424 



SCIENCE 



[N. S. Vol. XLII. No. 1082 



Then why object to the earth as a third body ? 

 We, for our part, thank the Lord for the 

 Earth ! We are satisfied with it ! 



Yes, but the balance compares the forces 

 with which the earth pulls on two bodies — the 

 weights of the two bodies. Very true, but just 

 here is involved the one thing above all others 

 which makes physics a mathematical science, 

 and it is a thing which many of our mathe- 

 maticians seem to think least about, namely, 

 the establishment of invariant one-to-one corre- 

 spondences by experimental tests. Use a bal- 

 ance on a batch of sugar and you get always 

 and everywhere the same numerical result,^ 

 use it on a part of the batch and you get a 

 different result. This is the only condition 

 that is necessary to justify the use of the re- 

 sult as a measure of quantity of sugar. The 

 purely arithmetical condition that ten units of 

 sugar break up into a batch of seven units, and 

 a batch of three units might also seem to be a 

 necessary condition, but it is not necessary, 

 but only convenient, in that it leads to a simple 

 system of sugar-arithmetic.^ 



1 This statement is somewhat idealized for the 

 sake of simplicity. If the use of the balance did 

 always lead to invariant results, the rational theory 

 of the balance would be of interest to the balance 

 maker and to the speculative philosopher, but it 

 would be of no consequence whatever to the ex- 

 perimental or mathematical physicist. As things 

 stand, however, the rational theory of the balance 

 is of importance in the elimination of what we call 

 systematic errors, for under ordinary conditions 

 the balance does not lead to invariant results. 

 Many such cases arise in physics, and it is the 

 common practise to keep clear of such complica- 

 tions in the earlier stages of the development of 

 physical theory by framing definitions on the basis 

 of ideal conditions. 



2 As an example of the kind of thing here re- 

 ferred to let us agree to measure "amperes" by 

 the number of units of heat generated in a given 

 wire per second. Then 3 "amperes" from one 

 branch of a circuit joining with 2 "amperes" 

 from another branch would give 11.9 "amperes" 

 in the main circuit. In this system the arithmetical 

 form of BarehhofE's law would be as follows: The 

 current in the main circuit is equal to the square 

 of the sum of the square roots of the currents in 

 the various branches of the circuit. Similarly 



We respect the experience of two thousand 

 years in that we base our definition of mass 

 on the use of the balance; and we look at the 

 identity of inertia ratio and mass ratio as a 

 discovery, but we refuse to depart from the 

 point of view of men who buy flour and sugar 

 by the pound. We are not ashamed of the bal- 

 ance! 



We also respect the broader view of mathe- 

 matics as the logic of fixed relations in our 

 acceptance of experimentally established one- 

 to-one correspondences as the essential basis 

 of mathematical physics rather than the mere 

 readings of numbers on sets of weights, and 

 yard sticks and clock faces! 



W. S. Frai^klin, 

 Barry MaoNdtt 



powdery scab of potatoes in oregox 

 The occurrence of the Spongospora scab dis- 

 ease of potatoes in Tillamook County, Oregon, 

 has recently come to the attention of the de- 

 partment of plant pathology of the Oregon Ex- 

 periment Station, and since this important 

 trouble has apparently not been reported west 

 of the Eocky Mountains the record may be of 

 general interest.^ 



The lot of potatoes in which the disease was 

 first found was raised on a farm in the rather 

 isolated coast district of Oregon referred to 

 above. The owner stated that the seed of this 

 variety had been introduced from twelve to 

 fifteen years ago from an eastern state and that 

 new seed had not been introduced on his farm 

 since that time. 



The diseased tubers first found came from a 

 lot that had been shipped to the writer for ex- 

 perimental study, this particular lot being 

 badly affected with an internal browning ap- 

 parently of non-parasitic origin and with the 



sugar could be easily measured so that you would 

 pay 5 cents for one unit, 7 cents for two units, 8.65 

 cents for three units, and so forth, without mak- 

 ing the serious mistake of giving your sugar at a 

 cheaper rate to the wealthy man who gets more 

 than he needs than to the poor man who needs more 

 than he gets. Figure it out for yourself. 



1 Since the above was written a record of the ap- 

 pearance of this disease in Seattle on potatoes from 

 British Columbia has been reported. 



