Nov. I, 1877] 



NATURE 



9 



quently been expressed to me before in the same manner and in 

 the like terse and elegant language, is now enforced by what he 

 deems to be Prof. Carey Foster's judicial opinion, delivered at 

 the Plymouth meeting ; and I find myself, therefore, fully jtisti- 

 fied in my opinion that by his introduction of the word '* inten- 

 tionally " Prof. Carey Foster made his judgment legitimately 

 bear a meaning, which, as he has stated, he would consider 

 insulting to my character. And I cannot but believe that 

 Prof. G. Carey Foster will regret having thus given a new 

 handle to a man who obviously wishes to insult me on account of 

 my antagonism to spiritualism. As the writer of the post- card 

 continues to use Prof. G. C. Foster's authority, after that gentle- 

 man's explicit disavowal of the offensive meaning here attached 

 to it, and as I may, of course, expect that he will continue to 

 avail himself of that authority, I should like him to know 

 through your columns that it is scarcely worth while for him to 

 trouble himself to repeat these attacks, since they have long 

 since ceased to do anything else than amuse me, and will only 

 furnish me with materials for amusing other people. 



It seems much to be regretted that neither spiritualism nor 

 attendance at the meetings of the British Association, nor even 

 the reading of Nature seems able to teach this person to behave 

 like a gentleman. WiLLiAM B. Carpenter 



October 29 



Potential Energy 



Your correspondent '* X." has described some of his troubles 

 respecting potential energy. Many a learner could describe 

 similar troubles respecting force and energy in general. They 

 who earnestly contend for definiteness and accuracy do not 

 always teach with definiteness and accuracy. For example : in 

 his "Treatise on Heat," p. 137, Dr. Tyndall tells me that by 

 raising a weight from the floor I have conferred upon the weight 

 potential energy. Presently he tells me that this energy is 

 derived (not from me, but) from the pull of gravity. He next 

 tells me that we might call the energy with which the weight 

 descends, moving force, i.e. he teaches me to confuse force and 

 energy ; and after all this he bids me remember that " exactness 

 is here essential. We must not now tolerate vagueness in our 

 conceptions." 



Take another example. In his lecture on " Force " (Nature, 

 vol. xiv. p. 462), Prof. Tait teaches that force is a mere name, 

 and that it has no objective existence ; he also teaches that the 

 product of this non-existence by its displacement has an objective 

 existence. Few learners would say that is a very lucid state- 

 ment. Again, in the same lecture he says "there is no such 

 thing as centrifugal force, and accelerating force is not a physical 

 idea at all ; " but in his " Nat. Phil." he speaks of both these 

 forces, and describes their effects (Nos. 185, 187, 598, 248). 



When teachers deservedly eminent make statements like' the 

 foregoing, so likely to mystify and confuse a novice, it is no 

 wonder that there is a good deal of smattering in popular 

 science. 



Prof. Tait says " the so-called accelerating force is really no 

 force at all, but another name for the kinematical quantity accele- 

 ration." I venture to entirely disagree with this statement, and 



for the following reason : — — — is a number, and may be that 



number of units oi force, or that number of units of acceleration. 

 When it is called accelerating force it is the representative of 



fn — , when m = i, and m does not appear in the expression ; 



c^ t' 



dv 



and it means - — units oi force. 



d t ^ 



it means — ^ units of acceleration, 

 d t 



When it is called acceleration 



Accelerating force is just as 



real as moving force, for- it is, in fact, the wth part of the 

 moving force. In like manner v may mean either v units of 

 velocity, or v units of momentum ; in the latter case it is the 

 representative of mv, when w = i, and means the momentum 

 of a unit of mass which has v units of velocity. In like manner 

 VI may mean either m units of mass, or m units of momentum, or 

 m units of kinetic energy ; in the two latter cases it is the 

 representative of mv or of fwz/' when v — \, and means the 

 momentum, or the vis viva of m units of mass moving with unit 

 of velocity. 



A few simple definitions would remove the difficulties re- 

 pecting force. Thus : If a mass of m un'ts of mass is at any 



instant receiving an acceleration of a units of acceleration in 

 any given direction, the force which is acting on it at the given 

 instant in the given direction is ma units of force. The force 

 acting on the mass in the direction of its motion is called the 

 moving force. The force in the normal to the direction of its 

 motion and towards the centre of curvature is called the 

 centripetal force. An» equal and opposite force is called the 

 centrifugal force. The mih. part of the moving force is called 

 the accelerating force, which is the moving force acting on a 

 unit of mass. 



In the case of a planet's orbit it is too common to give the 

 name centrifugal force to two forces which generally differ both 

 in magnitude and in direction, one of them being in the direction 

 of the normal, the other in the direction of the radius-vector. 

 This is the last instance which I shall give of sins against 

 definiteness and accuracy. E. G. 



Bardsea 



' Hartlaub's "Birds of Madagascar" 



The excellent review, exhibiting traces of a master's hand, of 

 the above-named useful work, which appeared in Nature 

 (vol, xvi. p. 498) prompts me to offer some remarks on the orni- 

 thology of Madagascar and its neighbouring islands, and to take 

 exception on two points therein laid down. 



The first of these is propounded by your reviewer and seems 

 to me absolutely contrary to fact. He says :— " Compared with 

 Madagascar itself the appendent island groups ' are poor in 

 species, although in every case there are many interesting forms 

 among their winged inhabitants. The Comoro Islands muster 

 only some forty-four species of birds, Mauritius about sixty, of 

 which fifteen or sixteen have been introduced by man's agency, 

 and Bourbon about the same number, while Rodriguez appears 

 to have only about twenty-five species now existing in it, of 

 which four or five are certainly recent introductions." 



Now twenty years ago my friend, Mr. Sclater, in that remarkable 

 paper of his on the geographical distribution of birds {y^mrn. Linn. 

 Sac. Zoology, ii. p. 130), which so happily laid the tiue foundation 

 for our present researches into the subject, showed that the 

 proper mode of comparing the wealth or poverty of one fauna 

 with another was to state the proportion which the number of 

 species composing it bears to the area over which they range. 

 The same view was adopted very shoitly after by Mr. Wallace, 

 who took occasion (Idis, 1859, p. 449) to question certain of 

 Mr. Sclater's results, and its correctness seems to have been since 

 generally admitted. Yet, applying this test to Madaga9car and 

 its neighbouring islands, we find a state of things to exist very 

 different from that which your reviewer has alleged. The area 

 of Madagascar is said^ to be 10,751 German square miles, that 

 of the Comoros collectively 38 '57, of Mauritius 3476, of Bourbon 

 42*05, and of Rodriguez 5. It will be sufficient for my purpose 

 to compare the first and last of these. Your reviewer is willing 

 to allow twenty indigenous species to Rodriguez ; then — 



Area of 

 Rodriguez. 



5 



Area of 

 Madagascar. 



10,751 : 



_ 10,751 X20 



Species in 



Rodriguez. 



20 



• 43.004- 



Sp-cies in 

 Madagascar. 



: X 



But instead of an avifauna of 43,004 species, or about four 

 times the number known to exist throughout the whole world. 

 Dr. Hartlaub gives it 218, and your reviewer generously adds 

 two more, making 220 ! Suppose (an extravagant supposition) 

 that future explorations enable us to double the last number, it 

 is Madagascar that will still be out of all proportion " poor in 

 species" compared with "the appendent island groups," and 

 not these with Madagascar. 



The next point to which I must demur is that "the indi- 

 viduality of the fauna of Madagascar is so unique that even that 

 of New Zealand can hardly be compared with it." I will leave 

 to fitter hands than mine to show that this is not the case gene- 

 rally, and shall only remark here that it is not so with birds. Of 

 the sub-class Ratita there have been until lately five strongly- 

 marked groups, each of which is equivalent to an " order " 

 amon^ the Carinatce. Now two of these groups were peculiar to 

 New Zealand, and one (Apterygida;) is so now, while the other 

 (containing the families Dinornithidce and Palapterygidce) is but 

 recently extinct. Willingly granting that ^pyornis, when we 



' Behin"und Wagner, "Arealund Bevolkerung der Erde" (Petennaon's 

 Geogr. Mittheilungen, Erganzungsheft, November 10, 1876). 



Ba 



