ON GRAnriC METHODS IN MECUANICAL SCIKNCE. 433 



to be noted that the theory of the instrument is the same as that of the 

 VVettle- Starke, being simply a disc and roller integrator. 



Closely allied to instraments for obtaining the area of the surface 

 are the moment planimeters. There are two possible ways of employing 

 planimeters for this purpose. The first of these ways was suggested in 

 connection with the disc, globe, and cylinder integrator by Sir William 

 Thomson,' and amounts to the integration of a simple linear differential 

 equation. This method has been treated in a paper- in connection 

 with sphere and roller mechanism. Another principle is to cause the 

 measuring roller to be directly turned at a rate which is made to vary, 

 not, as in the simple planimeter, with the value of the ordinate (y), but 

 with its second or third power. Though no method of directly doing 

 this has apparently been suggested, yet the same result is practically 

 effected by the beautiful application of a mathematical principle in the 

 ' moment integrator ' of Professor Amsler. 



This instrument can be employed for obtaining the contents of 

 embankments and the material moved in cuttings for civil engineering 

 purposes, in which not only the cross-sections vary, but the slope and 

 surface of the ground. These and other matters are described at length, 

 and also the limits of accuracy of planimeters are given, in a paper 

 already alluded to on mechanical integrators, in the ' Proceedings of the 

 Institution of Civil Engineers,' vol. Ixxxiii. For the history of plani- 

 meters the following paper by Favaro may also be cited : ' Beitriige zur 

 Geschichte der Planimeter,' von Dr. Antonio Favaro, 1873, published by 

 V. Waldheim, Vienna. 



The writer wishes to express his acknowledgment of the valuable 

 aid rendered him by his assistant lecturers, Mr. R. Holt (Whit. Schol.), 

 in preparing many of the diagrams, and Mr. J. F. Conradi, in connection 

 with the references in the Appendix, 



APPENDIX. 



CLASSIFIED LIST OF REFERENCE TO GRAPHICAL 



METHODS. 



The following is a list of Transactions, Proceedings, and Periodicals 

 which have been examined : — 



Transactions and Proceedings. 



Tleport of the British Association for the Advancement of Science. 

 Transactions of the Chesterfield and Midland Institution of Engineers. 

 Transactions of the Institution of Engineers and Shipbuilders in Scotland. 

 Proceedings of the Institution of Civil Engineers. 

 Proceedings of the Institution of Mechanical Engineers, 

 Journal of the Iron and.Steel Institute. 



' Proceedings of the Rnjal Socief;/, vol. xxiv. p. 262, and vol. xxvii. p. 371. 

 = ' Theory of Continuous Calculating Machines,' by ProfesEor Hele-Shiw. PMlo* 

 jopkiral Transactions of the Royal Society, Part 11. 1885. 



1892. F f 



