberality of his contributions to the 
science of microscopy must place him far above any such suspicion. 
