JANUAKT 22, 1915] 



SCIENCE 



111 



vance it. If there is any question as to 

 what Gauss meant, we have only to turn to 

 his biography to find the answer. He did 

 not care to touch in print any subject that 

 he felt he could not exhaust; merely to 

 contribute to it seemed to hitn like pluck- 

 ing unripe fruit. Thus his published work, 

 extensive though it is, represents only a 

 part, and it may be only a small part, of 

 the unremitting labor of this wonderfully 

 fertile brain. We know, for example, that 

 Gauss had developed the principles of the 

 method of least-squares while he was still 

 in his teens, but it was not until fourteen 

 years later that he ventured into print on 

 this subject. He would doubtless have 

 wished to delay even longer had not Legen- 

 dre in the meantime unearthed and pub- 

 lished the same principles. "We can make 

 a good gTiess at the reasons for Gauss's 

 delay. The method of least-squares is 

 founded upon an assumption which can 

 be put in various forms, but which al- 

 ways remains an assumption. Gauss 

 would doubtless have wished to prove this 

 assumption from fundamental principles 

 or at least to have given it a more axio- 

 matic dress; but this neither he nor any 

 one that has come after him has succeeded 

 in doing. An even better illustration of 

 the former attitude of men of science in 

 the matter of their obligations to science, 

 is afforded by Gauss's part in the history 

 of non-Euclidean geometry. In a letter 

 to a friend he states that he had occupied 

 himself extensively with Euclid's axiom 

 concerning parallels and goes on to out- 

 line very briefly some of the results he had 

 obtained. This letter contains all that is 

 known of these researches. A few years 

 after it was written Lobatchewski pub- 

 lished the little book in which he proves 

 that the parallel axiom is no axiom at all, 

 but a pure assumption, and shows that 

 another kind of geometry is imaginable in 



which the opposite assumption is made. 

 In view of this work, it would have been 

 necessary for Gauss to revise what he had 

 already done before publishing it. He 

 preferred, however, to suppress it alto- 

 gether, and when after his death his scien- 

 tific effects were overhauled, no trace of 

 this subject was found among his papers. 

 It will be understood that it is not Gauss 

 that I am presuming to criticize, but 

 rather the times in which he lived. That 

 was an age when it was taken for granted 

 that a man should think of his scientific 

 reputation as coming first, and when the 

 form in which he gave his researches to the 

 world was considered as important as their 

 content. In more recent times the man of 

 science has taken a new view of his calling 

 and of his duties, and it is largely because 

 of this new policy that progress has been 

 so rapid in some directions. In astron- 

 omy, for example, the great strides that 

 have been made in the present generation 

 can be attributed to two things ; first, there 

 is the unprecedented concentration of ef- 

 fort. Great telescopes have been erected 

 and great observatories have been built 

 for the purpose of solving single problems 

 or a single group of closely related prob- 

 lems. If these problems should remain un- 

 solved in our time the work will be carried 

 forward by a succeeding generation and 

 perhaps completed many years after those 

 who initiated it have passed away. Co- 

 operation is another powerful implement 

 that time has placed in the hands of the 

 astronomer, more precious to him than any 

 telescope or any observatory can be. 

 Thanks to it, no pressing problem appears 

 at present above our horizon that is too 

 great for him to attack. If you will ex- 

 amine the working programs of our astro- 

 nomical institutions, you will find that 

 much the greater half of what they are 

 doing is being carried out with direct ref- 



