BURNHAM FUND INC
N-30B-2, 1998-11-04
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                              BURNHAM FUND [LOGO]

                                                                October 26, 1998
Dear Shareholders:

We are pleased to present to you the Third Quarter Report of the Burnham Fund
for 1998.

BURNHAM FUND THIRD QUARTER DATA
- -------------------------------
On September 30, 1998 The Burnham Fund's net asset value per share for Class A,
B and C shares was $28.40, $29.12, and $28.60, which represent decreases for
third quarter of 13.36%, 13.54% and 13.02%, respectively. In comparison, the
average growth and income fund, according to Lipper Analytical Services, was
down 12.19%.

On October 8, 1998, the Fund paid a third quarter dividend of $0.06 per share
from net investment income to Class A shareholders of record on September 30,
1998. There were no investment income distributions to Class B and C
shareholders.

THIRD QUARTER MARKET REVIEW
- ---------------------------
Our last letter to shareholders was written to you during the throes of a market
correction. In the third quarter, the average equity fund was down over 15%, the
S&P 500 was down 9.9%, and the DJIA was down 12.0%. The well-known factors we
have discussed over the last year--recession and economic instability in Asia,
currency movements, earnings estimate revisions, and U.S. political
scandal--moved the majority of investment professionals into the bearish camp.
The catalyst that brought about this negativism was a sudden, dramatic global
financial and liquidity crisis that resulted from the convergence of a series of
financial events: the collapse of the Russian capital market spilling over and
impacting the valuation of emerging market securities, the resulting "flight to
quality" of assets into U.S. government bonds, causing a sharp decline in
long-term interest rates, which in turn brought about a decline in the U.S.
dollar. The sharp decline in long interest rates caused an inversion of the
"yield curve" (when short-term rates are higher than long term rates), and
tightening of credit conditions at lending institutions. This inversion also
spurred accelerated prepayments of mortgage-backed securities (due to increased
mortgage refinancing), disrupting fixed income markets. The U.S. equity markets
were flooded with sell orders: mutual fund redemptions for August reached $11.2
billion as investors reviewed their portfolios and decided to take shelter in
money market and treasury instruments. No sectors were spared, except for funds
with an investment objective designed specifically for bear markets.

Your investment committee believes that this crisis bears some similarity to the
emerging markets crisis of 1994. In that year, emerging markets were embattled
in sympathy with the decline of the Mexican and Latin American capital markets.
The U.S. government, in a politically controversial move, came to the aid of the
Mexican government because stabilizing the region was in our economic "national
interest". The program was ultimately successful, although emerging market funds
performed poorly. Later that year, the Federal Reserve raised interest rates to
avert an increase in the rate of inflation due to continued economic strength.
This took portfolio managers by surprise, particularly those that hedge their
porfolios with derivative contracts, and the equity markets reacted negatively.

We see several comparisons that lead us to be cautiously optimistic. First, as
in 1994, the Federal Reserve has acted quickly and decisively in order to
provide liquidity to the markets. During this crisis, the Fed has lowered the
Federal funds rate twice (for a total of 50 basis points) and the discount rate
once (25 basis points) and may possibly cut rates again in November. Their
comments about "not allowing the U.S. economy to slide into a recession" should
be taken seriously by investors. Second, in 1994, hedge funds and traders who
utilize complex derivative strategies were caught unaware, and their "unwinding
of




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BURNHAM FUND [LOGO]

positions" exacerbated an already volatile market. This situation stabilized in
the months to follow. In comparison, now well-known hedge fund managers (Long
Term Capital and others) have had their illiquid, hedged positions assumed by
their creditors, who are in a position to hold the securities, or, hopefully,
dispose of them without disrupting markets. Lastly, it was the strength of the
U.S. executive branch that pushed through a successful Mexican "bailout". We are
amazed at the ability of President Clinton to function under the strain of the
impeachment process. Yet, he handled this financial crisis with strength and
conviction, as he did in 1994, and has pushed through a budget package that
reverses much of the fiscal restraint seen in past years. (The Wye River
Agreement between Israel and the Palestinians most likely would not have been
accomplished without his personal intervention.) The Executive Branch's
leadership may encourage foreign governments to join the United States in
shoring up international institutions like the IMF and take the steps necessary
to avert further economic deterioration in other regions of the world.

During the third quarter, however, we took some temporary cautious measures for
which our investment objective provides. We moved the percentage of the fund
invested in common stocks from 89% to 81%, and cash and cash equivalents from 6%
to 16%. We shifted the equity sector allocation to where we believed we would
see sustained growth in a possible economic slowdown. Computer products and
software is now our largest industry representation. We believe that the
slowdown in earnings due to the inventory build up of past years is behind this
industry and earnings look healthier going forward. The other sectors we are
emphasizing include Energy (we believe oil prices have "bottomed"),
Pharmaceuticals, selected Financial Services (domestic banks and services),
REITs (for income) and Telecommunications. Throughout 1998 we have pared back on
companies that had Asian exposure, so we had few left in the portfolio at the
start of the third quarter. Those that we sold for Asian-related reasons
included Franklin Resources, Chase Manhattan Bank, Estee Lauder, Procter &
Gamble and Gillette. We added a few new companies to the portfolio: Coca Cola
(unreasonable price decline), Schlumberger, and Dell Computer.

OUTLOOK
- -------
Looking forward, we believe that volatility will continue through the end of
1998 as managers and investors adjust their portfolios for a year of losses
after two quarters of spectacular paper profits, and in many cases, realized
gains. We are also concerned that the Asian crisis will spread to Latin America,
in particular, Brazil, where the extent of the U.S. banking industry's financial
holdings are significant, and not well disclosed. (Money-center banks' Asian
losses and hedge fund exposure at this point have been disclosed to the public
in third quarter financial reports). Despite this, we are moderately optimistic
as we near 1999. With Fed funds now at 5%, and the discount rate at 4.75%, banks
have the flexibility to narrow "real interest rates" by reducing prime and
mortgages rates over the months ahead. This bodes well for corporate liquidity,
earnings and consumer balance sheets next year. In looking at corporate profits,
many analysts have cut earnings estimates and investment ratings on companies
that earn revenues from Asian or Latin American export. Some also believe that
consumers will cut back on expenditures as the "wealth effect" of the market
correction works its way through the economy. However, the decline of the U.S.
dollar in recent weeks, if sustained, strengthens the earnings outlook for
companies with proprietary (as opposed to commodity) business abroad as their
local sales convert into more dollars. It also allows foreign companies to
reduce prices of their goods for sale in the United States


                                        2

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                                                             BURNHAM FUND [LOGO]

and grow their exports, which means price competition for domestic manufacturers
(this is not positive for U.S. basic industries.) The historic high trade
deficit reported on October 21 reflects this disproportionately high level of
imports vs. exports; the U.S. is defacto financing a foreign recovery. The low
prices of commodities, specifically crude oil, is positive for Asian countries
which purchase oil in dollars. Lastly, common stock prices are more reasonable
at a multiple on the S&P 500 of 22x 1998 estimates and 20x 1999 estimates. This
contraction of p/e ratios indicates that investors are discounting many of the
negatives that we have discussed.

The major question remains whether the U.S. economy experiences a slowdown or a
recession. If, as we suspect, the Asian crisis has begun to stabilize, and our
exports to that region are "bottoming", then we would be positively inclined
toward equities at this time. If the situation worsens in Latin America, we
would anticipate another round of market shocks.

We continue to hold and look for opportunities to invest in companies with
earnings growth potential of at least 15% to 20% per year for three to five
years, product leadership, innovative management with a shareholder-value
orientation, superior financial underpinnings, and a healthy dividend history
(when pertinent). We also search for companies whose stock is undervalued
relative to its past, or those which may benefit from restructuring actions.
Most importantly, at this time we look for predominantly liquid,
large-capitalization companies with relatively little or no exposure to Asia
and/or Latin America, or where the exposure is well understood. We are also
monitoring Year 2000 issues as they affect our investments, and to the extent to
which companies in the Fund are on track with their Y2k planning.

Portfolio Manager Jon Burnham continues his monthly appearances on CNBC, CNN/fn
and Bloomberg. If you would like to be notified by fax of his appearances
beforehand, please call our toll free number, 1-800-874-FUND and we would be
happy to include you on our fax broadcast of his schedule.

We appreciate your confidence in the Burnham Fund.

Very truly yours,


/s/ I. W. Burnham, II          /s/ Jon M. Burnham
I. W. Burnham, II              Jon M. Burnham,
Chairman                       President &
                               Portfolio Manager


The performance data quoted represents past performance and is not indicative of
future performance. The investment return and principal value of an investment
will fluctuate so that an investor's shares, when redeemed, may be worth more or
less than their original cost. Average total return for Class A shares, assuming
the reinvestment of dividends and excluding the maximum sales charge for the
one, five and ten year periods ended September 30, 1998 were 2.15%, 12.38% and
11.99%, respectively. Such performance assuming the imposition of the Class A
shares' maximum 5% sales charge for the same periods would have been (2.95%),
11.23% and 11.41%, respectively. For Class B and C shares, average total return
for the one year period ended September 30, 1998 and life of class total return
for the period October 18, 1993 (inception date) to September 30, 1998 were
1.29% and 1.93% and 11.71% and 11.78%, respectively. Class B shares bear a
maximum contingent deferred sales charge at a rate of 5% if they are redeemed
within the first six years of purchase. Such performance assuming the imposition
of the contingent deferred sales charge of 4% for the one year period ended
September 30, 1998 and life of class were (2.71%) and 11.37%, respectively.
Class C shares bear a maximum contingent deferred sales charge at a rate of 1%
if they are redeemed within the first year of purchase.

                                       3


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BURNHAM FUND [LOGO]

                             INVESTMENT PERSPECTIVE



                         EQUITY PORTFOLIO DISTRIBUTION
                           by Industry Classification
                               September 30, 1998

<TABLE>
<CAPTION>
                                                               % Total
                                                          Equity Portfolio
                                                          ----------------
<S>                                                             <C>  
Computer Products & Software ................................   15.3%
Energy--Oil & Gas ...........................................   11.9%
Pharmaceuticals .............................................    9.8%
Financial Services ..........................................    8.5%
Banking .....................................................    8.0%
Real Estate Investment Trusts ...............................    6.1%
Telecommunication Network Services ..........................    5.8%
Automotive ..................................................    5.1%
Telecommunication Equipment .................................    4.5%
Food Products ...............................................    4.2%
Other .......................................................   20.8%
                                                              -------
Total Equities .............................................. 100.00%
                                                              =======
</TABLE>


                  TOTAL PORTFOLIO DISTRIBUTION BY ASSET CLASS
                               September 30, 1998

Cash & Cash Equivalents 16%

                                   Convertible
                                   Preferred Securities 1%

        [PIE CHART]
                                     Corporate & Convertible
                                     Bonds 2%




                     Common Stocks 81%



                           TOP 25% PORTFOLIO HOLDINGS
                       (EXCLUDING SHORT-TERM INVESTMENTS)
                               September 30, 1998



<TABLE>
<CAPTION>
                                        Number of                        % of
                                          Shares        Value         Net Assets
                                          ------        -----         ----------
<S>                                      <C>         <C>                 <C>  
The Bank of New York Co., Inc. ......    200,000     $ 5,475,000         4.09%
Exxon Corporation ...................     70,000     $ 4,913,125         3.67%
Travelers Group Inc. ................    120,000     $ 4,500,000         3.36%
Microsoft Corp. .....................     40,000     $ 4,403,750         3.29%
Pfizer Inc. .........................     40,000     $ 4,237,500         3.16%
Ford Motor Co. ......................     90,000     $ 4,224,375         3.15%
Cisco Systems Inc. ..................     60,000     $ 3,710,625         2.77%
Lucent Technologies Inc. ............     50,000     $ 3,453,125         2.56%
                                                     -----------        ----- 
Top 25% Holdings ...............................     $34,917,500        26.05%
                                                     ===========        ===== 
</TABLE>



                               CUMULATIVE RETURN
                     OF A HYPOTHETICAL $10,000 INVESTMENT*
                         FROM INCEPTION (JUNE 16, 1975)
                           THROUGH SEPTEMBER 30, 1998

                           THE BURNHAM FUND--CLASS A
                        Value of hypothetical investment
                        on September 30, 1998: $181,429

<TABLE>
<S>           <C>                     <C>            <C>
6/16/75        $10,000                   2/87          56,170
   8/75          9,514                   5/87          56,567
  11/75          9,911                   8/87          61,493
   2/76         10,998                  11/87          51,604
   5/76         11,137                   2/88          57,209
   8/76         11,434                   5/88          56,377
  11/76         11,527                   8/88          57,468
   2/77         11,437                  11/88          59,568
   5/77         11,340                   2/89          62,357
   8/77         11,546                   5/89          66,812
  11/77         11,716                   8/89          70,974
   2/78         11,070                  11/89          71,089
   5/78         12,491                   2/90          70,280
   8/78         13,899                   5/90          72,539
  11/78         12,808                   8/90          69,839
   2/79         13,346                  11/90          71,459
   5/79         13,947                   2/91          75,301
   8/79         15,796                   5/91          78,044
  11/79         15,968                   8/91          79,325
   2/80         17,622                  11/91          79,354
   5/80         17,277                   2/92          86,673
   8/80         19,143                   5/92          85,384
  11/80         22,509                   8/92          87,127
   2/81         21,202                  11/92          89,836
   5/81         22,741                   2/93          93,453
   8/81         20,551                   5/93          95,724
  11/81         21,766                   8/93         100,595
   2/82         20,375                  11/93          98,794
   5/82         20,740                   2/94          99,703
   8/82         22,122                   5/94          96,689
  11/82         25,502                   8/94         100,244
   2/83         27,130                  11/94          98,016
   5/83         28,910                   2/95         102,777
   8/83         28,750                   5/95         109,211
  11/83         29,500                   8/95         114,164
   2/84         28,077                  11/95         119,438
   5/84         27,394                   2/96         127,075
   8/84         30,463                   5/96         131,894
  11/84         30,724                   8/96         127,870
   2/85         33,209                  11/96         146,166
   5/85         35,844                   2/97         149,787
   8/85         36,285                   5/97         159,374
  11/85         39,481                   8/97         171,146
   2/86         44,533                  11/97         176,690
   5/86         48,822                   2/98         191,141
   8/86         50,708                   5/98         209,439
  11/86         50,564                   8/98         181,430
</TABLE>

          LIFE OF FUND
     CUMULATIVE PERCENT RETURN:
                      1,714.29%
ANNUAL COMPOUND RATE OF RETURN:
                          13.23%



                                    [GRAPH]


                                             $10,000 INVESTMENT ON JUNE 16, 1975
                                                               (INCEPTION DATE).


1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990
1991 1992 1993 1994 1995 1996 1997 1998


* All performance analyses shown herein represent past performance and are not
indicative of future performance. All dividends and distributions from income
and capital gains have been continually reinvested. Performance does not include
the imposition of the maximum 5% sales charge. Performance for other classes of
the Fund will be greater or less than the data shown in the graph and tables
based on differences in sales charges and fees paid by shareholders investment
in the different classes of the Fund.

                          AVERAGE ANNUAL TOTAL RETURN
                        Period ended September 30, 1998

<TABLE>
                        <S>                      <C>  
                         One Year ..............  2.15%
                         Five Years ............ 12.38%
                         Ten Years ............. 11.99%
                         Fifteen Years ......... 12.94%
                         Twenty Years .......... 13.80%
</TABLE>

                                       4


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                                                             BURNHAM FUND [LOGO]


                            STATEMENT OF NET ASSETS
                         September 30, 1998 (Unaudited)



<TABLE>
<CAPTION>
                                                     Number
                                                   of Shares       Value(c)
                                                   ---------       --------
<S>                                        <C>       <C>         <C>        
COMMON STOCKS                               81.22%
AEROSPACE                                    0.82%
  General Motors Corp., Class H .................    30,000      $ 1,104,375
                                                                 -----------
AUTOMOTIVE                                   4.23%
  Chrysler Corp. ................................    30,000        1,436,250
  Ford Motor Company ............................    90,000        4,224,375
                                                                 -----------
                                                                   5,660,625
                                                                 -----------
BANKING                                      6.63%
  The Bank of New York Co., Inc. ................   200,000        5,475,000
  Fleet Financial Group Inc. ....................    20,000        1,468,750
  Mellon Bank Corp. .............................    35,000        1,927,188
                                                                 -----------
                                                                   8,870,938
                                                                 -----------
BEVERAGES                                    0.86%
  Coca Cola Co. .................................    20,000        1,152,500
                                                                 -----------
COMPUTER PRODUCTS &
  SOFTWARE                                  12.59%
  Cisco Systems Inc. ............................    60,000(a)     3,710,625
  Compaq Computer Corp ..........................    30,000          948,750
  Dell Computer Corp. ...........................    15,000(a)       986,719
  EMC Corp. .....................................    20,000(a)     1,143,750
  International Business Machines Corp. .........     25,00(a)     3,200,000
  Microsoft Corp. ...............................    40,000(a)     4,403,750
  Phoenix Technologies Ltd. .....................    80,000(a)       460,000
  Siebel Systems Inc. ...........................    70,000(a)     2,005,937
                                                                 -----------
                                                                  16,859,531
                                                                 -----------
CONGLOMERATES                                0.91% 
  Textron Inc. ..................................    20,000        1,212,500
                                                                 -----------
CONSUMER PRODUCTS                            2.89%
  Blythe Industries Inc. ........................    25,000(a)       685,938
  General Electric Co. ..........................    40,000        3,182,500
                                                                 -----------
                                                                   3,868,438
                                                                 -----------
DOMESTIC AIRLINES                            0.73%
  Delta Airlines, Inc. ..........................    10,000          972,500
                                                                 -----------
ENERGY--OIL AND GAS                          9.85%
  Amoco Corp. ...................................    30,000        1,616,250
  British Petroleum PLC ADS .....................    20,000        1,745,000
  Exxon Corporation .............................    70,000        4,913,125
  Mobil Corporation .............................    40,000        3,037,500
  Texaco Inc. ...................................    30,000        1,880,625
                                                                 -----------
                                                                  13,192,500
                                                                 -----------
ENGINEERING/INDUSTRIAL
  PRODUCTION                                 0.07%
  Thermolyte Corp. ..............................    10,000(ab)      100,000
                                                                 -----------
<CAPTION>
                                                     Number
                                                   of Shares       Value(c)
                                                   ---------       --------
<S>                                        <C>       <C>         <C>
FINANCIAL SERVICES                           7.05%
  American Express Co. ..........................    40,000      $ 3,105,000
  Associates First Capital Corp. ................    28,104        1,833,786
  Travelers Group Inc. ..........................   120,000        4,500,000
                                                                 -----------
                                                                   9,438,786
                                                                 -----------
FOOD PRODUCTS                                3.47%
  American Italian Pasta Co. ....................    90,000(a)     2,362,500
  General Mills Inc. ............................    20,000        1,400,000
  Ralston Purina Co. ............................    30,000          877,500
                                                                 -----------
                                                                   4,640,000
                                                                 -----------
HEALTHCARE FACILITIES                        0.76%
  Rehabcare Group Inc. ..........................    85,000(a)     1,012,031
                                                                 -----------
INSURANCE                                    2.49%
  Allstate Corp. ................................    80,000        3,335,000
                                                                 -----------
MEDIA BROADCASTING                           0.72%
  CBS Corporation ...............................    40,000          970,000
                                                                 -----------
MEDICAL SUPPLIES                             0.86%
  Medtronic Inc. ................................    20,000        1,157,500
                                                                 -----------
OIL DRILLING                                 2.11%
  Diamond Offshore Drilling Inc. ................    70,000        1,820,000
  Schlumberger Ltd. .............................    20,000        1,006,250
                                                                 -----------
                                                                   2,826,250
                                                                 -----------
PHARMACEUTICALS                              8.12%
  Merck & Co. ...................................    25,000        3,239,062
  Pfizer Inc. ...................................    40,000        4,237,500
  Warner Lambert Inc. ...........................    45,000        3,397,500
                                                                 -----------
                                                                  10,874,062
                                                                 -----------
REAL ESTATE INVESTMENT
  TRUSTS                                     5.02%
  Chateau Communities Inc. ......................    40,000        1,117,500
  Developers Diversified Realty Corp. ...........    60,000        1,095,000
  Franchise Finance Corp. .......................    70,000        1,920,625
  Golf Trust of America, Inc. ...................    45,000        1,338,750
  National Golf Properties Inc. .................    45,000        1,243,125
                                                                 -----------
                                                                   6,715,000
                                                                 -----------
SEMICONDUCTORS                               2.56%
  Intel Corp. ...................................    40,000        3,431,250
                                                                 -----------
TELECOMMUNICATION
  EQUIPMENT                                  3.68%
  ECI Telecom Ltd. ..............................    60,000        1,477,500
  Lucent Technologies Inc. ......................    50,000        3,453,125
                                                                 -----------
                                                                   4,930,625
                                                                 -----------
</TABLE>

                                       5


<PAGE>
<PAGE>


[BRUNHAM FUND LOGO]

                            STATEMENT OF NET ASSETS
                         September 30, 1998 (Unaudited)

<TABLE>
<CAPTION>

                                                 Number of Shares
                                                   or Principal
                                                       Amount         Value(c)
- --------------------------------------------------------------------------------
<S>                                          <C>        <C>        <C>         
TELECOMMUNICATION NETWORK
  AND SERVICES                               4.80%
  GTE Corp. .................................           40,000     $  2,200,000
  Qwest Communication International Inc. ....           50,000(a)     1,559,375
  SBC Communications Inc. ...................           60,000        2,666,250
                                                                   ------------
                                                                      6,425,625
                                                                   ------------
  TOTAL COMMON STOCKS
   (cost: $69,259,922)                                              108,750,036
                                                                   ------------
CONVERTIBLE PREFERRED
  SECURITIES                                 1.27%
PASSENGER CRUISE LINES                       1.27%
  Royal Caribbean Cruises,
   conv. Preferred Cl. `A' ..................           20,000        1,701,250
                                                                   ------------
  TOTAL CONVERTIBLE PREFERRED
    SECURITIES  (cost: $1,084,100)                                    1,701,250
                                                                   ------------
CONVERTIBLE BONDS                            0.82%
DATA PROCESSING                              0.82%
  Adaptec, Inc. 4.75% sub. deb 
   conv. 2/1/04 ..............................      $1,000,000          703,750
  Data General Corp., 6% sub. deb
   conv. 5/15/04 .............................         500,000          399,375
                                                                   ------------
  TOTAL CONVERTIBLE BONDS
   (cost: $1,271,000)                                                 1,103,125
                                                                   ------------
CORPORATE BONDS                              1.02%
HOTELS                                       1.02%
  Marriott Corp., 93/8% deb. 6/15/07 ........        1,265,000        1,364,682
                                                                   ------------
  TOTAL CORPORATE BONDS
   (cost: $1,273,606) ........................                        1,364,682
                                                                   ------------
COMMERCIAL PAPER                            16.87%
  American Express Credit Corp.,
   5.45% 10/01/98 ............................       3,400,000        3,400,000
  Associates First Capital Corp.,
   5.25% 10/02/98 ............................       4,800,000        4,800,000
  CIT Group Inc. 
   5.20% 10/06/98 ............................       1,635,000        1,635,000
  Ford Motor Credit Corp.
   5.25% 10/06/98 ............................       2,900,000        2,900,000
  General Electric Capital Corp. 
   5.20% 10/05/98 ............................       3,400,000        3,400,000
  General Motors Acceptance Corp. 
   5.20% 10/05/98 ............................       1,950,000        1,950,000
  Norwest Financial Inc. 
   5.54% 10/05/98 ............................       4,500,000        4,500,000
                                                                   ------------
  TOTAL COMMERCIAL PAPER
   (cost: $22,585,000) .......................                     $ 22,585,000
                                                                   ------------

<CAPTION>
                                                     Principal
                                                       Amount         Value(c)
- --------------------------------------------------------------------------------
<S>                                        <C>                     <C>
TOTAL INVESTMENTS                          101.20%
 (cost: $95,473,629)                                                135,504,093
CASH AND OTHER ASSETS,
LESS LIABILITIES                            (1.20%)                  (1,602,060)
                                           ------                  ------------
NET ASSETS                                 100.00%                 $133,902,033
                                           ======                  ============
</TABLE>

CLASS A SHARES
(Equivalent to $28.40 per share based on 4,631,329 shares of Capital Stock
outstanding)

CLASS B SHARES
(Equivalent to $29.12 per share based on 66,801 shares of Capital Stock
outstanding)

CLASS C SHARES
(Equivalent to $28.60 per share based on 15,638 shares of Capital Stock 
outstanding)

- --------------------------------------------------------------------------------

(a) Non-income producing security.

(b) A unit consisting of one share of common stock of Thermolyte Corporation and
one redemption right.

(c) Investments in securities traded on a national securities exchange are
valued at the last reported sales price on the primary exchange on which they
are traded on the last business day of the period. Securities traded in the
over-the-counter market (including securities listed on exchanges whose primary
market is believed to be over-the-counter) and listed securities for which no
sale is reported on that date are valued at the mean between the last reported
bid and asked prices. Short-term money market instruments which have a maturity
of more than 60 days are valued at prices based on market quotations for
securities of similar type, yield and maturity. Short-term money market
instruments which have a maturity of 60 days or less are valued at amortized
cost which approximates value.


                                       6


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OFFICERS OF THE FUND

I.W. Burnham, II Chairman
Jon M. Burnham, President
  and Chief Executive Officer
Michael E. Barna, Executive Vice President
  Chief Financial Officer, Treasurer and Secretary
Debra B. Hyman, Executive Vice President
Ronald M. Geffen, Vice President
Frank A. Passantino, Vice President and
  Assistant Secretary
Louis S. Rosenthal, Vice President

INVESTMENT ADVISER
Burnham Asset Management Corporation
1325 Avenue of the Americas
New York, New York 10019

DISTRIBUTOR
Burnham Securities Incorporated
1325 Avenue of the Americas
New York, New York 10019
Telephone: 1 (800) 874-FUND

CUSTODIAN AND TRANSFER AGENT
State Street Bank and Trust Company
225 Franklin Street
Boston, Massachusetts 02110

LEGAL COUNSEL
Hale and Dorr LLP
60 State Street
Boston, Massachusetts 02109

SERVICING AGENT
Boston Financial Data Services, Inc.
2 Heritage Drive
North Quincy, Massachusetts 02171

http://www.burnhamfunds.com

This report has been prepared for the information of shareholders of The Burnham
Fund Inc. and is not authorized for distribution to prospective investors unless
preceded or accompanied by an effective prospectus that includes information
regarding the Fund's objectives, policies, management, records and other
information.



QUARTERLY REPORT

SEPTEMBER 30, 1998



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CONTINUITY            KNOWLEDGE



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GROWTH                INCOME





BURNHAM Securities Inc.
PRINCIPAL DISTRIBUTOR



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