372 Mr. G. U. Yule on a Simple 



must be used. In cases of physical curves {e.g. E.M.F. 

 curves of alternators, conduction- of-heat curves) one is 

 generally free to choose the limits of the period so as to 

 bring the curve to the desired type. 



The accuracy of the instrument will be measured by the 

 accuracy of the planimeter. This cannot be fairly stated in 

 percentages, as an error of unity in the vernier reading is 

 never difficult, and may be anything per cent, in a small 

 total. I strongly recommend drawing curves on cardboard ; 

 it is much more favourable to the planimeter than drawing- 

 paper. The following tests may be taken as typical of the 

 results that are obtained with care : the curves were drawn 

 on card : — 



(1) Actual curve, 



3-13 + 4-60 cos + 1-82 cos 2(9 + *39 cos 30 + "045 cos 40. 



Analyser, 

 3-14 + 4-58 cos + 1-84 cos 2(9 + '39 cos 3(9 + -042 cos 4(9. 



(2) Actual curve (sloping straight line), 



6-37 sin (9-3-18 sin 20 + 2-12 sin 30-1-59 sin 40. 

 Analyser, 



6-39 sin 0-3-20 sin 20 + 211 sin 30-1*58 sin 40. 



The units are centimetres. 



§ 6. So much for the accuracy and range of the instrument. 



To get any desired coefficient, the ruler is set with its edge 

 parallel to the curve-base and with the proper disk in gear. 

 Ruler and disk are then adjusted till the tracing-dot stands 

 over the point P (fig. 1), and the base-line of the disk is 

 either vertical or horizontal according as a sine or cosine 

 term is wanted. The planimeter-point is finally dropped 

 into the hole provided for it, and the tracing-dot carried com- 

 pletely round the curve. The resulting planimeter reading 

 will be the area of the curve plus or minus 10 n times the 

 desired coefficient. 



Both hands must be used in guiding the disk, as rack and 

 disk have to be held together while the latter is turned. The 

 operator forms, in fact, an essential link of our mechanism 

 which without him is unconstrained. It is this liberal use of 

 the operator that enables me to dispense with slides, carriages, 

 and other expensive things, and thus gain in simplicity. 



§ 7. This analyser arose from a simple form of step-by-step 

 integrator or " adder " which may be worth a brief descrip- 

 tion. The instrument is shown diagrammatically in fig. 4 : it 

 was made from materials at hand and I describe it as made. 

 A B C D is a square sheet of card with a foot-rule glued along- 

 one edge A B. A set square PEG can be slid up and down 



