328 



Rev. S. Haughton on some 



[May 2, 



to such a point for the purpose of guarding against undue expectations 

 and of disclaiming excessive pretensions. The work that has been executed 

 in India is of such a character, as attested by an enormous accumulation 

 of results treated with absolute rigour, that, as respects some branches of 

 it, I do not shrink from saying that improvement is scarcely possible. In 

 respect to horizontal angles, the most important of all its branches, an 

 elaborate investigation by Colonel Walker, R.E., F.R.S., the present head of 

 the Survey, shows that the probable error of such angles, deduced impar- 

 tially from a vast mass of materials, lies between -f0"'28 and + 0"'20, 

 according as the circumstances are more or less favourable *. I believe that 

 residual errors of that small amount contain hardly any instrumental or 

 observational element, but that they are chiefly due to atmospheric dis- 

 turbances, which no instrumental perfection can control. 



As to vertical angles, the test of direct levelling compared with trigono- 

 metrical levelling, applied to a distance of 2700 miles, shows a difference 

 between the results of these two independent methods averaging 7'3 inches 

 per 100 miles, or of an inch per mile. There seems little room for 

 instrumental improvement here. 



In respect to astronomically determined azimuths, I hope the present 

 instrument will give improved results, on account of the superior steadiness 

 of level which I thiuk it possesses. 



For the determination of astronomical latitudes it has more powerful and 

 more complete vertical appliances than any former theodolite, and it should 

 therefore give better results. 



Finally, I believe it will be found to be more permanent in its adjust- 

 ments, and more convenient both to adjust and to use, than any of its pre- 

 decessors. To these points, as those which makers, not being observers, 

 are peculiarly prone to overlook or mismanage, I have given the most 

 earnest attention, knowing how indispensable it is that a man engaged in 

 the most difficult and refined of all observations should be spared every 

 anxiety and inconvenience which it is in the power of mechanical contriv- 

 ance to prevent. If I have in some measure only attained this apparently 

 humble object, I shall feel that the labour of years and the anxious pon- 

 derings of many a sleepless night have not been in vain. 



II. " On some Elementary Principles in Animal Mechanics. — No. V. 

 On the most perfect form of a Plane Quadrilateral Muscle 

 connecting two Bones." By the Rev. Samuel Haughton, 

 F.R.S., M.D. Dubl., D.C.L. Oxon., Fellow of Trinity College, 

 Dublin. Received April 3, 1872. 



Let us suppose two bones, A B and A' B', lying in the same plane, joined 

 by muscular fibres, and any two planes drawn through these bones inter- 



* Account of the operations of the Great Trigonometrical Surrey of India, by Col. 

 J. T. Walker, E.E., F.R.S., &c., Superintendent of the Survey, vol. i. pp. So, 84, 



