January 3, 1901] 



NATURE 



229 



system must be free from chromatic aberration. Now 

 let us, for simplicity, deal with two lenses in contact ; let 

 y, /' be their focal lengths, /x, /*' their refractive indices, 

 and let i/V ijv represent their dispersive powers, so that 

 v = (/ii - i)/(/i„-/Xr), M" and /x, being the indices for the rays 

 it is desired to rachromatise, while /x refers to some 

 mean ray. 

 Then the condition for achromatism is 



Now it is shown in the book that for this case the 

 condition that the field may be flat — Seidel's fourth con- 

 dition — reduces to 



I 





o. 



Thus the focal lengths must be of opposite sign, and 

 the lens with least focal length — the concave lens that 

 is in a photographic combination— must have the greatest 

 refractive index. But, in order to satisfy the condition 

 for achromatism, this same lens must have the greatest 

 value for v. 



Now achromatic lenses have usually been made by 

 combining a convex lens of crown glass with a concave 

 lens of flint ; with such glasses, however, it is found that 

 when \i. is large v is small, and vice versd. Thus, for 

 example, ordinary light flint has a greater refractive 

 index than silicate crown glass, and hence an achromatic 

 combination is possible ; but since the value of v for 

 such flint is less than for crown, the combination when 

 made will not give a flat field. 



Dr. Lummer defines as an " old achromat " a pair of 

 achromatised lenses made of such glass. 



One of the results, however, of the experiments of 

 Abbe and Schott at Jena has been the discovery that by 

 the addition of barium salts a crown glass can be ob- 

 tained having both a high refractive index and a high 

 value for v. Such a glass could take the place of the 

 flint glass in an achromatic combination, and with this 

 advantage, that the condition for flattening the field 

 could be nearly, if not completely, satisfied. 



The condition above given for a flat field was dis- 

 covered by Petzval in 1843 ; in principle it had already 

 been published by Airey (" Coddington's Optics," 1829). 

 Von Seidel, however, was the first to point out that it was 

 impossible with the lenses then available to satisfy both 

 it and the condition for achromatism, and it was not 

 until the Jena glass became available that an achromatic 

 lens with a flat field was possible. Such lenses are called 

 by Lummer " new achromats." 



Having shown, in the first eight or nine chapters of the 

 book, what are the conditions to be satisfied. Prof Lummer 

 proceeds to describe the various ways in which this is 

 done in practice. The condition of no distortion is 

 readily satisfied by combining two identical sets of lenses 

 symmetrically placed into a double object glass with the 

 stop midway between. These, if of the new "anoma- 

 lous " glasses, can have a flat field. But such a com- 

 bination will not be completely stigmatic ; to secure this, 

 other conditions must be satisfied besides those which 

 are possible in a symmetrical combination, and the best 

 result has been obtained by combining, in what is known 

 as an anastigmatic-aplanat, a new achromat with an old 

 achromat. The astigmatic effect of the old achromat is 

 NO. 1627, VOL. 63 I 



opposite to that of the new ; hence by the combination 

 it is possible to secure a flat image which is also stig- 

 matic and achromatic, while, by adjusting the distance 

 between the lenses and properly placing the stop, the 

 condition of no distortion is satisfied. 



Details of combinations satisfying these various con- 

 ditions are given in the book, and not the least of Dr. 

 Thompson's services are the chapters in which he calls 

 attention to the excellent work done by various well- 

 known English makers. His description of Dallmeyer's 

 Tele-objective is specially welcome, while Miethe's two 

 views of Munich from a distance of about two miles — the 

 one taken with an ordinary lens, the other with his tele- 

 objective — show what a powerful weapon the latter is. 



The appendix contains some more detailed accounts 

 of von Seidel's analysis, and also a valuable example of 

 the computation of a lens. 



The book is published by Messrs. Macmillan and Co. 

 in their usual admirable style, and supplies a very real 

 addition to the literature of a subject too much neglected 

 in England. R. T. G. 



OUR BOOK SHELF. 



A Handy Book of Horticulture. By F. C. Hayes, M.A. 

 Pp. xi -I- 225. (London : John Murray, 1900.) 



This is a little book intended " for the class of fairly in- 

 telligent young men who are placed in sole charge of 

 small gardens, who have little natural aptitude for 

 gardening and no training, and who look in vain to their 

 employers for teaching or suggestions of any kind." The 

 questions naturally arise how such men come to have 

 charge of gardens, and whether any book is likely to be 

 of material service to them. For a class of better in- 

 formed readers with a real interest in the subject the 

 present book is better adapted, as the directions are 

 simple and clear. The practical instruction conveyed is 

 good, but, although the book is not intended for botanists, 

 we may fairly look for accuracy and correct spelling of 

 names. 



In the following passages we have examples of loose 

 writing, which are not the only ones that might be 

 found : — 



" The lilium is a popular family of hardy, bulbous 

 flowers. No garden should be without a variety of them, 

 but the species is so numerous that it would be impos- 

 sible in one brief chapter to lay down general rules for 

 their culture." 



Here is another paragraph which is not remarkable 

 for accuracy : — 



" Speaking generally, a fern may be defined as a plant 

 which bears leaves only and no flowers. The name of 

 their order is Cryptogamia, i e. hidden flowers ; they 

 have organs which produce spores, but the attractive 

 petals are absent, and the spore cases are hidden away 

 or take strange forms." 



On the following page we have such misspelling as 

 Calcidonicum and tigranum ; elsewhere we find nemerosa, 

 pyraeanthus, azalias, Charles Lefebre ; while the use or 

 disuse of capital letters seems to be entirely a matter 

 of caprice. 



The Construction of Large Lnduction Coils ; a Work- 

 shop Handbook. By A. T. Hare, MA. Pp. 155. 

 35 illustrations. (London : Methuen and Co., 1900.) 

 This book, written by an amateur primarily for 

 amateurs, will be found of the greatest use for all those, 

 amateurs and professionals alike, who desire to construct 

 Rhumkorf induction coils according to the most approved 

 methods. 



