130 NEW BOOKS, WITH SHORT NOTICES. 



lancing compensations, yet their practical adjustments were innunier- 

 able and tediously accomplished.* At this stage of the research, 

 frequent consideration of the well-known optical equations for a 

 vanishing aberration fortunately suggested to me the idea of searching 

 the axis I mechanically for aplanatic foci. In reference to these equa- 

 tions, which would be out of place here, it has been observed by Mr. 

 Parkinson, F.E.S.,:}: ' If the aberration for rays parallel at incidence 

 of a compound lens of given focal length, consisting of several thin 

 lenses in contact, be examined, it will consist of a series of terms 

 similar to that in Art. 129, one term for each lens, and the condition 

 that the aberration shall vanish will lead to an equation involving 

 more than one unknown quantity, and consequently admitting an un- 

 limited number of solutions.' " 



Mr. Lister, whose paper in the ' Phil. Trans.,' 1830, accomplished so 

 much for the development of the modern microscope, though no mathe- 

 matician, ascertained the positions of two aplanatic foci, the longer and 

 shorter ; but it would appear from this research that a great number 

 of aplanatic foci exist at different points of the axis. And that whilst 

 many objectives refuse to define well at the standard distance a varia- 

 tion of the distance, as attained by the new instrument, the aj^lauatic 

 searcher, may be rewarded with success ; especially when it is con- 

 sidered that the searcher automatically changes its own aberrations by 

 a simple traverse. One of the advantages attending its use is thus 

 described : — 



"When it is desii'able to view an object through a very thick 

 refracting medium, the searcher is brought as close as possible to the 

 objective, which action lengthens the focus of the objective ; and the 

 same thing is necessary when the observer wishes to throw the eidola 

 of an upper structure above and away from the true image of the lower 

 but contiguous stratum — as when the lower beads of the Podura arc 

 requii'cd, or when it is required to give additional negative aberration 

 to an objective too positively corrected in which the front glasses arc 

 already in dangerous proximity." 



" On the contrary, when the searcher is traversed the opposite 

 way the objective lenses require to be brought nearer together; the 

 instrument is then more adapted for viewing objects or particles lying 



* " During 18G5-1869 many experiments were tried with complete objectives 

 and various parts of them, either over or under corrected, by means of a sliding 

 tube carrying them and fitting into the ' draw-tube.' 



" Professor Listing, of Bonn, more recently has in two papers confirmed the 

 value of this method of amplification quite independently. Nachr. d. hgl. Gesell. 

 der Wissen, 1869, No. 1, and Poggend Annalen, 1869, t. 16, p. 467 ('Nature,' 

 Jan. 27, 1870). 



" In the first he recommended an inverted Huyghenian eye-piece, and in the 

 second intermediate achromatic lenses. 



" As regards intermediate lenses, the writer has ascertained (Nov. 1870) that 

 Dr. Goring (' Micrographia,' ed. 1837) has anticipated both these methods. — 

 Note added Nov. 1870." ' 



t This term " searching the axis " was early employed by Dr. Pigott, viz. in 

 his first essay, received May 21, 1869. He says, "A search for the real focus or 

 best image should not be neglected along the axis of the instrument " (p. 297, Dec. 

 No. 1869). 



t " Griffin's ' Optics,' by Parkinson, p. 122." 



