MOTION. 



417 



will be drawn to P. In this case the contrac- 

 tile force is more than sufficient for the object 

 to be attained. All other things remaining 

 the same, the space C P will be greatest 

 when the obliquity is that which is stated in 

 the proposition. If A P = f A C, the . 

 A C P is 48 35' nearly. 



From the researches of the Professors Weber 

 we learn that the weight of the extensor muscles 

 generally predominates over that of the flexors; 

 those of the leg being selected, their propor- 

 tions in two well-formed healthy subjects were 



found to be as ^2403.2 + _l^ 2 llL) : 810.3 



1021.1 

 H = 2913.75 : 1320.85,* or as 11 



to 5 in favour of the extensors, the proportions 

 are divided by 2, or halved, to allow for 

 the double office which some muscles perform 

 of both flexion and extension, according as 

 either end becomes the fixed point. The pre- 

 ponderance of the weight of the extensors be- 

 comes greater if the double action of each be 

 omitted in the computation and the whole 

 weight of each set be substituted ; the prp- 

 portion then becomes, 2403.2 : 810.3, or as 

 3 to 1 nearly. 



The weight of the extensor muscles, when 

 compared with that of the rest of the leg, is in 

 the proportion of 5 to 9, and to the whole of 

 the muscles, including the flexors, as 3 to 4, 

 consequently the extensor muscles of the leg 

 weigh three-fourths of the whole series. 



Borelli has given approximate values for 

 the powers of a great number of the muscles 

 of the human body, from which we select a 

 few computations which will convey an idea of 

 the enormous amount of their absolute power 

 and the large proportion of it which is sacri- 

 ficed in order to gain velocity. Borelli states 

 that the whole force expended by the muscles 

 of the arms, when stretched horizontally, is 

 209 times greater than that of any weight sus- 

 pended at its extremity, and that the force of 

 the biceps to that of the brachialis is as 3 to 2.6, 

 or as 15 to 13, and their absolute forces as 300 

 to 260. He estimates the force of the deltoid 

 at 61600 pounds, the sum of the forces of the 

 intercostal muscles at 32040 pounds, and of 

 the glutaei at 375420 pounds. The extensor 

 muscles of the hip, knee, and ankle-joints 

 have also a large proportion of their power 

 sacrificed to velocity; the amount of this inter- 

 change has been estimated upon the following 

 principles of Borelli. 



Let us suppose a porter carrying a weight to 

 be in the act of stooping in order to enter a door- 

 way with his load ; his body is bent, with one leg 

 raised from the ground, and the heel of the 



* 2403.2 = the weight of the muscles in 

 grammest acting over one joint of the lea, v i z . the 

 glutfei = 936.0, vasti and cruralis = 1092 so- 

 leus = 375.2, and 1021.1 = the weight of those 

 flexors and extensors of the leg acting over two 

 joints viz therectu S== 199.2, semitendinosus 

 = U8.2, semimembrariGsus = 206.5, biceps 

 = l-iy, gastrocnemius 358. 



t A grain = 0.067508 gramme. 



VOL. IK. 



Fig. 219. 



other elevated, as in fig. ?19 ; he is sustained in 

 this positton by the glutei (f), the quadratus 

 femons ( y), and the gastrocnemius and soleus 

 (/). Then if the weight r = 120lb., the weight 

 of the porter 150lb., the line r s be the direc- 

 tion of the force of gravity cutting the femur 

 and tibia in c and x, the centre of gravity of 

 the man be at 6, and the common centre of 

 gravity of the man and his load be at a, then 

 the weight of the man from the head to b will 

 be = 'fib. = 75lb., and of the section b 

 to c, by supposition, is = 47, therefore the 

 weight of the arc a b c == 75 + 47 = 122, 

 also by supposition the section c v x = 2o[ 

 and consequently the whole arc a b v x ~ 

 142, also the distances of the directions of the 

 muscles from the axes of the joints to the dis- 

 tances of the line of gravity are, according 

 to Borelli, in the following ratio: 1 the distance 

 / b is to the distance m b as 1 is to 8; \ o v 

 is to t v as 1 to 6; 1 2 k d is to p d as 1 to 3; and 

 t v to b m as 3 to 4 ; hence we derive these 

 proportions : 



t v : b m . : : r -f- a b v x : z } 

 or 3 : 4 : : 120 + 122 : 322lb. = the pressure 

 of the weight of man and load at the point g. 



a p : b m : : r + a b v d f : s, 

 or 3 : 8 : : 120 + 150 : 720 = the force of th = 



whole weight at s. 

 i 



b j : >/i b : : r 



2 i: 



