NA TURE 



[May 3) 1883 



British Association, 1833, the attention of the mathe- 

 matical and physical section was largely given to the 

 subject, and Herschel, Airy, and others spoke warmly in 

 praise of the discovery. In the introductory discourse 

 with which the proceedings of that meeting was opened, 

 Prof. Whewell made it a topic, and expressed himself in 

 the following words : ' In the way of such prophecies few 

 things have been more remarkable than the prediction 

 that under particular circumstances a ray of light must be 

 refracted into a conical pencil, deduced from the theory 

 by Prof. Hamilton and afterwards verified experimentally 

 by Prof. Lloyd.' Previously, in the same year, Prof. 

 Airy had publicly recorded his impression upon the sub- 

 ject as follows: ' Perhaps the most remarkable prediction 

 that has ever been made is that lately made by Prof. 

 Hamilton.' " 



The view Hamilton himself took of the discovery of 

 conical refraction was characteristic. " It was," he 

 writes to Coleridge on February 3, 1833, "a subordinate 

 and secondary result when compared with the object I 

 had in view to introduce harmony and unity into the con- 

 templations and reasonings of optics regarded as a branch 

 of pure science." 



At the close of this volume we still leave Hamilton 

 quite a young man. The great labour of his life has 

 not yet commenced ; its nature has not indeed even 

 dawned upon him. We shall therefore look forward with 

 pleasure to the continuation of the present most interest- 

 ing work. The development of Hamilton's more mature 

 genius, his correspondence with De Morgan, in itself no 

 inconsiderable mass, and above all the gradual evolution 

 of quaternions, will form most attractive materials for his 

 biographer. 



It is by the liberality of the Board of Trinity College, 

 Dublin, that the present instalment of the work has been 

 brought out, and we sincerely trust that the same liberality 

 will be extended to enable the biographer to continue to 

 do real justice to his subject. But besides the present 

 work another debt is due to his memory. Hamilton's 

 earlier papers are very inaccessible : many of them are 

 scattered about in various periodicals, and his two noble 

 treatises on quaternions are out of print. A complete 

 edition of Hamilton's works would be an appropriate 

 sequel to this biography, and they would be not unfitting 

 companions for the works of Lagrange and of Gauss. 

 It is not often that a University has so gifted a son as 

 Hamilton. Let us hope that the University which is 

 proud to claim him will see fit to raise this further 

 monument to his genius. 



LETTERS TO THE EDITOR 



[The 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, rejected manuscripts. 

 No notice is taken of anonymous communications. 



[The Editor urgently requtsts correspondents to keep their letters 

 as short as possible. The pressure on his space is so great 

 that it is impossible otherwise to insure the appearance even 

 of communications containing interesting and novel facts.] 



Sheet- Lightning 



In Nature, vol. xxvii. p. 576, a statement is made that the 

 "opinion so long and generally entertained" that "sheet-lightning 

 and the so-called summer or heat-lightning are nothing else than 



the reflection of, or the illumination produced by distant elec- 

 trical discharges, is not supported by observation." This state- 

 ment surprises nie, fur I should have said that the opinion once 

 commonly entertained that sheet-lightning is a distinct form of 

 lightning unaccompanied by sound, is now for the most part 

 rejected, the results of observation being di-tinctly against it. 

 The question is an old one ; but as the writer of the above 

 statement only refers to the observations made at Oxford during 

 the twenty four yeats ending 1876, I will confine myself in the 

 main to an examination of these. I must premise that I do not 

 assert that lightning never occurs at such an altitude that the 

 thunder accompanying it is not audible. In rare instances in 

 Europe lightning is observed in the zenith, followed after an inter- 

 val of twenty seconds or more by faint rolling thunder immediately 

 overhead. It is therefore antecedently probable that lightning 

 may occur at too great an elevation for the thunder to be heard 

 at the earth's surface at all ; and this is especially likely to 

 happen in some of those thunderstorms within the tropics, the 

 altitude of which i- extremely great. 



The distance at which the illumination produced by lightning 

 in a dark night can be observed depends upon the altitude and 

 the intensity of the discharge, and further upon the altitude, 

 character, and amount of the clouds. It is possible that the 

 diffused particles of ice (at a much greater altitude than the 

 cirri), which produce the phenomenon called "rayons du cre- 

 puscule," are capable in some cases of reflecting the illumina- 

 tion. However this may be, it is certain that the illuminations 

 of an ordinary thunderstorm at midnight, when there is no 

 moonlight, have an average radius of more than forty miles. 

 The distance at which thunder is heard depends on a variety 

 of conditions ; but we may safely state that in the open 

 country in calm weather a.' midnight the sound is rarely 

 heard at a greater radius than fifteen miles. At the Rad- 

 clifife Observatory, which is scarcely out of the reach of 

 rumbling sounds produced by the traffic of a town, the average 

 distance at which thunder is distinguished may probably be 

 safely reduced to seven miles. Assuming then that at Oxford 

 the area of illumination has a radius of forty-two miles, and 

 that of thunder one of seven miles (and in this assumption we 

 are probably not very far from the truth), we conclude that in 

 the darkest hours "lightning without thunder" should occur at 

 Oxford with a frequency which is expressed by the figures 

 35 : I as compared with " thunder with or without lightning." 

 A deduction ought, of course, to be made for the effects of 

 moonlight. But when this has been made, the figures quoted 

 by your reviewer are not only satisfied by the hypothesis for the 

 refutation of which he employs them, but further, if his mode of 

 reasoning were legitimate, they would lead us to the conclusion 

 that in nearly seven cases out of eight the thunder heard at Ox- 

 ford is not the result of electrical discharge at all ! Such thunder 

 does not occur elsewhere, and was not in vogue at Oxford "iD 

 my time." 



Practically, however, two considerations must not be omitted : 

 (I) some localities enjoy a special immunity from thunderstorms, 

 while others are responsible for the production of an exceptionally 

 large number ; in the former the frequency of illumination will be 

 greater in comparis on with the frequency of thunder, in the latter 

 it will be less : (2) (and this is a consideration of much more im- 

 portance, though frequently neglected when a conclusion is de- 

 duced from records of phenomena) the relative frequency of two 

 sets of occurrences often differs widely from the relative frequency 

 of the records of the occurrences. The relative frequency of re- 

 cords of thunder and of lightning is to a large extent dependent 

 on the position of the observer's residence, his habits, the keen- 

 ness of his eyes and ears respectively, and his attentiveness to 

 the impressions which those organs respectively experience. 



No one who has on a summer night carefully watched the 

 gradual approach of a great thunderstorm, counting the flashes, 

 and registering the time-interval and number of claps from the 

 minute when the first flickers begin above the southern horizon 

 to that at which the storm is in its full roar and ratile overhead ; 

 no one who in a long night journey by train has run into a 

 thunderstorm whose distant coruscations he has noticed two or 

 three hours beforehand ; no one, at least, who after watching 

 sheet-lightning in one particular direction has made careful 

 inquiries as to the occurrence or otherwise of thunder over the 

 district from which the light proceeded, will hesitate in pro- 

 nouncing the verdict that ordinary sheet or summer lightning is 

 simply the illumination produced by a distant thunderstorm. 



W. Clement Ley 



