678 



NA JURE 



[May 27, 1922 



experiments he carried out. Finally he formulates the 

 laws which we use to-day. In the second memoir the 

 formula for the mutual action between two infinitely 

 small elements of conductors carrying currents is 

 proved. Ampere's researches paved the way for 

 much of Faraday's work, and Clerk Maxwell makes 

 full use of his results in his treatise. Clerk Maxwell 

 well called Ampdre the Newton of Electricity. The 

 guiding experiments and the theory seemed to start 

 fully equipped from his. brain just as Pallas Athene 

 was born fully armed from the head of Zeus. 



Small Talk at Wreyland. By Cecil Torr. Second 

 series. Pp. vi+120. (Cambridge: At the Univer- 

 sity Press, 1 92 1.) 95. net. 



In his second series of " small talk," Mr. Torr, pro- 

 ceeding on the lines followed in his first volume, has 

 brought together a number of pleasantly written 

 discursive jottings on various matters drawn from his 

 own recollections and from the letters and diaries of 

 his father and grandparents. An antiquarian and a 

 scholar, he writes with a light and pleasant touch on 

 such matters as local lore and history, as well as of 

 events in the larger world. The value of these notes 

 lies in the light they throw on the social habits and 

 customs of the middle of the last century ; they deal 

 with those illuminating details which are apt to evade 

 the more formal historian. Interspersed are observa- 

 tions of and reflections on happenings which have 

 befallen Mr. Torr during his travels in the Mediterranean 

 and in Palestine. All topics, whether of a serious or a 

 lighter character, are touched upon in a manner which 

 can only be described as urbane. On one subject 

 alone does Mr. Torr's urbanity desert him, and that is 

 when he is moved to comment upon the Government 

 regulations for the cultivation of the land during the 

 war. 



Chemical Reactions and their Equations : A Guide and 

 Reference Book for Students of Chemistry. By Prof. 

 I. W. D. Hackh. Pp. viii + 138. (Philadelphia : P. 

 Blakiston's Son and Co., 1921.) 1.75 dollars. 



"The inability to balance a chemical equation is a 

 most common difficulty to students of chemistry." 

 The author has attempted to remedy this very common 

 weakness, and in addition to a concise explanation of 

 chemical notation, including difficult cases of oxidation 

 and reduction and ionic reactions, has provided a list of 

 more than four hundred classified and indexed chemical 

 equations. The book should prove a useful companion 

 to degree students. In the list of solubilities "to be 

 memorised " one finds : " Borates are soluble," which 

 is not strictly correct, since most borates are insoluble. 



The Practical Chemistry of Coal and its Products. By 

 A. E. Findley and R. Wigginton. Pp. 144. (Lon- 

 don : Benn Bros., Ltd., 1921.) 125. 6d. 



The analysis of coal, coke, ammonia liquor and am- 

 monium sulphate, tar and its distillation products, gas 

 (including calorimetry), pyrometry, and water analysis, 

 are the topics dealt with in this book. The volume is 

 very attractively printed and illustrated and should 

 prove most useful in works laboratories. 



NO. 2743, VOL. 109] 



Letters to the Editor. 



[TAe Editor does not hold himself responsible for 

 opinions expressed by his correspondents. Neither 

 can he undertake to return., or to correspond with 

 the writers of refected manuscripts intended for 

 this or any other part of NATURE. No notice is 

 taken of anonymous communications !\ 



Definition, Resolving Power, and Accuracy. 



In scientific writings the term " definition " most 

 often refers to the clearness with which details are 

 shown by optical instruments ; but by a convenient 

 generalisation it might be taken to mean the ratio 

 of the greatest to the least quantity which any kind 

 of apparatus can render apparent at the same time, 

 being thus distinguished from " sensitiveness " or 

 " resolving power," which is determined simply by 

 the smallest quantity measurable without reference 

 to the size of the field. 



In this sense the question of " definition " enters 

 into every kind of measurement. In telescopes and 

 microscopes, for example, it would denote the angular 

 or linear size of the field of view compared with the 

 smallest corresponding quantity which can be clearly 

 distinguished ; or, in a balance, the greatest arc 

 through which it can swing compared to the least 

 angle of swing giving a trustworthy measure of change 

 of weight. 



Since all measurements have in the end to be 

 recorded by the senses either of sight, hearing, or 

 touch (smell and taste have not yet been examined 

 quantitatively), it is of interest to inquire what kind 

 of definition can be expected in their case, and the 

 following notes contain some of the results of various 

 observations on the subject made at intervals during 

 many years. 



Sight and hearing are both dependent on wave- 

 motion, and the sensations produced vary with the 

 intensity, frequency, direction, and duration of the 

 waves. The total range of sensible intensities is 

 enormous ; for it is seldom that a night is so dark, 

 or a silence so complete, that absolutely nothing can 

 be seen or heard, yet the eye can work without 

 injury in bright sunlight, and the ear can hear with 

 such noises as thunder or great explosions. In these 

 cases the ratio of the greatest to the least appreciable 

 intensity must be of the order of millions. 



Although, however, the perceptions of intensities 

 have such wide limits, the differences which can be 

 recognised at any one time or in any constant condi- 

 tions are much more limited. 



In many respects the senses may be compared with a 

 musical instrument which, while of restricted compass, 

 can be tuned to almost any absolute pitch, so that 

 though for any one tuning comparatively few notes 

 can be sounded, yet by adjustment these notes may 

 take any desired position in the audible scale. Each 

 sense, in fact, seems to adjust itself to some kind of 

 level suitable to its surroundings, and to be able (so 

 far as my own observations go) to discern differ- 

 ences of from 5 to ^ per cent, of the range then 

 appreciable. 



The same order of definition was found not only 

 for each sense but also for the co-ordination of the 

 senses with muscular action. 



The following experiment on the greatest difference 

 between the intensities of light which can be perceived 

 at the same time always gave fairly consistent results. 

 A long tube AB, Fig. i , about two inches in diameter, 

 and well blackened inside, was provided with a white 

 paper flange at A, and a movable piston, C, also 

 covered with white paper. A disc of white paper, D, 

 of rather less diameter than the tube was placed at 



