November 7, 1919] 



SCIENCE 



437 



rest, believed by many to be closely related to 

 present ignorance of the laws of fatigue and 

 the best modes of applying them in practise, 

 has emphasized the importance of this branch 

 of research. — British Medical Journal. 



SCIENTIFIC BOOKS 



Constructional Data for Small Telescope Oh- 

 jectives. Calculated at the National Phys- 

 ical Laboratory. By T. Smith and R. W. 

 Cheshire. 4to. Pp. 82. Additional data 

 for the construction of small telescopes oh- 

 jectives. By the same authors. Prepared 

 at the request of the Director General of 

 Munitions Supplies. 4to. Pp. 82. London, 

 Harrison and Sons, 1915 and 1916. Price, 

 2s. 6d. and 5s. 



During the war every possible stimulus and 

 aid was offered to manufacturers by the Eng- 

 lish government no less liberally than by our 

 own, and of course some years earlier. The 

 present volume is intended to save the manu- 

 facturer of small telescopes a large part of 

 the time and expense that would be con- 

 sumed in perfecting his models. British 

 glass factories, aroused to the emergency, had 

 succeeded in producing new varieties and a 

 large quantity of optical glass, duplicating in 

 feverish haste inventions evolved at leisure 

 by German scientists and artisans during the 

 previous thirty years. But the grinding of 

 lenses and their combination into eilective 

 sets for binoculars, gun-sights, range-finders 

 and photographic cameras can not be begun 

 until protracted mathematical calculations are 

 finished. Tears of preliminary study have 

 often gone into the making of an improved 

 objective. One must conjecture, design, cal- 

 culate and compare. Obviously, carefully 

 systematized records of previous studies would 

 save labor: cooperation is economy. These 

 tables mark a new application of this prin- 

 ciple. Glass factories supply, with a list of 

 available melts, their indices of refraction and 

 dispersion. By the tables one can decide 

 quickly upon the comparative merits of 

 doublets made from those materials. 



Objectives are usually made of from two to 

 six separate lenses. Each component by 



itself gives a defective image. Eings of blue 

 or red encircle each bright object, and in 

 place of points of light there appear hazy 

 circles or fantastic comet-like shapes. If at 

 the center of the field a picture is fairly good, 

 the parts toward the edge are distol-ted. To 

 improve such crude images, at least two 

 lenses must be used in combination. Accord- 

 ingly data are here given for suitably 

 matched two-lens objectives, one lens of 

 crown glass, the other of flint glass, so pro- 

 portioned as to eliminate at least two of the 

 so-called aberrations, or defects of the image. 

 The figures relate to six kinds of crown glass 

 (a seventh in the supplement) and six kinds , 

 of flint glass. The selection of typical sorts 

 is not made at random, nor at equal intervals 

 in the whole range of possibilities, but near 

 what we may call, borrowing a statistical 

 term, " accumulation " points of the cata- 

 logue list. To suit each of six sets of con- 

 ditions the proper dimensions are found for 

 every combination of one kind of crown with 

 one kind of flint, so that every table contains 

 36 entries. 



The first set of tables {A) eliminates color 

 and spherical aberration; not, of course, for 

 all kinds of light and for objects at all 

 possible distances, but for two different wave 

 lengths of light and for objects at a distance 

 so great that the rays striking the glass are 

 practically parallel ("object at infinity"). 

 To the removal of color from the image corre- 

 sponds an algebraic equation of the first 

 degree between the focal lengths of the two 

 lenses, both considered as " thin " ; while that 

 for spherical aberration is of the third degree 

 in the curvatures, or reciprocals of the radii 

 of the spherical surfaces of the lenses. But 

 when the two lenses are to be in contact, and 

 their contiguous surfaces are exactly alike so 

 that they may be cemented, the third degree 

 equation for that common radius is reduced 

 by one degree, to a quadratic. For this equa- 

 tion then there are two solutions, and so two 

 tables of curvatures. Indeed all the pairs 

 here tabulated are cemented lenses. Since 

 two of the four spherical surfaces have equal 

 radii for any desired focal length, there re- 



