

OX A NEW FORM OF THE PLATOMETER. 237 



When the tracing point is made to traverse the boundary of a plane figure, 

 there is a continued rotation of the radius-vector combined with a change of 

 length. The rotation causes the index-sphere to roll on the fixed hemisphere, 

 while the length of the radius-vector determines the rate of its motion about its 

 axis, so that its whole motion measures the area swept out by the radius-vector 

 during the motion of the tracing point. 



The areas measured by this instrument may either lie on one side of the 

 pillar, or they may extend all round it. In either case the action of the 

 instrument is the same as in the ordinary case. In this form of the instrument 

 we have the advantages of a fixed stand, and a simple motion of the tracing 

 point ; but there seem to be difficulties in the way of supporting the spheres 

 and arranging the slide ; and even then the instrument would require a tall 

 pillar, in order to take in a large area. 



16. It will be observed that I have said little or nothing about the prac- 

 tical details of these instruments. Many useful hints will be found in the large 

 work on Platometers, by Professor T. Gonnellu, who has given us an account 

 of the difficulties, as well as the results, of the construction of his most 

 elaborate instrument. He has also given some very interesting investigations 

 into the errors produced by various irregularities of construction, although, as 

 far as I am aware, he has not even suspected the error which the sliding of 

 the index-wheel over the disc must necessarily introduce. With respect to this, 

 and other points relating to the working of the instru lent, the memoir of 

 Mr Sang, in the Transactions of this Society, is the rr )st complete that I 

 have met with. It may, however, be as well to state, t] at at the time when 

 I devised the improvements here suggested, I had not se n that paper, though 

 I had seen the instrument standing at rest in the Crystal Palace. 



EDINBURGH, 30th January, 1855. 



NOTE. Since the design of the above instrument was submitted to the Society of Arts, 

 I have met with a description of an instrument combining simplicity of construction with 

 the power of adaptation to designs of any size, and at the same time more portable than 

 any other instrument of the kind. Although it does not act by perfect rolling, and there- 

 fore belongs to a different class of instruments from that described in this paper, I think 

 that its simplicity, and the beauty of the principle on which it acts, render it worth the 

 attention of engineers and mechanists, whether practical or theoretical. A full account of 

 this instrument is to be found in Moigno's " Cosmos," 5th year, Vol. VIII., Part vni., p. 213, 

 published 20th February 1856. Description et Throne du planim&tre polaire, invente" par 

 <f. Amsler, de Schaffouse en Suisse. 



CAMBRIDGE, 30th April, 1856. 



