330 Rev. S. Haughton on some [May 2 3 



2. Llama. Pectineus Muscle. 



in. 



a. Length of pubic origin 1*91 



b. „ femoral insertion 3*50 



c. ,, anterior fibre 3*05 



d. „ posterior fibre 6*91 



e. First diagonal 4'09 



f. Second diagonal 6*77 



Hence we find 



a5 = 1'91 x3-50= 6-68 

 c^=3'05x 6-91 = 21-07 

 ah + cd =27*75 



e/=4-09x 6-77=2^69 

 Difference = 0*06 

 This difference amounts to P ar<: °^ * ne wn °l e - 



IH. tc On some Elementary Principles in Animal Mechanics. — 

 No. VI. Theory of Skew Muscles, and investigation of the con- 

 ditions necessary for Maximum Work." By the Rev. Samuel 

 Haughton, F.R.S., M.D. Dubl., D.C.L. Oxon., Fellow of Tri- 

 nity College, Dublin. Received April 3, 1872. 



Let us suppose two bones, AB and A'B', not lying in the same plane, 

 connected by muscular fibres ; and through these bones let us draw any two 

 planes intersecting in a line P Q ; if the bone A B be fixed and the bone 

 A' B 1 be movable and compelled to turn round the line P Q regarded as 

 an axis of rotation, it is required to find the conditions necessary in order 

 that the work done by the contraction of the muscle shall be a maximum. 



A muscle such as is here imagined will form a skew surface, and no 

 two of its fibres will intersect in space. I have succeeded in demonstrating 

 the following propositions in the case of maximum work : — 



1. The axis of rotation P Q must be formed by the intersection of rect- 

 angular planes passing through A B and A' B'. 



2. A certain hyperboloid of one sheet may be drawn passing through 

 the bones A B and A' B'; and the axis of maximum work is a generator of 

 this hyperboloid belonging to the group different from that to which A B 

 and A' B' belong. 



3. The generator which is the axis of rotation of maximum work is 

 found by the solution of a biquadratic equation. 



4. In the muscles which are found in nature, the root of the biquadratic 

 which fixes the axis of maximum work is always nearly equal to zero. 



5. If there be n fibres in the skew muscle, we can draw a certain line 

 O O', joining two points on A B and A B' (or A B and A B' produced), 

 such that a single fibre acting in the line O O', with n times the force of a 



