SOLID MEASUREMENTS. 231 



point, resolved at every instant at right angles to the bar, and the suc- 

 cess of the instrument depends on the little wheel recording that 

 transverse component only. The other points are mere details of 

 mechanism. One form of the instrument is shown here. Practically, 

 these are not generally made of a size to be used for any other 

 than small diagrams, but they really measure with great accuracy. In 

 fact,' when I was in the School of Naval Architecture we used to try it 

 upon squares, and we invariably found that it measured a square with 

 at least as great accuracy as we were able to draw it, and I need hardly . 

 tell you that in surface measurements it is not necessary to obtain an 

 accuracy that goes beyond the drawing. 



There is another kind of Planimeter founded on a principle that is 

 well known to mechanicians in the form of a continuous indicator. 

 Suppose there is a disc turning on its centre and we have another little 

 disc at some point of it in rolling contact with it, the travel of this disc 

 will depend not only on the rapidity with which the primary disc 

 moves, but also largely on its distance from the centre, and, moreover, 

 supposing that the travel of the primary disc is uniform, the travel 

 of the follower will be exactly proportionate to its distance from 

 the centre. That circumstance is taken advantage of in a little 

 machine I have here. The disc you see the edge of is the following 

 disc, and the one which is horizontal when the instrument is in its 

 proper position is the driving disc. The bar that you see with a little 

 wire upon it is always kept parallel to a base line, and a tracing point 

 follows exactly the curve. Now, when this following disc is on the 

 line of centres it records nothing, but as it moves away from the line 

 of centres there is a specific ordinate to which the travel of the following 

 wheel is proportional, consequently the operation of the instrument is 

 to add this exactly as we do in ordinary algebraic integration. In that 

 way we get the surface recorded with as great accuracy as the drawings 

 are framed. In point of fact, I have very little doubt its performance is 

 quite equal to that of any drawings that can be submitted to it. A 

 modification of that is to be found in Professor James Thomson's 

 instrument down stairs. I do not propose to describe that, because it 

 it really very much more than an instrument for measuring an area, 

 and mav be applied to a great many things, but in its simplest form 

 it is a case of measurement of area, on exactly the same principle as 



