March 15, 1900J 



NATURE 



469 



been in our possession for three years, we can still obtain sue 

 cessful cultures in gelatine ; the various forms, which we have 

 previously described, have been observed as before. 



Our object in sending this note is to call attention to the 

 extraordinary vitality of this organism under such untoward cir- 

 cumstances, owing doubtless to its carefully entrenched position. 



V. H. Veley, 



Oxford, March lo. Lli.iAN J. Veley. 



Drunkenness and the Weather, 



On reading the letter of Prof. Dexter on "Assaults and 

 Dunkenness " (p. 365), I notice that there is one great fallacy in 

 the argument. 



When a man is intoxicated and commits an assault, the result 

 is entered in pwlice reports as "assault," the more serious 

 oflTence overshadowing the less. So that, in all probability, 

 many of the cases of assault referred to in the statement were 

 also cases of drunkenness, but were not tabulated as such. 



The temperature is an important element ; for its variations 

 are probably the cause of the change of character of the offences 

 recorded. The same quantity of alcohol will, as has often been 

 noticed, have very different effects in the summer and in the 

 winter. In hot weather alcohol has a stimulating influence; 

 this is much less marked in the winter, and during this season 

 the sedative effect is certainly more noticeable. 



Studying Prof. Dexter's curves in this light, and assuming the 

 absence of any other fallacies, we may reasonably conclude that 

 the number of those arrested for drunkenness or its results varies 

 but little throughout the year. Probably the same people supply 

 the cases of drunkenness in winter and of assaults in summer. 



R. C. T. Evans. 



9 Heathcote Street, Gray's Inn Road, W.C., March 3. 



Mechanical Methods of Calculating Logarithms. 



The following mechanical method of finding logarithms 

 seems to be as simple as any that have been proposed, and has 

 the advantage that it gives the logarithms of all numbers without 

 interpolation, and at the same time affords a proof of the funda- 

 mental property of the function. 



Let a flat ruler AB be provided at one end, A, with a hatchet 

 edge (like that of the hatchet planimeter), so arranged that when 

 the ruler is held horizontally, and the hatchet allowed to touch 

 the paper, it touches at a point vertically below the edge of the 

 ruler. The hatchet must lie in a vertical plane inclined at a 

 convenient angle (say 45^) to the ruler. Let the ruler be held 

 thus, with its edge touching a pin. On moving the ruler so 

 that the hatchet does not slip sideways, the latter will trace a 

 spiral curve on the paper. From its mode of generation the 

 spiral clearly cuts all radii vectores at the same angle, and thus 

 is the well-known equiangular spiral. Let OA be a radius 

 vector of unit length, and OP one of length r. Let AOP = fl 

 where 9 may be expressed in terms of any convenient unit, 

 then we may define the logarithm by the equation e = log r. 

 Of course, depends on the angle of the spiral and on the unit 

 of angle adopted as well as on r, and so is not yet completely 

 defined. We can, however, immediately prove the fundamental 

 property of the logarithmic function. 



Imagine a copy O'A'P' of the diagram to be made on some 

 extensible material, and to be extended equally in all directions 

 in the ratio R : i. All angles remain unaltered, and the new 

 curve is an equiangular spiral with the same angle as before. 

 If, now, O' be placed on O, and the new diagram turned till A' 

 lies on the old spiral, the two spirals, having the same angle, 

 must coincide, and hence P' lies on the old spiral. Now 

 OA' = R, OP' = rR. AOP' - AOA' -f A'OP' = AOA'-f AOP, 

 which gives log rR = log r-|-log R, the fundamental property. 

 If we further chose our unit angle so that log 10= I, the spiral 

 will give Briggian logarithms. It would, perhaps, be more 

 convenient practically to adjust the angle of inclination of the 

 hatchet so that log 10 is represented by 100°, or perhaps by 

 360° if we divide the circle centesimally. It may seem that the 

 logarithm, as defined above, still depends on the angle of the 

 spiral, but this idea can be readily disproved by means of the 

 equation logrR^log r + log R. The logarithm, having been 

 defined without reference to indices, may now be used to define 

 the quantity x", where n is negative or fractional, and to give the 

 index laws in a manner rather less artificial than that usually 

 adopted (the fact that no indication is given of the many-valued 

 character of a fractional power is, however, a drawback). 



NO. 1585. VOL. 61] 



The hatchet planimeter may be used to obtain logarithms, 

 but in a less simple manner. If the planimeter be placed with 

 its point on a given straight line, and its length perpendicular 

 to the line, and the point be moved through a distance x along 

 this line, the inclination 6 of the planimeter to the line is given 

 hy x-a log cot «/2, where a is the length of the planimeter. 

 This gives an obvious mechanical construction for a logarithm. . 



Leeds, March 5. H. C. Pocklington. 



THE CENTENARY OF THE BERLIN 

 ACADEMY OF SCIENCES} 

 T T is with feelings of pleasure that we call the attention 

 •■■ of our readers to the fact that rather more than one 

 month ago the Academy of Sciences at Berlin, at its 

 meeting on the 25th of January, commemorated with 

 great rejoicing and some very pardonable pride the work 

 which its members have done in the world during the 

 last hundred years. The subjects which have been in- 

 vestigated by this distinguished body include almost 

 every branch of human knowledge, and although at this 

 date we are too near in point of time to be able to judge 

 definitely and finally as to the value of the work which 

 the German scholars and men of science, whose names are 

 written on its books, have done, there is no room for 

 doubting that they have enlarged the bounds of human 

 knowledge in every direction, and have brought us 

 many degrees nearer to the goal sought by all honest 

 investigators. 



The Berlin Academy has kept in mind what the true 

 functions of an Academy of Sciences should be, for 

 it has not sought to limit the number of subjects which 

 its members desired to investigate, and it has not at- 

 tempted to patronise or to foster the growth of one class 

 of sciences, or of one branch of learning, to the exclusion 

 of all others. It has encouraged knowledge of every 

 kind, and has supported by its influence and money the 

 workers in the most recondite branches of human 

 learning, and its influence for good has been so far- 

 reaching that it would need a volume if we attempted to 

 describe the work which has been well and efficiently 

 performed under its auspices. And the Academy of 

 Sciences at Berlin has not only helped the world posi- 

 tively, as it may be termed, that is to say, by enabling its 

 members to formulate and build up sciences, but nega- 

 tively, by making it impossible for the faddist, and crank, 

 and charlatan to press his views upon the non-expert, but 

 well-educated, section of the German public. In this 

 last capacity it has performed, very quietly and unob- 

 trusively, but effectively, a most important duty, and it 

 has succeeded in obtaining and holding a position of 

 authority which cannot be gainsaid. It has proved to all 

 the world that when it sets its seal of approval on a 

 man's methods or works, those methods and works have 

 permanent value. We may almost say that the work of 

 German scholars and thinkers is so good because they 

 possess in their country a high authority for the approval 

 of which they are content to toil long and arduously, 

 knowing well that its stamp is a hall-mark which the 

 intellectual world will honour, and the full value of 

 which will be duly credited to it. Of the universality of 

 learning the Academy at Berlin has been a consistent 

 and powerful patron, and the long list of great names 

 which Herr Waldeyer, one of the secretaries of the 

 Physical Section, brought to the notice of the members 

 at its festival meeting is a splendid proof of this 

 statement. Among historical investigators and jurists 

 may be mentioned Fichte, Schleiermacher, Schelling 

 and Trendellenburg ; among students of linguistics 

 and archaeologists, Boeckh, Bekker, Bopp, Curtius, 



1 SitzHHgsberickte der KSniglich Prtussisclun Akadeinie der Wissen- 

 schaften zu Berlin. 25 Januar. Offentliche Sitzung zur Feier de^ 

 Geburtsfestcs Sr. Majestiit des Kaisers und KSnigs und des Jahrestagtt 

 KSnig Fritdrick's II. In Commission bei Georj? Reimer, Berlin. 



