1883] 



MICROSCOPICAL JOURNAL. 



79 



of Microscopists and printed in the Pro- 

 ceedings : — 



On page 247, for increase read decrease. 



On page 240, in the approximate rule 

 given for computing the probable error of 

 a single observed value of a given series, 

 the coefficient two-thirds was inadvert- 

 ently omitted, and the results obtained 

 should have been -(- 0.24JM and -\- o.o8/< 

 instead of the values given. 



The following are the more exact form- 

 ulae for probable errors : — 



r = .6745 



Vn — I 

 r 



id) 



{a') 



in which 



n = the number of values of a given 



function x. 

 V ^ the difference bet\veen each value 



of X and the arithmetical mean of all 



the values. 

 [7'] = the sum of the separate residuals 



without regard to sign. 

 r = the probable error of a single value. 

 r^ := the probable error of the arithmeti- 

 cal mean. 



Nearly equivalent formulae have been 

 developed by Peters, which are rather 

 more convenient in application. 



They are : — 



= .8453 ^ ^ ^ 



^^^ s/ii (n — I) 



ro = .8453 



[v] 



n \^n 



(^) 



ib') 



For convenience of reference the ex- 

 ample given on page 240 is here repeated. 



looo.c^ 



1000.2 



1 000. 1 



icoo.6 



10C0.5 



1000.9 



1 000.0 



1000.4 



1000.3 



looi.o 



Mean 1000.4 [f] := 2.8 [7/7']=!. 12 



According to (a) and (a') 



r = -J- .6745 -^~Ji = ± 0.24/i 

 sj 10 — I 



0.24 



r, = ± -^ = i .08/* 



V 10 



According to (b) and (b') 



.2SH 



^o = i -7^ = i -oSji 



The quotient obtained by dividing the 



difference between the greatest and the 



least values of a given series by 3.8 



will give a rough approximation to the 

 value of r. 



In this case we shall have : — 



W. A. Rogers. 

 MICROSCOPICAL SOCIETIES. 



The Microscopical Society of Central 

 Illinois met on Feb. 15th, and after the 

 transaction of routine business listened to 

 the reading of the second section of T. B. 

 Jennings' paper on " Animal Life in the 

 Reservoir-Park Waters." This section 

 treated entirely of the Amoebae found 

 there, the first part, however, being a 

 technical description of what constitutes 

 a Rhizopod. 



The Wellesley College Micro- 

 scopical Society is still actively engaged 

 in work for the mutual instruction of its 

 members. At one of its meetings not 

 long ago the general subject, " Ehrenberg 

 and his Work," was brought forward by 

 several members. Miss Tyler read an 

 article on " Microscopists before Ehren- 

 berg." Miss Dunbar another on the 

 "Life of Ehrenberg" and Miss Luce 

 spoke on " The Works of Ehrenberg." 

 This plan of designating certain mem- 

 bers to prepare articles treating of speci- 

 fied parts of a subject, seems worthy of 

 imitation in many other societies. We 



