March 20, 1879] 



NATURE 



467 



:he notes on the keyboard, in the same way Fig. 11 shows 

 hat the horse, at the moment when he falls back upon 

 -he earth, is supported only by one foot ; then, when the 

 two diagonal feet strike the ground together in their turn, 

 the horse has at this moment a triple support. Without 

 the notation of paces we had certainly failed to distingxiish 

 this series of supports. 



The gallop of the racecourse used generally to be con- 

 sidered as a pace of two steps, in which the horse struck 

 the ground alternately with the two fore-feet and the two 

 hind-feet. This gaUop shows itself in the notation as a 

 pace of four steps ; the tracing dissociates the two fore- 

 feet and the two hind-feet, although they foUow each 

 other at a very short interval. 



The transition from one pace to another, impossible to 

 determine by direct observation, is clearly inscribed in 

 Fig. 12. 



IV. Artistic Representation of the Horse and other 

 Animals. — The artistic representation of animals requires 

 a special and varied acquaintance with their peculiarities. 

 Nothing can replace the patient study by which the 

 painter or the sciilptor acquires an anatomical knowledge 

 of the limbs of animals and the aspects which they assume 

 in different positions. But if the painter or the sculptor 

 wishes to animate his work, if he wishes to show the horse 

 putting forth its efforts in powerful traction, or to repre- 

 sent it urged rapidly forward in the race, it is necessary 

 to have an exact acquaintance with different paces. 



That which is true of the horse is equally so of other 

 animals ; but all present among themselves such great 

 analogies in this respect, that if we are acquainted with 

 the paces of the horse, we can represent those of any 

 other animal 



The summary analysis we have just now made of the 

 rhythms of steps in each pace is not yet sufficient to 

 express the attitudes which represent them ; we have as 

 yet only examined in connection with these movements 

 one of the two essential ideas. We are acquainted with 

 the relations of time ; it is necessary also to become ac- 

 quainted with the relations of space, that is to say, to 

 know at each moment in what place to find each of the 

 members raised or planted upon the ground. Obliged to 

 abridge this already long discourse, I will not tell you 

 how one determines graphically the phases of the move- 

 ment of a foot that is raised, but I will show you sum- 

 marily how we determine the place where each foot is 

 broughtdown. This indication is furnished by the im- 

 print wnich the horse leaves upon the groimd. M. de 

 Curnieu, Capt. Raabe, and M. Lenoble du Teil have 

 studied with particular care these imprints or tracks of 

 the horse at different paces. The smooth sand of the 

 sea-shore presents a surface admirably adapted for this 

 study. Persons who have acquired the habit, easily 

 decipher such imprints. But in order to render them 

 easily read by every one, we have conceived the idea of 

 giving a different form to the shoes of the fore-feet from 

 those of the hind-feet by furnishing the latter with clamps. 

 The principal paces represented by their tracks have 

 been thrown together in Fig. 13, which I have borrowed 

 from M. Lenoble du Teil. In combining with the 

 idea of the rhythms, that of the place where each foot 

 would be planted, the errors of attitude which disfigure so 

 many chefs d'asuvres, would be avoided. You will, 

 perhaps, say that few persons are capable of recognising 

 faults of this kind. On this point one might repeat what 

 Baron Dupin said with respect to perspective in its rela- 

 tion to the art of painting. " In proportion as exact 

 knowledge becomes more widely diffused, many faults 

 which to-day only shock a small number, will shock the 

 general public, and artists will no longer be able to 

 perpetrate them with impimit)'." 



Those artists who at the present time make such praise- 

 worthy efforts for the correct representation of the horse, 

 would find great assistance from making use of the 



notation of paces. Let us see in what way. Take, for 

 example, the notation of the trots. We all grant, in the 

 first place, the possibility of dividing each step into a 

 series of successive instants, ten or twenty, for example. 

 At each of these instants the horse will have a different 

 attitude, but throughout the time the limbs diagonal to each 

 other will be executing the same motions at the same time. 



Let us take one of these instants at random and mark 

 it by a vertical line (Fig. 14). The notation shows txs 

 that at this instant the right hind-foot and the left fore- 

 foot are planted upon the ground, but that the right fore- 

 foot and the left hind-foot are still raised, and are about 

 to be set down. That is exactly as represented in the 

 figure. 



Upon another notation (Fig. 15) we have chosen 

 another instant, that in which the horse is suspended in 

 the air, and when the hind-feet have already quitted the 

 ground, whilst the fore-feet do not yet touch it. 



Let us pass on to the pace of the gallop (Fig. 16). The 

 moment chosen is that in which the horse falling back 

 upon the hind-foot has just made his first step. Two 

 limbs in diagonal relationship are about to strike the 

 groimd at the same time, namely, the right hind-foot and 

 the left fore-foot, represented as already being lowered 

 towards the earth. As to the right fore-foot, that will 

 strike the ground last, accordingly it is shown as still the 

 furthest removed from the earth. 



With regard to the foot pace, which is the most diffi- 

 cult to explain, three instants have been selected on the 

 notation : i. That where the hind-foot is about to be 

 raised, and where the fore-foot is in the middle of its ele- 

 ration (Fig. 17). At this moment there are three feet at 

 rest, which only takes place with horses when making an 

 effort of traction. 2. The moment in which the two 

 diagonal feet are raised, the one having just quitted the 

 ground and the other being about to be placed upon it 

 (Fig. 18). 3. The moment when the animal, supported 

 by two feet on the same side, is raising one of its fore-feet 

 and is about to set down one of the hind-feet on the same 

 side (Fig. 19). 



These pictures have no other pretensions than to be 

 correct as regards the position of the members ; it would 

 be the artist' s duty to add elegance of form. But is it not 

 something to have a simple and sure means of representing 

 a horse in any pace and in any phase of the steps in that 

 pace ? The employment of the graphic notation would give 

 to the artist the double advantage of representing the paces 

 with truthfulness and of varying them to an extent almost 

 illimitable. Now, imperfection in art is not displayed 

 solely by errors that may be conmiitted, for too often an 

 artist who is thoroughly acquainted with a correct attitude 

 repeats it with regrettable monotony. 

 {To be continued.) 



GEOLOGY OF NATAL AND ZULULAND 



COME years have now passed since Mr. Griesbach 

 •^ gave to the Geological Society his paper and map 

 illustrating the geology of Natal and the borders of 

 Zululand. Passing events now g^ve to his investigations 

 the greatest interest, not simply due to the possible light 

 that may be thrown on unsolved, or partly kno^vn, problems 

 by the sojoium in that area of the contingent that has 

 lately left our shores, but from the fact that the safety 

 and success of our forces in great measure depends on 

 the surface contour and physical character of the country 

 to be traversed, which are necessarily directly dependent 

 on its geological structure. 



Few can have studied a geological map, without noticing 

 the close connection between long lines of escarpment 

 and belts of level plains with particular rocks, or noticing 

 the marked imiformity in direction of strike of geological 

 formations over large portions of the earth's surface ; 

 rock series after rock series plimging beneath its neigh- 



