1903-4.] J. Erskine Murray on a Differentiating Machine. 277 
A Differentiating Machine. By J. Erskine Murray, D.Sc. 
(Read March 21, 1904. MS. received May 28, 1904.) 
It was pointed out to me a few months ago, by my friend 
Professor W. H. Heaton, that our knowledge of the laws of physical 
variations might he greatly increased if their study were facili- 
tated by the invention of a machine which would automatically 
deduce the rate of change of a function from the curve represent- 
ing that function. In cases where the physical law is already 
known, and is expressible in terms of known mathematical 
quantities, such a machine is not essential, though it provides an 
excellent illustration of mathematical laws ; there is, however, a 
vast and ever-increasing mass of numerical results awaiting 
discussion and co-ordination, and it is in reducing these to law 
and order that the differentiator should prove a useful tool. As 
instances of a few cases in which rates of change are of the first 
importance, I may mention the following : — 
(1) Meteorological observations of Temperature, Pressure, 
Humidity and Rainfall. 
(2) Terrestrial Magnetic records. 
(3) Experimental results in Physics and Chemistr} T which 
involve changes, whether in time or space. The determination of 
thermal conductivity by Forbes’ method is an example. 
(4) Statistics of Population, Mortality, and Migration. 
(5) Statistics of Wages, Prices, and Commerce. 
(6) Medical records. 
(7) Engineering calculations, such as the deduction of Tractive 
Force from a Time and Space or Time and Yelocity diagram. 
Up to the present all determinations of rates of change of 
quantities like those above mentioned have had to be made by 
laborious arithmetical or graphical methods, involving so great an 
expenditure of time for their completion that but little has been 
done. The differentiator reduces enormously the necessary labour, 
