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 = $A C, the Z 
A CP 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 +) : 810.3 
4} — == 2913.75 :1320.85,* or as 11 
a “* 
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- 
onderance of the weight of the extensors be- 
‘comes greater ifthe double action of each be 
omitted in the computation and the whole 
weight of each set be substituted; the pro- 
‘portion then becomes, 2403.2 : 810.3, or as 
8 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- 
at 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 glutei 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 
bein 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 leg, viz. the 
_ glutei = 936.0, vasti and cruralis = 1092.0, so- 
. is == 375.2, and 1021.1 = the weight of those 
_ flexors and extensors of the leg acting over two 
eins, viz the rectus = 199.2, semitendinosus 
== 128.2, semimembranosus = 206.5, biceps 
== 129, gastrocnemius 358. 
_ + A grain = 0.067508 gramme. 
VOL. 111. 
MOTION. 
417 
other elevated, as in fig. 219; he is sustained in 
this position by the glutei (f), the quadratus 
femoris (y), and the gastrocnemius and soleus 
(2). Then if the weight r = 120lb., the weight 
of the porter 150lb., the line rs be the direc- 
tion of the force of gravity cutting the femur 
and tibia in c and a, 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 6 will 
be = '3%lb. = 75lb., and of the section 4 
to c, by supposition, is = 47, therefore the 
weight of the are a b c = 75 +47 = 122, 
also by supposition the section c v = 20, 
and consequently the whole arc ¢ bv gr = 
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: } the distance 
J 6 is to the distance m b as 1 is to 8; ov 
is tot vasito 6;}kdistopdas1 to 3; and 
t v to b m as 3 to 4; hence we derive these 
proportions ;— 
tv:bm::r-abvr:gz, 
or 3:4:: 120-4 122: 3223lb. = the pressure 
of the weight of man and load at the point z. 
ap:bm::r+abvdf:s, 
or 3:8::120 $- 150 : 720 = the force of the 
whole weight at s. 
Lb fi:mb::r+tabc:g, 
2E 
