5°4 



NATURE 



[July 



191, 



very approximate reproduction of this effect, whereas 

 I have heard an expert break down hopelessly over 

 a similar passage at an exhibition recital of a com- 

 mercial machine. 



With regard to the connection between tone quality 

 and touch, I do not think Dr. F. J. Allen's explana- 

 tion meets the case. Unless there is distinct experi- 

 mental evidence to the contrary, I do not think we 

 ought to exclude the possibility of a double or mul- 

 tiple impact between the hammer and string; indeed, 

 some of my experiences favour this hypothesis. But 

 I am inclining more and more to the belief that the 

 differences may be largely due to the elasticity and 

 inertia of the stem of the hammer. The introduction 

 of these elements converts the hajmmer into a 

 dynamical system capable of independent vibration. 

 The method of normal coordinates then enables us 

 to represent this system by a simpler system having 

 the same vibration periods ; for example, a system of 

 two or more particles connected by elastic springs 

 and moving in a straight line. It is clear that the 

 duration of contact of a pair of such particles with 

 the wire will depend largely on the state of com- 

 pression between them and "their relative velocity at 

 the instant of impact. The interval between the re- 

 lease of the hammer and its striking the wire is 

 probably short compared with the time of a free 

 oscillation of the hammer itself, and certainly shoit 

 compared with the time in which such an oscillation 

 would die out. On setting the hammers of the hori- 

 zontal piano low down, the variations of tone quality 

 entirely disappear, as one would expect. 



I find another favourable condition by developing 

 Kaufmann's method in connection with the problem 

 of a single inelastic particle striking a wire near 

 one end. The duration of contact is determined by 

 the vanishing of a function which has one or more 

 minimum values before it actually vanishes, some of 

 these being small. A very small difference in the 

 assumed conditions might therefore convert one of 

 these minimum values into a negative value. Remem- 

 bering that such assumed conditions are probably not 

 even approximately satisfied in practice, we still have 

 a result indicating that the pianoforte hammer and 

 string may be highly susceptible to any cause which 

 tends to vary their duration of contact. 



I am specially pleased to receive Dr. Heaviside's 

 views on this subject, and to find that he has been 

 long- interested in these difficult problems. 



Since writing this I have read Prof. Morton's letter, 

 and am very glad to receive his references to previous 

 work on the subject. With regard to his own experi- 

 ments, I think something more is necessary for mv 

 purpose than what he mentions in Nature, namely a 

 comparison of the striking velocities of pianoforte 

 hammers in different parts of the scale. I notice 

 Prof. Morton does not mention what particular notes 

 were struck in his observations. It would also be 

 important to compare the striking velocities for two 

 notes, one in the treble and one in the bass, when 

 simultaneously excited by a common pneumatic 

 impulse of long or short duration, such as can be 

 produced in these piano-player experiments with 

 properly cut chords. With regard to the other ques- 

 tion, I think it is unfortunate that authors like M iu1m\ 

 have used the terms "good " and "bad " touch in this 

 connection. I freely admit that the heavy, inelastic 

 impacts produced by the inexperienced performer pro- 

 duce such a harsh effect as to be very objectionable 

 (and possibly this may be due to Dr. Allen's so-called 

 '"xylophone" effect); on the other hand, any playing 

 sounds to me mechanical which does not involve con- 

 siderable variation of tone quality. This appears to 

 me to be particularly necessary in studying piano 

 arrangements of orchestral music, where the sharp, 

 NO. 228l, VOL. 91] 



metallic tones of the brass instruments have to be 

 brought out in contrast to the softer tones of the 

 strings. Possibly when fingers are used the pianist 

 usually has too many other matters requiring his 

 attention. But whether a metallic effect is "good" 

 or "bad" must depend on how and when it is used, 

 and personally I should think a constant tone quality 

 the worst effect of all. Prof. Morton's letter, how- 

 ever, raises a number of other questions which would 

 take a long time to answer, and may have to be 

 explained in subsequent correspondence. 



G. H. Bryan. 

 Plas Gwyn, Bangor, North Wales. 



Mackerel and Calanus. 



We all believe that most of our common food-fishes 

 at some stage of life feed upon plankton, but those 

 who have looked into sea-fisheries questions know that 

 there is a great want of actual observations connecting 

 the occurrence of some planktonic organism in quan- 

 tity with the presence of a particular fish. Conse- 

 quently the following record may be of interest to both 

 marine biologists and fisheries experts. 



We are out on a scientific fisheries cruise, and in 

 addition to members of my own family, two well- 

 known naturalists, Prof. Newstead and Mr. Alfred O. 

 Walker are with us on the yacht, and w-e have just 

 had what we regard as a satisfactory demonstration 

 of the connection between a large shoal of mackerel 

 and the occurrence of Calanus finmarchicus in un- 

 usual quantity. 



On arriving in this bay last night we found that 

 the local boats had been catching abundance of 

 mackerel close to. We bought some for supper (good 

 fish for a halfpenny each), and on dissection found 

 that the stomachs of all of them were crammed full 

 of fresh-looking Calanus (the individual Copepods 

 being for the most part distinct and perfect), along 

 with a few immature Nyctiphanes and larval Deca- 

 pods. Prof. Newstead and my daughter then noticed, 

 while fishing over the side of the yacht, about 8 p.m., 

 that the gulls in the bay were feeding in groups 

 around patches of agitated water evidently caused by 

 shoals of fish. On rowing out to these we saw dis- 

 tinctly the mackerel, large and small, darting about 

 in great numbers in the clear water, and we also 

 noticed every here and there on the smooth surface 

 of the water — it was a beautifully calm evening — 

 innumerable small whirls or circular marks which, on 

 looking closely, I found to be caused by large Cope- 

 poda close to the surface. 



About twenty years ago I sent a note to Nature, 

 from the yacht Argo, in regard to large Copepoda (I 

 think it was Anomalocera on that occasion, and the 

 locality was further north, off Skye) splashing on the 

 surface so as to give the appearance of fine rain ; and 

 this present occurrence at once reminded me of the 

 former occasion, but here the Copepod was Calanus 

 finmarchicus of large size and in extraordinary abund- 

 ance. They could be clearly seen with the eye on 

 leaning over the side of the boat, a small glass collect- 

 ing jar dipped at random into the water brought out 

 twenty to thirty specimens at each dip, and a coarse 

 grit-gauge tow-net of about 34 cm. in diameter caught 

 about 20 cubic centimetres of the Copepoda in five 

 minutes. The mackerel were obviously darting about, 

 occasionally leaping to the surface (which gave the 

 gulls their opportunity) where the whirls caused by 

 the Copepoda were thickest, and an examination of 

 the stomach-contents of the fish on the yacht after- 

 wards showed us that the amount in one mackerel 

 was about the same quantitv as that caught by the 

 tow-net in five minutes. Prof. Newstead and I have 

 made a count of 8 c.c. of the tow-net gathering, and 

 estimate that it contains about 2400 specimens of 



