NATURE 



401 



THURSDAY, JULY 24, u^ig. 



A GUIDE TO LENS CALCULATIONS. 



Applied Optics: The Computatioti of Optical 

 Systems. Being- the " Handbuch der ange- 

 wandten Optik " of Dr. Adolph Steinheil and 

 Dr. Ernest Voit. Translated and edited by 

 James Weir French. Vol. ii. Pp. vi + 207 + v 

 plates. (London: Blackie and Son, Ltd., 

 1919.) Price I2S. 6d. net. 



THE introductory section of this volume ^ con- 

 tains an explanation of the symbols em- 

 ployed and of the sign conventions adopted, to- 

 g-ether with extensive tables of formulae designed 

 to cover the trigonometrical calculation of rays 

 through a series of centred refracting surfaces. 

 The system described is probably far more exten- 

 sively employed than any other by practical 

 opticians. It is constructed throughout with a 

 view to convenience in logarithmic computation, 

 and only minor improvements have been effected 

 since it was first published. Its popularity has 

 not been seriously affected by the introduction of 

 the calculating machine into the workshop. 



After a chapter on the measurement of refrac- 

 tive indices and the calculation of achrornatic 

 prisms come three chapters on achromatic doublet 

 objectives, which include fully worked examples 

 of the application of the formulae given earlier. 

 The authors set out to record their experience in 

 designing optical systems, and to this end have 

 tabulated the results obtained with series of objec- 

 tives corrected for spherical and chromatic aberra- 

 tions. They have not indicated which zone of 

 the objectives should be corrected to yield the 

 most satisfactory performance, nor the maximum 

 amount of the aberrations present for uncorrected 

 zones, but, owing to the care with which the 

 objectives have been calculated, the results given 

 are of sufficient value to ensure for the book a 

 place on the reference shelf of the optical com- 

 puter. In finding- the forms for the lenses the 

 authors have been guided by a number of prin- 

 ciples derived from the calculation of rays through 

 a series of single lenses (see vol. i.). Of these, 

 that relating to the influence of the lens form on 

 spherical aberration may be singled out as of para- 

 mount importance in designing- doublet objectives. 

 The principle states that the spherical aberration 

 of a single lens is a minimum when the deviation 

 of a ray is divided equally between the two sur- 

 faces, and subsequent developments show that 

 this is regarded as an exact law rather than as 

 a rough approximation. This conclusion is 

 decidedly surprising, as the spherical aberration 

 has previouslv been found to be less when the 

 deviation is divided in the ratio t, : 2 than when 

 it is equally divided. It is not difficult to prove 

 that, for minimum aberration, the deviation at 

 the first surface must be greater or less than that 

 at the second according as the dimensions of the 



J A review of the first volume was published in Nature, September 26, 

 1918, vol. cii., p. 61. 



NO. 2595, VOL. 103] 



object are greater or less than those of the image. 

 The extent of the difference involves the refrac- 

 tive index as well as the magnification, and cases 

 may easily arise in which the supposed law leads 

 to serious errors. The forms given for the lenses 

 with flattest possible flint components are incor- 

 rect, owing to this error of principle. 



It may be noted that some conclusions which 

 were correct at the time the book was written do 

 not necessarily apply if types of glass produced 

 within the last thirty years are employed. 



The original German edition was not free from 

 a number of important errors, and most of these 

 are present in this translation. In a second 

 edition the formulae should be carefully revised, 

 and errors in the constructional data of the objec- 

 tives corrected by recalculation. The original 

 text is not always adhered to, and the new defini- 

 tion for the sign of the deviation gives the wrong 

 result for a ray below the axis. The avvkward ± 

 sign, which occurred frequently in the original, has 

 generally been avoided. Changes have been 

 made in the symbols, but tt is retained as a vari- 

 able angle. The table of differences between arcs 

 and sines, intended for use in removing small 

 residuals of spherical aberration, has been 

 omitted. The appendices by Steinheil and Seidel 

 on the determination of the best mean dispersion 

 ratio, and by Seidel on the derivation of the 

 formulae for tracing a general ray, have been in- 

 cluded in this volume. 



The translator has written a clear English text. 

 The book is very well printed, and the thickness 

 of the paper will be appreciated by those who 

 require to refer to it frequently. One of the most 

 serious omissions of the original has been reme- 

 died by the inclusion of a very complete index. 

 No pains have been spared to make the volume 

 worthy of the position it is intended to take as 

 a standard book of reference for the optical com- 



puter. 



T. S. 



COLLOID-CHEMISTR Y. 

 A Handbook of Colloid-Chemistry. The Recogni- 

 tion of Colloids, the Theory of Colloids, and 

 their General Physico-Chemical Properties. By 

 Dr. Wolfgang Ostwald. Second English 

 edition, translated from the third German 

 edition by Prof. Martin H. P'ischer. With 

 numerous notes added by Emil Hatschek. 

 Pp. xvi4-284. (London: J. and A. Churchill, 

 1919.) Price 155. net. 



THE increasing recognition of the importance 

 of a study of colloidal matter, both for 

 physical theory and for industrial practice, has led 

 to a growing demand for text-books dealing speci- 

 ally with this branch of science. Hitherto this de- 

 mand has been chiefly met by works in the German 

 language or by translations of these, and of such 

 works the one before us has for a number of years 

 occupied a foremost place. This, doubtiess, ^ is 

 due in no small measure to the marked activity 

 of the author both as an investigator and as 



Y 



