212 



NATURE 



\Jan. 13, 1876 



then, the entrance between the margins of the upper lip 

 being completely closed, they forcibly break it open with 

 their fore-legs, grasping with them between the margins, 

 and shaking the anthers in order to gain their pollen ; 

 thus a good deal of the smooth, powdery pollen grains, 

 falling out of the shaken anthers, is received within the 

 brushes and feathery hairs of their fore-legs, and thence 

 carried to the pollen-collecting orifice of the posterior 

 tibiae. This incommodious and wearisome labour, al- 

 though performed by the humble-bees with admirable 

 dexterity and perseverance, contrasts remarkably with 

 the swift and light manner of their gathering pollen, and 

 at the same time sucking honey in flowers adapted to 

 them ; * and many peculiarities of the flowers of Rh. alpi- 

 nus. would be quite unintelligible under the supposition 

 that pollen-collecting humble-bees were the true and ori- 

 ginal fertilisers of them. The honey, so copiously secreted 

 in the base of these flowers, would be quite useless to 

 the plant if pollen-collecting humble-bees were its true 

 fertiUsers ; the minute opening between the two lateral 

 flaps at the tip of the beaked prolongation of the upper 

 lip would likewise be useless, and the closeness of the 

 usual entrance between the margins of the upper lip 

 would be a mere embarrassment to the fertilisers. Sup- 

 posed, on the contrary, that Lepidoptera are the original 

 fertilisers of Rh. alpinus, all these pecuharities are easily 

 to be understood as very useful, nay, as indispensable to 

 the plant ; for honey is the only food eagerly searched for 

 by butterflies, and the closeness of the usual entrance, as 

 well as the existence of the minute opening in its very 

 place, are required in order to induce visiting butterflies 

 to insert their proboscis in the only manner which can 

 effect cross-fertilisation. Hence, in spite of the frequent 

 visits of pollen-collecting humble-bees, and in spite of 

 their probably effecting many cross-fertilisations, the 

 flowers of Rh. alpinus are without any doubt to be con- 

 sidered as adapted exclusively to butterflies. 



But considering the original function of the under lip 

 as a landing-place for bees, and considering that the 

 most nearly-allied genera, Euphrasia, Mclampyrmn, 

 Pedicidaris, as well as Rhinatithus crista-galli, are all 

 adapted to bees, we can hardly doubt that also the 

 ancestors of Rh. alpinus have been adapted to cross-ferti- 

 lisation by bees, and the question maybe started, by what 

 connecting forms these ancestors could be transformed 

 into the present form of Rh. alpiiius. We may confi- 

 dently suppose that they retained the usual entrance for 

 humble-bees, until the beaked prolongation of the upper 

 lip, the minute opening at its tip, and the lateral flaps of 

 this opening were so developed as to secure cross-fertilisa- 

 tion by butterflies. 



In this respect Rhinanthus ahctorolophus is of especial 

 interest ; for it represents really what by reflection we are 

 induced to suppose once existed in the connecting forms 

 between Rh. alpinus and its ancestors (compare Figs. 

 76-81). Rh. alectorolophus has indeed retained the usual 

 entrance by which humble-bees may insert their pro- 

 boscis in order to suck the honey {e, Figs. 79, 80), and 

 may be regularly cross-fertilised by sucking humble-bees, 

 whilst at the same time the minute opening {p, Figs. 76- 

 81) and all those peculiarities which secure cross-fertilisa- 

 tion by sucking butterflies, are developed. 



From the structure of its flowers, as shown by Figs. 

 78-81, we should expect that this species would be cross- 

 fertilised as well by sucking humble-bees as by butterflies. 

 My direct observation of the fertilisers, however, in the 

 same localities with Rh. alpinus, shows no remarkable 

 difference between Rh. alectorolophus and Rh. alpinus. 

 Two species of butterflies — Colias Phicomotie arvdi Pieris 

 Napi — repeatedly inserted their thin proboscis into the 

 minute opening at the tip of the upper lip of Rh. alectoro- 

 lophus, apparently sucking honey ; numerous specimens 



• Compare /Esculus Hippocastanum in " H. Miiller, Die Befruchtung 

 der Blumen durch Insecten," p. 155. 



of Bombus mastrucafus, Gerst., ^ % terrestris, L. ^ , 

 Proteus, Gerst., ^ , and p>ratorum, L. ^ , were occupied 

 in collecting the pollen of Rh. alectorolophus in cuite 

 the same manner as in Rh. alpinus. Only twice I saw 

 humble-bees {B. mastrucatus, Gerst,, ^ ) sucking the 

 honey of Rh. alectorolophus, but not legitimately, by the 

 entrance between the margins of the upper lip, but rapa- 

 ciously ; once by inserting their proboscis on the under- 

 side between calyx and corolla, and piercing the corolla- 

 tube a little above its centre ; another time by forcibly 

 passing its proboscis through calyx and corolla. 



Finally, it is to be noted that self-fertilisation of Rh. 

 alectorolophus is apparently impossible, for the stigma 

 always projects, just as in Rh. major and alpinus; and 

 when the corolla drops off (in the line xx. Fig. 77), and 

 brings its anthers in contact with the stigma, this is 

 already withered. Hermann Muller 



BEATS IN MUSIC* 



/^NE of the subjects treated of in Helmholtz's great 

 ^^ work on Acoustics is that of " Beats." It is one of 

 much interest, both theoretically and practically : theo- 

 retically, because of the difficulty that attends the inves- 

 tigation of the phenomena, and of the discussions and 

 misunderstandings that have taken place thereon among 

 writers on scientific harmonics ; practically, because beats 

 might form an element of great utility in regard to certain 

 practical operations, were it not that their nature and use 

 are at present almost entirely unknown to practical 

 musicians. 



The history of the knowledge of beats is curious. They 

 were mentioned as early as 1636 by Mersenne, and were 

 afterwards noticed by Sauveur and others, but no suffi- 

 cient explanation of their theory was given till the publi- 

 cation in 1 749 of the learned work on Harmonics by the 

 celebrated mathematician Dr. Robert Smith, Master of 

 Trinity College, Cambridge. Dr. Younj;^ and Dr. Robison, 

 both eminent writers on acoustics, quarrelled about 

 Smith's work. Young said it added nothing to the know- 

 ledge of the subject, whereas Robison declared that it 

 contained the greatest discoveries made since the days of 

 Galileo ; the fact, however, being probably that neither 

 of them appreciated the main portions of the work at all. 

 Chladni appears never to have studied the more difficult 

 portion of the subject, and though he gives generally his 

 references very freely, he does not mention Smith's 

 name. 



It was only in 1858 that Mr. De Morgan, in an able 

 paper, published in the Cambridge Philosophical Trans- 

 actions, pointed out the merit of Dr. Smith's investig-a- 

 lion, and cleared up its learned obscurity. 



Helmholtz treats the subject with his usual ability, but 

 it is very singular that he, like Chladni, makes no allusion 

 whatever to Smith's work, and as it is incredible that he 

 should have passed over such a remarkable and profound 

 theoretical investigation if he had been acquainted with itjj 

 I am inclined to believe that the book was unknov 

 to him. 



Considering the very few sources of information tha 

 exist in regard to beats, and the difficult shape in whicl 

 this information is embodied, I have thought it might ' 

 useful, especially to practical musicians, to attempt to give 

 some account of the subject in a more popular form ; an<f 

 in doing so I wili endeavour to introduce the investiga 

 tions of Smith, in combination with those of the late 

 investigator. 



There are chree distinct kinds of beats, differing con^ 

 siderably from each other in the nature of their cause 

 and in the circumstances that attend them, and the coi 

 fusion between them has caused much error in their| 



* By W, Pole, F.R.S., Mus. Doc. Oxon. 



