596 



NATURE 



[August 7, 191 



just as an oak is a perfectly definite type of a tree. 

 Taking q=x + yi+zj'+wk as the type of a quaternion 

 we may generalise the " scalars " x, y, z, w, by 

 making them ordinary complex numbers, or elements 

 of some other algebra, commutative with i, j, k, and 

 combining according to laws of their own. We' thus 

 embed the quaternion algebra, so to speak, in a larger 

 composite algebra; but it is most undesirable to call 

 this an extension, still less a completion, of quater- 

 nions. 



The reader should be warned that the author often 

 says "must" when there is no logical necessity at all 

 For instance, we are told that, /3 having one dimension 

 in length, B- "must" have two; yet on the next page 

 we are told that */3 7 5 means a solid angle, thus appar- 

 ently having no dimensions in length, at any rate 

 not four. This kind of fogginess is very common 

 even among quaternionists. Thus ij = k, so the pro- 

 duct of two vectors can be a vector, and the law of 

 dimensions is violated, or rather does not apply. Of 

 course, in physics, it is convenient to represent areas 

 moments, &c, by vectors, and then the quaternion 

 formulae become more significant. We might, if we 

 liked, put ij=k 1 , jk = u, ki = j„ regarding t„, ;., k, as 

 area] units, and then have what Grassmann would 

 call a regressive multiplication, t\,j', = k, j,k 2 = i, k 2 i 2 = j 

 bringing us back to one dimension again. ' Bu't anyone 

 can see that this is unnecessary complication ; in all 

 physical applications of quaternions it is easy to see 

 whether a vector is to be interpreted literally, or as 

 the representative of some areal quantity. 



Whatever may be the ultimate fate of this particular 

 algebra Dr. Macfarlane's researches deserve recogni- 

 tion. He has the spirit and the courage of a heretic 

 and every honest heretic helps to advance the truth 



G. B. M. 



UNITED STATES METEOROLOGICAL 

 PUBLICATIONS. 1 

 (I) 'J'HE first thirty pages of the report of the Chief 

 of the Weather Bureau for the year 1911-12 

 contain a summary of the work accomplished by 

 that department during the year. This is followed by 

 a general statement of the weather conditions prevail- 

 ing in the individual months, while the last and bv 

 far the longest part of the report is devoted to tabu- 

 lated statistics of the different meteorological elements 

 with summaries of sunshine, excessive rainfall &c 



An account of the work done at the upper-air station 

 on Mount Weather is given first place in the volume 

 and from this we learn that it is proposed to modify 

 the plan hitherto followed of attempting to obtain a 

 kite or balloon flight on each day, regardless of the 

 weather conditions, and to substitute a series of 

 special ascents made to investigate particular problems 

 It is interesting to learn that a special department is 

 being inaugurated at this observatory for the training 

 of observers for duty at the 200 out-stations of the 

 weather service. At the central office a synoptic 

 weather chart is prepared each day for the whole of 

 the northern hemisphere, and on this map are based 

 general forecasts of the weather and temperature 

 conditions over the United States for a week in 

 advance. It is intended shortly to institute a service 

 of wireless reports from shins in the Atlantic, and to 

 transmit information as to the location and movements 

 of dangerous storms to vessels from one of the high- 

 power stations on the coast. Extensive observations 

 are now being made on the snowfall of the western 

 mountain ranees, and it is hoped to be able in the 

 future to give useful forecasts of the flow of those 



■ O. L. Fassis. 



rivers which are fed in the spring and Minim.,- b\ 

 the thawing snow. A feature of the report is th 

 of new book, added to the library during the vear 

 Many of the more important of these "works' are- 

 referred to individually, and a short account is given 

 of the scope covered bv each book. This should prove 

 useful for purposes of reference. It is evident from 

 a perusal of the volume that the operations of the 

 bureau are conducted on a verv large scale, as befits 

 an institution dealing with meteorological information 

 from an area like that of the United States. 



(2) The impending opening of the Panama Canal 

 renders the subject of the second paper of especial 

 importance at the present time. In addition to deal- 

 ing with the" West Indian hurricanes, the author sets 

 out comparative data for the typhoons of the Pacific 

 and the cyclones of the Bay of Bengal. All these 

 disturbances are of the same type, characterised by 

 a moderate decrease of atmosphe'ric pressure to within 

 forty or fifty miles of the centre, and then the rapid 

 fall associated with the destructive winds which cause 

 such havoc in the belt passed over bv the central 

 region of the disturbance. Nearly all the West 

 Indian hurricanes have their origin 'in a well-marked 

 area bounded by the parallels "of 12 and 26 X. 

 latitude, and lying between 56 and qo° W. longitude! 

 The_ typical track is parabolic in shape, the storm 

 moving W.X.W. at first, then curving round to the 

 N., and finally passing in a north-easterly direction 

 to the North Atlantic. The average rate of travel 

 of these storms is onlv 300 miles per day, so that the 

 forecaster is often enabled to give a fairlv long warn- 

 ing of their approach. Much useful information is 

 contained in the paper, and Dr. Fassig is to be con- 

 gratulated on the completion of a trustworthy piece 

 of work. j. s , D 



A- 



NO. 2284. VOL. 91] 



REFLECTION AS A CONCEALING AND 

 REVEALING FACTOR IN AOUATIC AND 

 SVBAOUATIC LIFE A 

 S a result of observations and experiments carried 

 out on ponds built for the purpose, and by the 

 use of apparatus for observing organisms in their 

 natural environments, I have arrived at certain con- 

 clusions as to the value of reflection as a concealing 

 factor in various forms of aquatic and subaquatic life. 

 The general principle upon which these ponds are 

 built is as follows :— In one bank of the pond is a 

 glass window, and beyond this window an under- 

 ground observation chamber. No light enters this 

 chamber except through the surface of the water. 

 By this means everything in the pond is seen by 

 entirely natural illumination, the observer cannot be 

 detected, and as there is no reflection from the glass 

 the making of photographic records is greatly simpli- 

 fied. In the first pond, built for the observation of 

 objects in the water, the glass is perpendicular. In 

 the second, for observing objects on the surface, the 

 glass is at an angle of 45 to the surface. 



Of apparatus I use a tube iS in. square and ^ ft. 

 long. On one side at the lower end is a window ; "into 

 this tube slides a reflex camera, so that the lens is 

 opposite the glass. When in use, a heavy weight 

 carrying a hook is lowered into the water, with the 

 end of the tube attached to the hook. The whole 

 apparatus can be tilted at any angle, and by this 

 means the incident rays from any object in any posi- 

 tion—except overhead— are made to strike the 

 glass at right angles, and thus distortion, due to 

 refraction through the glass, is rendered negligible. 



1 Discourse delivered at the Royal Institution on Friday, Tun* 6, by Dr. 

 Francis Ward. ' ■' 



