506 REPORT — 1894-' 



« 

 Anton Favaro, of Padua, called attention to them in his ' Beitrage zur 



Geschichte der Planimeter ' (' Allgemeine Bauzeitung,' Wien, 1873). In 

 this paper it is pointed out that Gonnella, even thougli anticipated in the 

 invention by Hermann, was the first to publish anything about a Plani- 

 meter. 



His first instrument was of Type I., with the recording wheel rolling 

 on a cone as described. Soon after he replaced the cone by a disc. 



Gonnella had one instrument made, but it seems he was unable from the 

 want of skilled labour in Florence to obtain a well-executed piece of me- 

 chanism. When the Archduke of Tuscany wished to add a well-made plani- 

 meter to his collection, Gonnella looked for its execution to Switzerland, 

 Avhere tlie flourishing watch industry had developed accurate workmanship. 

 He accordingly sent, in 1825 and 1826, through a Florence merchant, 

 numbers of drawings to different firms in Switzerland, without, however, 

 succeeding in getting Mdiat he wanted. 



In 1826 the Swiss engineer Oppikofer invented a planimeter, and this 

 was made in the following year. How much he had heard of Gonnella's 

 invention or of Hermann's cannot now be decided. It is, of course, quite 

 possible that he should have made an independent discovery. Bauern- 

 feind estimates that at that time about a billion areas had annually 

 to be evaluated in Europe. He also gives in the paper quoted a pretty 

 long list of various contrivances for facilitating this work, and which, 

 by the way, were called planimeters (they were not integrators). The 

 problem was, therefore, one that pressed for a solution, and it would be 

 quite in conformity with other instances in tlie history of science that 

 several men should perfectly independently make the same invention. 

 Nevertheless, there is a possibility if not probability that Oppikofer should 

 have heard of Gonnella's invention. Anyhow, it is his instrument which 

 became the starting-point of the further development of planimeters. 



Oppikofer, it seems, put himself in communication with the mechani- 

 cian Ernst in Paris (before 1836) to introduce the instrument in France. 

 Thus it comes that planimeters of Type I. are known in France by the 

 name of Ernst, who improved them and made them practical instru- 

 ments. He retained the wheel rolling on a cone, although Gonnella had 

 already in 1825 replaced the cone by a horizontal disc. Ernst received, 

 in 1837, a portion of the Montyon Prize as a reward. 



It will be remembered that the cone allows only of positive ordinates 

 of the curve. The engineer Wetli, of Ziirich, tiied (1849) to remedy this by 

 using two cones with their vertices opposite, so that the upper edges of 

 both formed one straight line. In order to make the path for the wheel 

 continuous he meant to cover both with one disc to be turned by the cones. 

 But then he found, of course, that he could do without the cones if only he 

 drove the disc so that its rotation was propoi'tional to the side motion of 

 the line QT. Having the idea of the disc given, we see at once that 

 this disc is only a special case of a cone which has degenerated into a 

 plane, but it is always of interest to learn the roundabout way in which 

 improvements are made.' 



This improvement was, as has already been mentioned, anticipated by 

 Gonnella, but was now introduced practically. Disc-planimeters were 

 made by Starke in Vienna under the name of Wetli-Starke Planimeters. 

 They were improved by the astronomer Hansen, of Seeberg, near Gotha, 



' These data concermng Wetli's invention of the disc I owe to Covadi, to whom 

 the late Professor Harlacher in Pras; had communicated them. 



