94 Transactions of the 



a low eye-piece and the objective, so as to admit of a traverse of 



two or three inches by means of a graduated milled head 



The focal length of the combination may vary from 1| to f of an 

 inch." And on reference to the j&gure annexed to the paper, 

 the two combinations appear to be of about equal power, that 

 towards the objective being a double-convex crown,' corrected by 

 a double-concave flint, and that towards the eye-piece, a double 

 convex corrected by a plano-concave ; but the focal lengths of these 

 compound lenses, their curvatures, and the distance between them 

 are not given. The chief subject of examination by Dr. Pigott 

 appears to be the image of an object with well-defined outlines, 

 such as the bulb and lower end of the scale of a finely-divided 

 thermometer; such image being formed in the focus of a deep 

 objective, placed as a condenser axially with the objective to be 

 examined. 



The writer has hoped to have been able on the present occasion 

 to bring before the Fellows some definite and intelligible principle 

 of action of this contrivance, in order that some idea might be 

 formed as to the mode of its action on the definition of certain test- 

 objects ; this he has essayed to do by means of both geometry and 

 analysis, and he has moreover sought the assistance of an emment 

 mathematician of the most recent type ; but he regrets to say that 

 his endeavours have not been attended by any success. But he is 

 far from desiring it to be inferred from this that no such definite 

 principle is discoverable, as it may perhaps be the case that, since 

 more than forty years have elapsed since he was a Wrangler at 

 Cambridge, his mathematical weapons are too rusty to contend with 

 the numerous phalanx of conditions arrayed against them. But 

 it may be doubted whether Dr. Pigott is in possession of any 

 more definite information than that which he has already made 

 public; and even the name of the instrument, a " searcher," seems 

 to imply that its application is wholly empirical : even in his own 

 hands it has been observed that while the desired appearance is 

 sometimes speedily produced, at other times a considerable amount 

 of manipulation has seemed to be required for that purpose. 

 Under these circumstances it appears that the controversy that has 

 existed as to whether the beaded appearance of the well-known 

 markings of the Podura scale is the result of improved definition, as 

 it is afiirmed to be on the one side, of some spectral illusion, as it 

 is assumed to be on the other, must still be considered an open 

 question. 



The writer, reviewing this question under the dictates of common 

 sense, when observing the familiar Podura notes of admiration well 

 defined and free from colour, cannot resist the inference that in the 

 objective all aberrations are nicely balanced, and the object truly 

 represented in the visual image ; on the contrary, when the same 



