FEB i-i 1896 



Kansas University Quarterly 



Vol. IV. JANUARY. 1896. No. 3. 



A Ciirvimeter. 



BY W. R. CRANE. 



Integrating machines, or engines, as they are often called, have 

 been in use for so many years, and have filled all the requirements 

 so satisfactorily, that they are now considered an indispensable 

 article for the engineer's office and the draughtsman's table. The 

 ordinary planimeter is so well known and is so widely used that it 

 is unnecessary to speak further of it here. There is, however, an- 

 other class of integrating instruments, which is not so widely 

 known as the planimeter, nor has the principal of the same been so 

 thoroughly investigated. This class of instruments is commonly 

 known as the curvimeter. 



Up to the present time no accurate or trustworthy instrument 

 has been devised for the purpose of measuring the length of figures 

 of one dimension, such as lines and curves of every description. 

 The possibilit}- of such an instrument is suggested by the simple 

 and excellent form of planimeter, known as the "stang" or 

 "hatchet" which has recently gained such wide-spread popularity, 

 and it was, in fact, this instrument which led to the investigations 

 that ended in the instrument to be described. 



As is well known, there are a large number of problems, such as 

 finding the length and area of curve^ between their co-ordinate 

 axes and certain prescribed limits, which up to a few years ago 

 could be solved only by means of differential and integral calculus. 

 At the present time there are quite a number of planimeters — area 

 measurers — to be found on the market, the one above mentioned 

 being the latest, but as far as I am able to ascertain there is not a 

 sin^ e instrument, which will more than approximate the length of 

 curves. 



The following is a description of a simple curvimeter and the 

 method of operating the same. It consists of a rigid steel shaft, 

 accurately turned and polished, upon which a sharp rimmed steel 



(131) KAN. UNI. QUAR., VOL. IV. NO. 3, JANUAUY, 189G. 



