Sept. 29, 18S1] 



NATURE 



527 



regarding / as a function of c, v\e have in (15) the equation 

 mathematically expressing the strength of ihe current maintained 

 by the dynamo \\hen its regular action is reached. Using (15) 

 in (10) we find — 



-'-i-^ ('^^ 



which V e all kneu forty year> ago from Joule. 



In the shunt-dynamo the whole current, c' , of the working coil 

 branches into two streams, c through tlie elec'ro-magnet, and 

 d ~ c through ihe external circuit, whose strengths are inversely 

 as the resistances (if their channels. Still calling the resistance 

 of the external circuit E, we therefore have — 



c R = (.-' - c) E, which gives c = ^^ c' . ^iS) 



Hence, by Joule's original law, the expenditures of work per 

 uuit of time in the three channels are respectively 

 R' c'" . . . . working C'lil 



(E \- , 

 \c- . . e ectro-magnet ' , ^ 

 R + e) ^ , . ^I9) 



Hence, denoting as above by r the ratio of the whole work to 

 the work developed in the external ci'cuit, we have — 



J! 

 + E, 



external circuit 



\R + Ej \R + E) 



\r + e) 



_ „,(^ + Ef 



+ R{R + E) 



R'R"- 



+ (/?+ R')E -^ R{2R' + R)\ 



(20) 



(21) 



Suppose now R and /" given, and E t j l.e fi.und ; to mal e r 

 minimum. The solution is — 



E = 

 and this makes 



' A- + A" 



, R'(R + A') 2A'+ R 

 A2 R 



(22) 



(23) 



(24) 



A' 



- = c . 

 R 

 (22) and (23) become 



E^V^ (35) 



and r = I + 2 v'{i'(l + e)} + 2e . . . (26) 



For good economy r must be but little gi-eater than unity ; 

 hence e mast be very small, and therefore approximately 



E=.J(RR')\ .^^ 



and r= I + 2^.Uf *-^' 



For example, suppose the resistance of the electro-magnet to 

 be 400 times the resistance of the w orking coil — that is e = 40c — 

 and we have, approximately, 



E — 20 R', and r = I + 15. 

 That is to say, the resistance in the external circuit is twenty 

 times the resistance of the working coil, and the u eful work in 

 the external circuit is approximately \^ of that lost in heating 

 the w ire in the dynamo. 



FUNCTIONAL METAMORPHOSIS OF 

 MUSCLES ' 

 'T'HERE is no system in the animal body to which the axiom 

 -*■ of Gueriii, viz., that " function makes the organ," applies 

 with greater force than to the muscular system. Every student 

 of comparative myology knows that according to the use required 

 of a muscle we have alterations in its volume and connections, 

 or indeed its total disappearance, should its further services in the 

 animal economy be dispensed w-ith. These are the factors w hich 

 render muscular homologies in many cases so difficult to deter- 

 mine. There is one change, however, which is much more 

 common than is generally believed, viz., the transformation of a 

 muscle into fibrous tissue, or, in other words, its replacement by 

 a ligamentous structure possessing attachments similar to those 



' Abstract of paper read at the York meeting of the British Association, 

 by D. J. Cunningh.^m, M.D., F.R.S.E.; S:nior Demonstrator of Anatomy, 

 University of Ecjiuburgh. 



of its muscular ancestor. It might almost be laid down as a law 

 that whenever a muscle cea es to be of use fur contractile pur- 

 poses, and when, from its attachments, it might be of service as a 

 ligament, that it gradually in course of time beccme,- transformed 

 into fibl■ou^ ti-sue, and is handed down to posterity in this c< ndi- 

 lion. Indeed should it merely be a case of comparative value, 

 and should the balance of utility he in favour of a ligament, then 

 also will this metamorphosis in all probability take place. Of all 

 adaptation^ in the muscular system this is perhaps the most 

 beautiful, and instances of it are by no means rare. Thus, in 

 the feet of the arm.adillo, orycteropu-, pig, walrus, and several 

 other animals, certain of the intrinsic pedal muscles have become 

 fit rous bands, indubitably retained for some definite purpose, 

 although their obvious function i^ often obscure. The most 

 striking examples of this, however, are lo be found in the feet of 

 the horse, ox, sheep, camel, and their allie-. In the^e we are 

 a)ile not only to demonstrate with the utmost precision the par- 

 ticular muscles that have become ligamentous, but also the pro- 

 cess \.y which the change has been brought about, and the 

 rational/ of the transformation. 



The stispt-nsay liganunt of the fetlock in the horse is an ex- 

 ceedingly powerful structure, which lies in the sole of the foot 

 (i.e. upon the posterior aspect of the metatarsal b&ne) under 

 cover of the flexor tendons. It plays an important part in 

 the mechanism of the limb. Its attachments are such that it 

 prevents over extension at the fetlock or metatarso- phalangeal 

 joint, aid its value in this respect is evidenced by the fact that 

 when it is ruptured the horse becomes what is termed by vete- 

 rinary surgeons "broken down." In this condition the fetlock 

 joint sinks downwards towards the ground, whilst the hoof is 

 tilted forwards and upwards. 



This ligament is admitted on all hands to be derived from the 

 intrinsic pedal muscles by a transformation of the muscular 

 elements into fibrous tissue ; indeed it bears its history written 

 upon its face. Almost invariably a nan-ow streak of striated 

 muscular fibres can be detected upon its superficial surface which 

 points to its muscular oigin. Upon its deep surface fleshy fibres 

 in greater abundance are observed, but these are very pale, 

 owing to a large admixture of fatty tissue. 



The question now comes to be-— Which of the. intrinsic pedal 

 mu-cl s have entered into the formation of this ligament ? In 

 making this inquiry we have to keep two points in view : (l) 

 that in the horse the middle or third digit is alone fully developed ; 

 and (2) that in a typ'cal pentadactylous foot this digit is supplied 

 by three intrinsicmuscles, viz. : a two-headed flexor brevis, and tw'o 

 abductors or dorsal interussei (the second and thiid) inserted one 

 upon either side of the digit. It is reasonable to conclude, 

 therefore, that the suspensory ligament of the fetlock is derived 

 from one or more of these muscles. But independent remnants 

 of the two dorsal intcrossei are present, in addition to the liga- 

 ment, w hich clearly proves \he flexor breiii medii to be the source 

 of this structure. 



The dorsal interossei in the foot of the horse are of peculiar 

 interest. They are so minute that they can exercise little or no 

 influence upon the movements of the pes. They are simply to 

 be regarded as vestiges of former greatness, and as pointing to 

 retrograde development. They undoubtedly constitute a link 

 in the soft parts between our modern monodactylous horse and 

 its three-toed ancestor. They lead us back to a time when in 

 the foot of this animal there were two distinct interosseous 

 spaces, each filled by a well-marked interosseous muscle.. 



Still stronger evidence that the suspensory ligament originates 

 solely from the fexor inz'ts of the middle digit is obtained by 

 making thin transverse sections through its substance. We then 

 ob-erve that the sparse remains of muscular tissue are not con- 

 fined to the surface of the structure, but penetrate into its midst. 

 When the specimen is held against a dark ground, two crescentic 

 opaque outlines are noticed lying side by side in its substance. 

 Thee undoubtedly represent tracings of the two heads of the 

 flexor brevis, out of which the ligament is developed. On sub- 

 jecting the outlines to microscopic examination, we find that they 

 are mainly composed of muscular fibres, but every here and 

 there the continuity of this tissue is broken by fatty tissue, in 

 which are observed transversely-divided nen-es and blood-vessels. 



In the ox, sheep, and camel the suspensory ligament performs 

 the same office as in the horse. The presence, however, of two 

 digits (the middle and annular) complicates somewhat its inferior 

 attachments, i 1 order that it may operate so as to prevent over- 

 extension at both metatars vphalangeal joints. In each of these 

 animals the structure is undoubtedly formed by the two heads of 



